id	sid	tid	token	lemma	pos
ap-6106	1	1	acta	acta	PROPN
ap-6106	1	2	polytechnica	polytechnica	PROPN
ap-6106	1	3	https://doi.org/10.14311/ap.2021.61.0068	https://doi.org/10.14311/ap.2021.61.0068	PROPN
ap-6106	1	4	acta	acta	PROPN
ap-6106	1	5	polytechnica	polytechnica	PROPN
ap-6106	1	6	61(si):68–76	61(si):68–76	NUM
ap-6106	1	7	,	,	PUNCT
ap-6106	1	8	2021	2021	NUM
ap-6106	1	9	©	©	ADP
ap-6106	1	10	2021	2021	NUM
ap-6106	1	11	the	the	DET
ap-6106	1	12	author(s	author(s	NOUN
ap-6106	1	13	)	)	PUNCT
ap-6106	1	14	.	.	PUNCT
ap-6106	2	1	licensed	license	VERB
ap-6106	2	2	under	under	ADP
ap-6106	2	3	a	a	DET
ap-6106	2	4	cc	cc	NOUN
ap-6106	2	5	-	-	PUNCT
ap-6106	2	6	by	by	ADP
ap-6106	2	7	4.0	4.0	NUM
ap-6106	2	8	licence	licence	NOUN
ap-6106	2	9	published	publish	VERB
ap-6106	2	10	by	by	ADP
ap-6106	2	11	the	the	DET
ap-6106	2	12	czech	czech	PROPN
ap-6106	2	13	technical	technical	PROPN
ap-6106	2	14	university	university	PROPN
ap-6106	2	15	in	in	ADP
ap-6106	2	16	prague	prague	PROPN
ap-6106	2	17	cell	cell	NOUN
ap-6106	2	18	-	-	PUNCT
ap-6106	2	19	centered	center	VERB
ap-6106	2	20	lagrangian	lagrangian	ADJ
ap-6106	2	21	lax	lax	NOUN
ap-6106	2	22	-	-	PUNCT
ap-6106	2	23	wendroff	wendroff	NOUN
ap-6106	2	24	hll	hll	PROPN
ap-6106	2	25	hybrid	hybrid	PROPN
ap-6106	2	26	scheme	scheme	NOUN
ap-6106	2	27	on	on	ADP
ap-6106	2	28	unstructured	unstructured	ADJ
ap-6106	2	29	meshes	meshes	PROPN
ap-6106	2	30	david	david	PROPN
ap-6106	2	31	fridricha	fridricha	PROPN
ap-6106	2	32	,	,	PUNCT
ap-6106	2	33	richard	richard	PROPN
ap-6106	2	34	liskaa,∗	liskaa,∗	PROPN
ap-6106	2	35	,	,	PUNCT
ap-6106	2	36	ivan	ivan	PROPN
ap-6106	2	37	taranta	taranta	PROPN
ap-6106	2	38	,	,	PUNCT
ap-6106	2	39	pavel	pavel	PROPN
ap-6106	2	40	váchala	váchala	PROPN
ap-6106	2	41	,	,	PUNCT
ap-6106	2	42	burton	burton	PROPN
ap-6106	2	43	wendroffb	wendroffb	NOUN
ap-6106	2	44	a	a	DET
ap-6106	2	45	czech	czech	PROPN
ap-6106	2	46	technical	technical	PROPN
ap-6106	2	47	university	university	PROPN
ap-6106	2	48	in	in	ADP
ap-6106	2	49	prague	prague	PROPN
ap-6106	2	50	,	,	PUNCT
ap-6106	2	51	faculty	faculty	NOUN
ap-6106	2	52	of	of	ADP
ap-6106	2	53	nuclear	nuclear	ADJ
ap-6106	2	54	sciences	science	NOUN
ap-6106	2	55	and	and	CCONJ
ap-6106	2	56	physical	physical	ADJ
ap-6106	2	57	engineering	engineering	NOUN
ap-6106	2	58	,	,	PUNCT
ap-6106	2	59	břehová	břehová	VERB
ap-6106	2	60	7	7	NUM
ap-6106	2	61	,	,	PUNCT
ap-6106	2	62	115	115	NUM
ap-6106	2	63	19	19	NUM
ap-6106	2	64	prague	prague	NOUN
ap-6106	2	65	,	,	PUNCT
ap-6106	2	66	czech	czech	PROPN
ap-6106	2	67	republic	republic	PROPN
ap-6106	2	68	b	b	PROPN
ap-6106	2	69	retired	retire	VERB
ap-6106	2	70	fellow	fellow	NOUN
ap-6106	2	71	,	,	PUNCT
ap-6106	2	72	los	los	PROPN
ap-6106	2	73	alamos	alamos	PROPN
ap-6106	2	74	national	national	PROPN
ap-6106	2	75	laboratory	laboratory	PROPN
ap-6106	2	76	,	,	PUNCT
ap-6106	2	77	los	los	PROPN
ap-6106	2	78	alamos	alamos	PROPN
ap-6106	2	79	,	,	PUNCT
ap-6106	2	80	nm	nm	PROPN
ap-6106	2	81	,	,	PUNCT
ap-6106	2	82	usa	usa	PROPN
ap-6106	2	83	∗	∗	NOUN
ap-6106	2	84	corresponding	correspond	VERB
ap-6106	2	85	author	author	NOUN
ap-6106	2	86	:	:	PUNCT
ap-6106	2	87	liska@siduri.fjfi.cvut.cz	liska@siduri.fjfi.cvut.cz	ADJ
ap-6106	2	88	abstract	abstract	NOUN
ap-6106	2	89	.	.	PUNCT
ap-6106	3	1	we	we	PRON
ap-6106	3	2	have	have	AUX
ap-6106	3	3	recently	recently	ADV
ap-6106	3	4	introduced	introduce	VERB
ap-6106	3	5	a	a	DET
ap-6106	3	6	new	new	ADJ
ap-6106	3	7	cell	cell	NOUN
ap-6106	3	8	-	-	PUNCT
ap-6106	3	9	centered	center	VERB
ap-6106	3	10	lax	lax	NOUN
ap-6106	3	11	-	-	PUNCT
ap-6106	3	12	wendroff	wendroff	NOUN
ap-6106	3	13	hll	hll	PROPN
ap-6106	3	14	hybrid	hybrid	NOUN
ap-6106	3	15	scheme	scheme	NOUN
ap-6106	3	16	for	for	ADP
ap-6106	3	17	lagrangian	lagrangian	ADJ
ap-6106	3	18	hydrodynamics	hydrodynamic	NOUN
ap-6106	3	19	[	[	X
ap-6106	3	20	fridrich	fridrich	X
ap-6106	3	21	et	et	PROPN
ap-6106	3	22	al	al	PROPN
ap-6106	3	23	.	.	PUNCT
ap-6106	4	1	j.	j.	PROPN
ap-6106	4	2	comp	comp	PROPN
ap-6106	4	3	.	.	PUNCT
ap-6106	5	1	phys	phy	NOUN
ap-6106	5	2	.	.	PUNCT
ap-6106	6	1	326	326	NUM
ap-6106	6	2	(	(	PUNCT
ap-6106	6	3	2016	2016	NUM
ap-6106	6	4	)	)	PUNCT
ap-6106	6	5	878	878	NUM
ap-6106	6	6	-	-	SYM
ap-6106	6	7	892	892	NUM
ap-6106	6	8	]	]	PUNCT
ap-6106	6	9	with	with	ADP
ap-6106	6	10	results	result	NOUN
ap-6106	6	11	presented	present	VERB
ap-6106	6	12	only	only	ADV
ap-6106	6	13	on	on	ADP
ap-6106	6	14	logical	logical	ADJ
ap-6106	6	15	rectangular	rectangular	ADJ
ap-6106	6	16	quadrilateral	quadrilateral	ADJ
ap-6106	6	17	meshes	mesh	NOUN
ap-6106	6	18	.	.	PUNCT
ap-6106	7	1	in	in	ADP
ap-6106	7	2	this	this	DET
ap-6106	7	3	study	study	NOUN
ap-6106	7	4	we	we	PRON
ap-6106	7	5	present	present	VERB
ap-6106	7	6	an	an	DET
ap-6106	7	7	improved	improved	ADJ
ap-6106	7	8	version	version	NOUN
ap-6106	7	9	on	on	ADP
ap-6106	7	10	unstructured	unstructured	ADJ
ap-6106	7	11	meshes	mesh	NOUN
ap-6106	7	12	,	,	PUNCT
ap-6106	7	13	including	include	VERB
ap-6106	7	14	uniform	uniform	ADJ
ap-6106	7	15	triangular	triangular	NOUN
ap-6106	7	16	and	and	CCONJ
ap-6106	7	17	hexagonal	hexagonal	ADJ
ap-6106	7	18	meshes	mesh	NOUN
ap-6106	7	19	and	and	CCONJ
ap-6106	7	20	non	non	ADJ
ap-6106	7	21	-	-	ADJ
ap-6106	7	22	uniform	uniform	ADJ
ap-6106	7	23	triangular	triangular	NOUN
ap-6106	7	24	and	and	CCONJ
ap-6106	7	25	polygonal	polygonal	ADJ
ap-6106	7	26	meshes	mesh	NOUN
ap-6106	7	27	.	.	PUNCT
ap-6106	8	1	the	the	DET
ap-6106	8	2	performance	performance	NOUN
ap-6106	8	3	of	of	ADP
ap-6106	8	4	the	the	DET
ap-6106	8	5	scheme	scheme	NOUN
ap-6106	8	6	is	be	AUX
ap-6106	8	7	verified	verify	VERB
ap-6106	8	8	on	on	ADP
ap-6106	8	9	noh	noh	PROPN
ap-6106	8	10	and	and	CCONJ
ap-6106	8	11	sedov	sedov	PROPN
ap-6106	8	12	problems	problem	NOUN
ap-6106	8	13	and	and	CCONJ
ap-6106	8	14	its	its	PRON
ap-6106	8	15	second	second	ADJ
ap-6106	8	16	-	-	PUNCT
ap-6106	8	17	order	order	NOUN
ap-6106	8	18	convergence	convergence	NOUN
ap-6106	8	19	is	be	AUX
ap-6106	8	20	verified	verify	VERB
ap-6106	8	21	on	on	ADP
ap-6106	8	22	a	a	DET
ap-6106	8	23	smooth	smooth	ADJ
ap-6106	8	24	expansion	expansion	NOUN
ap-6106	8	25	test	test	NOUN
ap-6106	8	26	.	.	PUNCT
ap-6106	9	1	finally	finally	ADV
ap-6106	9	2	the	the	DET
ap-6106	9	3	choice	choice	NOUN
ap-6106	9	4	of	of	ADP
ap-6106	9	5	the	the	DET
ap-6106	9	6	scalar	scalar	ADJ
ap-6106	9	7	parameter	parameter	NOUN
ap-6106	9	8	controlling	control	VERB
ap-6106	9	9	the	the	DET
ap-6106	9	10	amount	amount	NOUN
ap-6106	9	11	of	of	ADP
ap-6106	9	12	added	add	VERB
ap-6106	9	13	artificial	artificial	ADJ
ap-6106	9	14	dissipation	dissipation	NOUN
ap-6106	9	15	is	be	AUX
ap-6106	9	16	studied	study	VERB
ap-6106	9	17	.	.	PUNCT
ap-6106	10	1	keywords	keyword	NOUN
ap-6106	10	2	:	:	PUNCT
ap-6106	10	3	lagrangian	lagrangian	ADJ
ap-6106	10	4	hydrodynamics	hydrodynamic	NOUN
ap-6106	10	5	,	,	PUNCT
ap-6106	10	6	lax	lax	NOUN
ap-6106	10	7	-	-	PUNCT
ap-6106	10	8	wendroff	wendroff	NOUN
ap-6106	10	9	,	,	PUNCT
ap-6106	10	10	hll	hll	PROPN
ap-6106	10	11	.	.	PROPN
ap-6106	10	12	1	1	X
ap-6106	10	13	.	.	X
ap-6106	11	1	introduction	introduction	NOUN
ap-6106	11	2	lagrangian	lagrangian	ADJ
ap-6106	11	3	hydrodynamical	hydrodynamical	ADJ
ap-6106	11	4	methods	method	NOUN
ap-6106	11	5	are	be	AUX
ap-6106	11	6	crucial	crucial	ADJ
ap-6106	11	7	for	for	ADP
ap-6106	11	8	simulations	simulation	NOUN
ap-6106	11	9	of	of	ADP
ap-6106	11	10	high	high	ADJ
ap-6106	11	11	speed	speed	NOUN
ap-6106	11	12	compressible	compressible	ADJ
ap-6106	11	13	fluid	fluid	NOUN
ap-6106	11	14	flows	flow	NOUN
ap-6106	11	15	as	as	ADP
ap-6106	11	16	e.g.	e.g.	ADV
ap-6106	11	17	in	in	ADP
ap-6106	11	18	astrophysics	astrophysic	NOUN
ap-6106	11	19	or	or	CCONJ
ap-6106	11	20	inertial	inertial	ADJ
ap-6106	11	21	confinement	confinement	NOUN
ap-6106	11	22	fusion	fusion	NOUN
ap-6106	11	23	(	(	PUNCT
ap-6106	11	24	icf	icf	PROPN
ap-6106	11	25	)	)	PUNCT
ap-6106	11	26	.	.	PUNCT
ap-6106	12	1	lagrangian	lagrangian	ADJ
ap-6106	12	2	hydrodynamics	hydrodynamic	NOUN
ap-6106	12	3	solves	solve	NOUN
ap-6106	12	4	euler	euler	NOUN
ap-6106	12	5	equations	equation	NOUN
ap-6106	12	6	for	for	ADP
ap-6106	12	7	compressible	compressible	ADJ
ap-6106	12	8	fluid	fluid	ADJ
ap-6106	12	9	flow	flow	NOUN
ap-6106	12	10	on	on	ADP
ap-6106	12	11	a	a	DET
ap-6106	12	12	computational	computational	ADJ
ap-6106	12	13	mesh	mesh	NOUN
ap-6106	12	14	moving	move	VERB
ap-6106	12	15	with	with	ADP
ap-6106	12	16	the	the	DET
ap-6106	12	17	fluid	fluid	NOUN
ap-6106	12	18	under	under	ADP
ap-6106	12	19	the	the	DET
ap-6106	12	20	assumption	assumption	NOUN
ap-6106	12	21	of	of	ADP
ap-6106	12	22	no	no	DET
ap-6106	12	23	mass	mass	ADJ
ap-6106	12	24	flux	flux	NOUN
ap-6106	12	25	between	between	ADP
ap-6106	12	26	the	the	DET
ap-6106	12	27	cells	cell	NOUN
ap-6106	12	28	.	.	PUNCT
ap-6106	13	1	staggered	stagger	VERB
ap-6106	13	2	lagrangian	lagrangian	ADJ
ap-6106	13	3	methods	method	NOUN
ap-6106	13	4	,	,	PUNCT
ap-6106	13	5	e.g.	e.g.	ADV
ap-6106	13	6	[	[	X
ap-6106	13	7	1–3	1–3	NOUN
ap-6106	13	8	]	]	X
ap-6106	13	9	,	,	PUNCT
ap-6106	13	10	using	use	VERB
ap-6106	13	11	an	an	DET
ap-6106	13	12	artificial	artificial	ADJ
ap-6106	13	13	viscosity	viscosity	NOUN
ap-6106	13	14	(	(	PUNCT
ap-6106	13	15	originally	originally	ADV
ap-6106	13	16	introduced	introduce	VERB
ap-6106	13	17	by	by	ADP
ap-6106	13	18	von	von	PROPN
ap-6106	13	19	neumann	neumann	PROPN
ap-6106	13	20	and	and	CCONJ
ap-6106	13	21	richtmyer	richtmyer	NOUN
ap-6106	14	1	[	[	X
ap-6106	14	2	4	4	NUM
ap-6106	14	3	]	]	PUNCT
ap-6106	14	4	)	)	PUNCT
ap-6106	14	5	as	as	ADP
ap-6106	14	6	a	a	DET
ap-6106	14	7	dissipative	dissipative	ADJ
ap-6106	14	8	mechanism	mechanism	NOUN
ap-6106	14	9	,	,	PUNCT
ap-6106	14	10	have	have	AUX
ap-6106	14	11	been	be	AUX
ap-6106	14	12	standard	standard	ADJ
ap-6106	14	13	for	for	ADP
ap-6106	14	14	many	many	ADJ
ap-6106	14	15	years	year	NOUN
ap-6106	14	16	.	.	PUNCT
ap-6106	15	1	staggered	stagger	VERB
ap-6106	15	2	methods	method	NOUN
ap-6106	15	3	define	define	VERB
ap-6106	15	4	thermodynamical	thermodynamical	ADJ
ap-6106	15	5	quantities	quantity	NOUN
ap-6106	15	6	(	(	PUNCT
ap-6106	15	7	density	density	NOUN
ap-6106	15	8	,	,	PUNCT
ap-6106	15	9	pressure	pressure	NOUN
ap-6106	15	10	,	,	PUNCT
ap-6106	15	11	internal	internal	ADJ
ap-6106	15	12	energy	energy	NOUN
ap-6106	15	13	)	)	PUNCT
ap-6106	15	14	in	in	ADP
ap-6106	15	15	the	the	DET
ap-6106	15	16	cells	cell	NOUN
ap-6106	15	17	,	,	PUNCT
ap-6106	15	18	while	while	SCONJ
ap-6106	15	19	velocity	velocity	NOUN
ap-6106	15	20	is	be	AUX
ap-6106	15	21	defined	define	VERB
ap-6106	15	22	at	at	ADP
ap-6106	15	23	mesh	mesh	NOUN
ap-6106	15	24	nodes	node	NOUN
ap-6106	15	25	.	.	PUNCT
ap-6106	16	1	a	a	DET
ap-6106	16	2	class	class	NOUN
ap-6106	16	3	of	of	ADP
ap-6106	16	4	high	high	ADJ
ap-6106	16	5	order	order	NOUN
ap-6106	16	6	staggered	stagger	VERB
ap-6106	16	7	finite	finite	ADJ
ap-6106	16	8	element	element	NOUN
ap-6106	16	9	methods	method	NOUN
ap-6106	16	10	on	on	ADP
ap-6106	16	11	meshes	mesh	NOUN
ap-6106	16	12	with	with	ADP
ap-6106	16	13	curvilinear	curvilinear	ADJ
ap-6106	16	14	cells	cell	NOUN
ap-6106	16	15	has	have	AUX
ap-6106	16	16	been	be	AUX
ap-6106	16	17	developed	develop	VERB
ap-6106	16	18	in	in	ADP
ap-6106	16	19	[	[	X
ap-6106	16	20	5	5	NUM
ap-6106	16	21	]	]	PUNCT
ap-6106	16	22	.	.	PUNCT
ap-6106	17	1	another	another	DET
ap-6106	17	2	form	form	NOUN
ap-6106	17	3	of	of	ADP
ap-6106	17	4	the	the	DET
ap-6106	17	5	dissipative	dissipative	ADJ
ap-6106	17	6	mechanism	mechanism	NOUN
ap-6106	17	7	,	,	PUNCT
ap-6106	17	8	which	which	PRON
ap-6106	17	9	comes	come	VERB
ap-6106	17	10	from	from	ADP
ap-6106	17	11	an	an	DET
ap-6106	17	12	approximate	approximate	ADJ
ap-6106	17	13	riemann	riemann	PROPN
ap-6106	17	14	solver	solver	NOUN
ap-6106	17	15	,	,	PUNCT
ap-6106	17	16	has	have	AUX
ap-6106	17	17	been	be	AUX
ap-6106	17	18	developed	develop	VERB
ap-6106	17	19	in	in	ADP
ap-6106	17	20	the	the	DET
ap-6106	17	21	cell	cell	NOUN
ap-6106	17	22	-	-	PUNCT
ap-6106	17	23	centered	center	VERB
ap-6106	17	24	methods	method	NOUN
ap-6106	17	25	[	[	X
ap-6106	17	26	6–12	6–12	NOUN
ap-6106	17	27	]	]	PUNCT
ap-6106	17	28	,	,	PUNCT
ap-6106	17	29	which	which	PRON
ap-6106	17	30	assign	assign	VERB
ap-6106	17	31	both	both	DET
ap-6106	17	32	velocity	velocity	NOUN
ap-6106	17	33	and	and	CCONJ
ap-6106	17	34	thermodynamical	thermodynamical	ADJ
ap-6106	17	35	quantities	quantity	NOUN
ap-6106	17	36	to	to	ADP
ap-6106	17	37	the	the	DET
ap-6106	17	38	cells	cell	NOUN
ap-6106	17	39	.	.	PUNCT
ap-6106	18	1	our	our	PRON
ap-6106	18	2	recently	recently	ADV
ap-6106	18	3	introduced	introduce	VERB
ap-6106	18	4	lax	lax	NOUN
ap-6106	18	5	-	-	PUNCT
ap-6106	18	6	wendroff	wendroff	NOUN
ap-6106	18	7	hll	hll	PROPN
ap-6106	18	8	hybrid	hybrid	PROPN
ap-6106	18	9	scheme	scheme	NOUN
ap-6106	18	10	[	[	X
ap-6106	18	11	13	13	NUM
ap-6106	18	12	]	]	PUNCT
ap-6106	18	13	is	be	AUX
ap-6106	18	14	also	also	ADV
ap-6106	18	15	a	a	DET
ap-6106	18	16	cell	cell	NOUN
ap-6106	18	17	-	-	PUNCT
ap-6106	18	18	centered	center	VERB
ap-6106	18	19	method	method	NOUN
ap-6106	18	20	.	.	PUNCT
ap-6106	19	1	the	the	DET
ap-6106	19	2	artificial	artificial	ADJ
ap-6106	19	3	dissipation	dissipation	NOUN
ap-6106	19	4	,	,	PUNCT
ap-6106	19	5	in	in	ADP
ap-6106	19	6	the	the	DET
ap-6106	19	7	form	form	NOUN
ap-6106	19	8	of	of	ADP
ap-6106	19	9	dissipative	dissipative	ADJ
ap-6106	19	10	part	part	NOUN
ap-6106	19	11	of	of	ADP
ap-6106	19	12	the	the	DET
ap-6106	19	13	hll	hll	PROPN
ap-6106	19	14	approximate	approximate	PROPN
ap-6106	19	15	riemann	riemann	PROPN
ap-6106	19	16	solver	solver	PROPN
ap-6106	19	17	flux	flux	NOUN
ap-6106	19	18	[	[	X
ap-6106	19	19	14	14	NUM
ap-6106	19	20	]	]	PUNCT
ap-6106	19	21	,	,	PUNCT
ap-6106	19	22	is	be	AUX
ap-6106	19	23	added	add	VERB
ap-6106	19	24	to	to	ADP
ap-6106	19	25	the	the	DET
ap-6106	19	26	momentum	momentum	NOUN
ap-6106	19	27	and	and	CCONJ
ap-6106	19	28	energy	energy	NOUN
ap-6106	19	29	equations	equation	NOUN
ap-6106	19	30	.	.	PUNCT
ap-6106	20	1	the	the	DET
ap-6106	20	2	original	original	ADJ
ap-6106	20	3	method	method	NOUN
ap-6106	20	4	is	be	AUX
ap-6106	20	5	improved	improve	VERB
ap-6106	20	6	by	by	ADP
ap-6106	20	7	applying	apply	VERB
ap-6106	20	8	another	another	DET
ap-6106	20	9	weighting	weighting	NOUN
ap-6106	20	10	in	in	ADP
ap-6106	20	11	the	the	DET
ap-6106	20	12	predictor	predictor	NOUN
ap-6106	20	13	.	.	PUNCT
ap-6106	21	1	the	the	DET
ap-6106	21	2	original	original	ADJ
ap-6106	21	3	paper	paper	NOUN
ap-6106	21	4	[	[	X
ap-6106	21	5	13	13	NUM
ap-6106	21	6	]	]	PUNCT
ap-6106	21	7	has	have	AUX
ap-6106	21	8	presented	present	VERB
ap-6106	21	9	numerical	numerical	ADJ
ap-6106	21	10	results	result	NOUN
ap-6106	21	11	only	only	ADV
ap-6106	21	12	on	on	ADP
ap-6106	21	13	logical	logical	ADJ
ap-6106	21	14	rectangular	rectangular	ADJ
ap-6106	21	15	,	,	PUNCT
ap-6106	21	16	quadrilateral	quadrilateral	ADJ
ap-6106	21	17	meshes	mesh	NOUN
ap-6106	21	18	.	.	PUNCT
ap-6106	22	1	here	here	ADV
ap-6106	22	2	we	we	PRON
ap-6106	22	3	present	present	VERB
ap-6106	22	4	results	result	NOUN
ap-6106	22	5	on	on	ADP
ap-6106	22	6	unstructured	unstructured	ADJ
ap-6106	22	7	meshes	mesh	NOUN
ap-6106	22	8	,	,	PUNCT
ap-6106	22	9	including	include	VERB
ap-6106	22	10	uniform	uniform	ADJ
ap-6106	22	11	triangular	triangular	NOUN
ap-6106	22	12	and	and	CCONJ
ap-6106	22	13	hexagonal	hexagonal	ADJ
ap-6106	22	14	meshes	mesh	NOUN
ap-6106	22	15	and	and	CCONJ
ap-6106	22	16	non	non	ADJ
ap-6106	22	17	-	-	ADJ
ap-6106	22	18	uniform	uniform	ADJ
ap-6106	22	19	triangular	triangular	NOUN
ap-6106	22	20	and	and	CCONJ
ap-6106	22	21	polygonal	polygonal	ADJ
ap-6106	22	22	meshes	mesh	NOUN
ap-6106	22	23	.	.	PUNCT
ap-6106	23	1	2	2	X
ap-6106	23	2	.	.	X
ap-6106	23	3	lagrangian	lagrangian	ADJ
ap-6106	23	4	finite	finite	ADJ
ap-6106	23	5	volume	volume	NOUN
ap-6106	23	6	in	in	ADP
ap-6106	23	7	lagrangian	lagrangian	ADJ
ap-6106	23	8	coordinates	coordinate	NOUN
ap-6106	23	9	we	we	PRON
ap-6106	23	10	define	define	VERB
ap-6106	23	11	the	the	DET
ap-6106	23	12	finite	finite	ADJ
ap-6106	23	13	volume	volume	NOUN
ap-6106	23	14	method	method	NOUN
ap-6106	23	15	on	on	ADP
ap-6106	23	16	a	a	DET
ap-6106	23	17	moving	move	VERB
ap-6106	23	18	finite	finite	ADJ
ap-6106	23	19	volume	volume	NOUN
ap-6106	23	20	v	v	NOUN
ap-6106	23	21	with	with	ADP
ap-6106	23	22	a	a	DET
ap-6106	23	23	surface	surface	NOUN
ap-6106	23	24	s.	s.	PROPN
ap-6106	23	25	the	the	DET
ap-6106	23	26	mass	mass	PROPN
ap-6106	23	27	mv	mv	PROPN
ap-6106	23	28	,	,	PUNCT
ap-6106	23	29	momentum	momentum	NOUN
ap-6106	23	30	mv	mv	PROPN
ap-6106	23	31	and	and	CCONJ
ap-6106	23	32	total	total	ADJ
ap-6106	23	33	energy	energy	NOUN
ap-6106	23	34	ev	ev	X
ap-6106	23	35	of	of	ADP
ap-6106	23	36	the	the	DET
ap-6106	23	37	moving	move	VERB
ap-6106	23	38	volume	volume	NOUN
ap-6106	23	39	v	v	NOUN
ap-6106	23	40	are	be	AUX
ap-6106	23	41	given	give	VERB
ap-6106	23	42	by	by	ADP
ap-6106	23	43	mv	mv	PROPN
ap-6106	23	44	=	=	NOUN
ap-6106	23	45	∫	∫	PROPN
ap-6106	23	46	v	v	NUM
ap-6106	23	47	ρ	ρ	PROPN
ap-6106	23	48	dv	dv	PROPN
ap-6106	23	49	,	,	PUNCT
ap-6106	23	50	mv	mv	PROPN
ap-6106	23	51	=	=	SYM
ap-6106	23	52	∫	∫	PROPN
ap-6106	24	1	v	v	INTJ
ap-6106	24	2	ρu	ρu	PROPN
ap-6106	24	3	dv	dv	PROPN
ap-6106	24	4	,	,	PUNCT
ap-6106	24	5	ev	ev	PROPN
ap-6106	24	6	=	=	SYM
ap-6106	24	7	∫	∫	PROPN
ap-6106	24	8	v	v	NUM
ap-6106	24	9	ρe	ρe	PROPN
ap-6106	24	10	dv	dv	PROPN
ap-6106	24	11	,	,	PUNCT
ap-6106	24	12	(	(	PUNCT
ap-6106	24	13	1	1	X
ap-6106	24	14	)	)	PUNCT
ap-6106	24	15	where	where	SCONJ
ap-6106	24	16	ρ	ρ	PROPN
ap-6106	24	17	is	be	AUX
ap-6106	24	18	density	density	NOUN
ap-6106	24	19	,	,	PUNCT
ap-6106	24	20	u	u	NOUN
ap-6106	24	21	velocity	velocity	NOUN
ap-6106	24	22	and	and	CCONJ
ap-6106	24	23	e	e	NOUN
ap-6106	24	24	total	total	ADJ
ap-6106	24	25	specific	specific	ADJ
ap-6106	24	26	energy	energy	NOUN
ap-6106	24	27	(	(	PUNCT
ap-6106	24	28	i.e.	i.e.	X
ap-6106	24	29	,	,	PUNCT
ap-6106	24	30	total	total	ADJ
ap-6106	24	31	energy	energy	NOUN
ap-6106	24	32	per	per	ADP
ap-6106	24	33	unit	unit	NOUN
ap-6106	24	34	mass	mass	PROPN
ap-6106	24	35	)	)	PUNCT
ap-6106	24	36	.	.	PUNCT
ap-6106	25	1	from	from	ADP
ap-6106	25	2	the	the	DET
ap-6106	25	3	reynolds	reynolds	PROPN
ap-6106	25	4	transport	transport	PROPN
ap-6106	25	5	theorem	theorem	VERB
ap-6106	25	6	one	one	PRON
ap-6106	25	7	can	can	AUX
ap-6106	25	8	derive	derive	VERB
ap-6106	25	9	the	the	DET
ap-6106	25	10	finite	finite	ADJ
ap-6106	25	11	volume	volume	NOUN
ap-6106	25	12	formulation	formulation	NOUN
ap-6106	25	13	of	of	ADP
ap-6106	25	14	lagrangian	lagrangian	ADJ
ap-6106	25	15	compressible	compressible	ADJ
ap-6106	25	16	gas	gas	NOUN
ap-6106	25	17	dynamics	dynamic	NOUN
ap-6106	25	18	equations	equation	NOUN
ap-6106	25	19	for	for	ADP
ap-6106	25	20	conserved	conserved	ADJ
ap-6106	25	21	quantities	quantity	NOUN
ap-6106	25	22	wv	wv	PROPN
ap-6106	26	1	=	=	SYM
ap-6106	26	2	(	(	PUNCT
ap-6106	26	3	v	v	NOUN
ap-6106	26	4	,	,	PUNCT
ap-6106	26	5	mv	mv	PROPN
ap-6106	26	6	,	,	PUNCT
ap-6106	26	7	ev	ev	PROPN
ap-6106	26	8	)	)	PUNCT
ap-6106	26	9	dwv	dwv	PROPN
ap-6106	27	1	d	d	PROPN
ap-6106	27	2	t	t	PROPN
ap-6106	27	3	=	=	SYM
ap-6106	27	4	∫	∫	PROPN
ap-6106	27	5	s	s	PART
ap-6106	27	6	f	f	PROPN
ap-6106	27	7	·	·	PUNCT
ap-6106	27	8	n	n	CCONJ
ap-6106	27	9	ds	ds	ADJ
ap-6106	27	10	,	,	PUNCT
ap-6106	27	11	(	(	PUNCT
ap-6106	27	12	2	2	X
ap-6106	27	13	)	)	PUNCT
ap-6106	27	14	where	where	SCONJ
ap-6106	27	15	n	n	PRON
ap-6106	27	16	is	be	AUX
ap-6106	27	17	the	the	DET
ap-6106	27	18	outward	outward	ADJ
ap-6106	27	19	normal	normal	ADJ
ap-6106	27	20	to	to	ADP
ap-6106	27	21	the	the	DET
ap-6106	27	22	surface	surface	NOUN
ap-6106	27	23	s	s	PART
ap-6106	27	24	and	and	CCONJ
ap-6106	27	25	the	the	DET
ap-6106	27	26	flux	flux	NOUN
ap-6106	27	27	f	f	PROPN
ap-6106	27	28	is	be	AUX
ap-6106	27	29	given	give	VERB
ap-6106	27	30	by	by	ADP
ap-6106	27	31	f	f	PROPN
ap-6106	27	32	=	=	PUNCT
ap-6106	27	33	(	(	PUNCT
ap-6106	27	34	u,−pi,−pu	u,−pi,−pu	PROPN
ap-6106	27	35	)	)	PUNCT
ap-6106	27	36	.	.	PUNCT
ap-6106	28	1	(	(	PUNCT
ap-6106	28	2	3	3	X
ap-6106	28	3	)	)	PUNCT
ap-6106	28	4	here	here	ADV
ap-6106	28	5	i	i	PRON
ap-6106	28	6	is	be	AUX
ap-6106	28	7	the	the	DET
ap-6106	28	8	unit	unit	NOUN
ap-6106	28	9	matrix	matrix	NOUN
ap-6106	28	10	and	and	CCONJ
ap-6106	28	11	p	p	NOUN
ap-6106	28	12	is	be	AUX
ap-6106	28	13	pressure	pressure	NOUN
ap-6106	28	14	,	,	PUNCT
ap-6106	28	15	for	for	ADP
ap-6106	28	16	which	which	PRON
ap-6106	28	17	we	we	PRON
ap-6106	28	18	employ	employ	VERB
ap-6106	28	19	the	the	DET
ap-6106	28	20	ideal	ideal	ADJ
ap-6106	28	21	gas	gas	NOUN
ap-6106	28	22	equation	equation	NOUN
ap-6106	28	23	of	of	ADP
ap-6106	28	24	state	state	NOUN
ap-6106	28	25	p	p	PROPN
ap-6106	29	1	=	=	X
ap-6106	29	2	(	(	PUNCT
ap-6106	29	3	γ	γ	X
ap-6106	29	4	−	−	PROPN
ap-6106	29	5	1)ρ(e−u2/2	1)ρ(e−u2/2	NUM
ap-6106	29	6	)	)	PUNCT
ap-6106	29	7	.	.	PUNCT
ap-6106	30	1	the	the	DET
ap-6106	30	2	system	system	NOUN
ap-6106	30	3	(	(	PUNCT
ap-6106	30	4	2	2	X
ap-6106	30	5	)	)	PUNCT
ap-6106	30	6	is	be	AUX
ap-6106	30	7	solved	solve	VERB
ap-6106	30	8	for	for	ADP
ap-6106	30	9	all	all	DET
ap-6106	30	10	cells	cell	NOUN
ap-6106	30	11	v	v	ADP
ap-6106	30	12	of	of	ADP
ap-6106	30	13	the	the	DET
ap-6106	30	14	moving	move	VERB
ap-6106	30	15	unstructured	unstructured	ADJ
ap-6106	30	16	computational	computational	ADJ
ap-6106	30	17	mesh	mesh	NOUN
ap-6106	30	18	.	.	PUNCT
ap-6106	31	1	for	for	ADP
ap-6106	31	2	all	all	DET
ap-6106	31	3	nodes	node	NOUN
ap-6106	31	4	of	of	ADP
ap-6106	31	5	the	the	DET
ap-6106	31	6	moving	move	VERB
ap-6106	31	7	mesh	mesh	NOUN
ap-6106	31	8	one	one	NUM
ap-6106	31	9	solves	solve	VERB
ap-6106	31	10	the	the	DET
ap-6106	31	11	ordinary	ordinary	ADJ
ap-6106	31	12	differential	differential	ADJ
ap-6106	31	13	equations	equation	NOUN
ap-6106	31	14	dx	dx	PROPN
ap-6106	31	15	d	d	X
ap-6106	31	16	t	t	PROPN
ap-6106	31	17	=	=	SYM
ap-6106	31	18	u	u	NOUN
ap-6106	31	19	=	=	SYM
ap-6106	31	20	(	(	PUNCT
ap-6106	31	21	u	u	NOUN
ap-6106	31	22	,	,	PUNCT
ap-6106	31	23	v	v	NOUN
ap-6106	31	24	)	)	PUNCT
ap-6106	31	25	,	,	PUNCT
ap-6106	31	26	(	(	PUNCT
ap-6106	31	27	4	4	X
ap-6106	31	28	)	)	PUNCT
ap-6106	31	29	where	where	SCONJ
ap-6106	31	30	x	x	X
ap-6106	31	31	=	=	PRON
ap-6106	31	32	(	(	PUNCT
ap-6106	31	33	x	x	NOUN
ap-6106	31	34	,	,	PUNCT
ap-6106	31	35	y	y	NOUN
ap-6106	31	36	)	)	PUNCT
ap-6106	31	37	are	be	AUX
ap-6106	31	38	coordinates	coordinate	NOUN
ap-6106	31	39	of	of	ADP
ap-6106	31	40	a	a	DET
ap-6106	31	41	node	node	NOUN
ap-6106	31	42	of	of	ADP
ap-6106	31	43	the	the	DET
ap-6106	31	44	mesh	mesh	NOUN
ap-6106	31	45	and	and	CCONJ
ap-6106	31	46	u	u	NOUN
ap-6106	31	47	is	be	AUX
ap-6106	31	48	the	the	DET
ap-6106	31	49	velocity	velocity	NOUN
ap-6106	31	50	of	of	ADP
ap-6106	31	51	the	the	DET
ap-6106	31	52	node	node	NOUN
ap-6106	31	53	.	.	PUNCT
ap-6106	32	1	68	68	NUM
ap-6106	32	2	https://doi.org/10.14311/ap.2021.61.0068	https://doi.org/10.14311/ap.2021.61.0068	PROPN
ap-6106	32	3	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-6106	32	4	https://www.cvut.cz/en	https://www.cvut.cz/en	PROPN
ap-6106	32	5	vol	vol	NOUN
ap-6106	32	6	.	.	PUNCT
ap-6106	33	1	61	61	NUM
ap-6106	33	2	special	special	ADJ
ap-6106	33	3	issue/2021	issue/2021	NOUN
ap-6106	33	4	lagrangian	lagrangian	ADJ
ap-6106	33	5	lax	lax	PROPN
ap-6106	33	6	-	-	PUNCT
ap-6106	33	7	wendroff	wendroff	NOUN
ap-6106	33	8	hll	hll	PROPN
ap-6106	33	9	scheme	scheme	VERB
ap-6106	33	10	the	the	DET
ap-6106	33	11	specific	specific	ADJ
ap-6106	33	12	quantities	quantity	NOUN
ap-6106	33	13	wv	wv	PROPN
ap-6106	34	1	=	=	SYM
ap-6106	34	2	wv	wv	PROPN
ap-6106	34	3	/mv	/mv	INTJ
ap-6106	34	4	(	(	PUNCT
ap-6106	34	5	i.e.	i.e.	X
ap-6106	34	6	quantities	quantity	NOUN
ap-6106	34	7	per	per	ADP
ap-6106	34	8	unit	unit	NOUN
ap-6106	34	9	mass	mass	PROPN
ap-6106	34	10	)	)	PUNCT
ap-6106	34	11	ηv	ηv	ADV
ap-6106	34	12	=	=	PUNCT
ap-6106	34	13	v	v	ADJ
ap-6106	34	14	mv	mv	NOUN
ap-6106	34	15	=	=	SYM
ap-6106	34	16	1	1	NUM
ap-6106	34	17	ρv	ρv	NOUN
ap-6106	34	18	,	,	PUNCT
ap-6106	34	19	uv	uv	NOUN
ap-6106	35	1	=	=	PUNCT
ap-6106	36	1	mv	mv	PROPN
ap-6106	36	2	mv	mv	PROPN
ap-6106	36	3	,	,	PUNCT
ap-6106	36	4	ev	ev	PROPN
ap-6106	36	5	=	=	X
ap-6106	36	6	ev	ev	X
ap-6106	36	7	mv	mv	PROPN
ap-6106	36	8	(	(	PUNCT
ap-6106	36	9	5	5	NUM
ap-6106	36	10	)	)	PUNCT
ap-6106	36	11	are	be	AUX
ap-6106	36	12	the	the	DET
ap-6106	36	13	specific	specific	ADJ
ap-6106	36	14	volume	volume	NOUN
ap-6106	36	15	ηv	ηv	ADV
ap-6106	36	16	,	,	PUNCT
ap-6106	36	17	the	the	DET
ap-6106	36	18	velocity	velocity	NOUN
ap-6106	36	19	uv	uv	NOUN
ap-6106	36	20	and	and	CCONJ
ap-6106	36	21	the	the	DET
ap-6106	36	22	specific	specific	ADJ
ap-6106	36	23	total	total	ADJ
ap-6106	36	24	energy	energy	NOUN
ap-6106	36	25	ev	ev	NOUN
ap-6106	36	26	.	.	PUNCT
ap-6106	37	1	the	the	DET
ap-6106	37	2	specific	specific	ADJ
ap-6106	37	3	quantities	quantity	NOUN
ap-6106	37	4	wv	wv	PROPN
ap-6106	37	5	=	=	PUNCT
ap-6106	37	6	(	(	PUNCT
ap-6106	37	7	ηv	ηv	ADV
ap-6106	37	8	,	,	PUNCT
ap-6106	37	9	uv	uv	INTJ
ap-6106	37	10	,	,	PUNCT
ap-6106	37	11	ev	ev	NOUN
ap-6106	37	12	)	)	PUNCT
ap-6106	37	13	will	will	AUX
ap-6106	37	14	be	be	AUX
ap-6106	37	15	our	our	PRON
ap-6106	37	16	variables	variable	NOUN
ap-6106	37	17	in	in	ADP
ap-6106	37	18	the	the	DET
ap-6106	37	19	lagrangian	lagrangian	ADJ
ap-6106	37	20	schemes	scheme	NOUN
ap-6106	37	21	.	.	PUNCT
ap-6106	38	1	3	3	X
ap-6106	38	2	.	.	X
ap-6106	38	3	meshes	mesh	VERB
ap-6106	38	4	for	for	ADP
ap-6106	38	5	the	the	DET
ap-6106	38	6	computational	computational	ADJ
ap-6106	38	7	mesh	mesh	NOUN
ap-6106	38	8	we	we	PRON
ap-6106	38	9	follow	follow	VERB
ap-6106	38	10	the	the	DET
ap-6106	38	11	p	p	PROPN
ap-6106	38	12	-	-	PUNCT
ap-6106	38	13	c	c	NOUN
ap-6106	38	14	notation	notation	NOUN
ap-6106	38	15	[	[	X
ap-6106	38	16	15	15	NUM
ap-6106	38	17	]	]	PUNCT
ap-6106	38	18	.	.	PUNCT
ap-6106	39	1	the	the	DET
ap-6106	39	2	unstructured	unstructured	ADJ
ap-6106	39	3	computational	computational	ADJ
ap-6106	39	4	mesh	mesh	NOUN
ap-6106	39	5	contains	contain	VERB
ap-6106	39	6	cells	cell	NOUN
ap-6106	39	7	c	c	NOUN
ap-6106	39	8	,	,	PUNCT
ap-6106	39	9	points	point	VERB
ap-6106	39	10	p	p	NOUN
ap-6106	39	11	and	and	CCONJ
ap-6106	39	12	edges	edge	NOUN
ap-6106	39	13	e.	e.	PROPN
ap-6106	40	1	each	each	DET
ap-6106	40	2	cell	cell	NOUN
ap-6106	40	3	is	be	AUX
ap-6106	40	4	a	a	DET
ap-6106	40	5	polygon	polygon	NOUN
ap-6106	40	6	.	.	PUNCT
ap-6106	41	1	a	a	DET
ap-6106	41	2	cell	cell	NOUN
ap-6106	41	3	with	with	ADP
ap-6106	41	4	n	n	ADP
ap-6106	41	5	vertices	vertex	NOUN
ap-6106	41	6	can	can	AUX
ap-6106	41	7	be	be	AUX
ap-6106	41	8	split	split	VERB
ap-6106	41	9	into	into	ADP
ap-6106	41	10	n	n	CCONJ
ap-6106	41	11	quadrilateral	quadrilateral	ADJ
ap-6106	41	12	subcells	subcell	NOUN
ap-6106	41	13	spc	spc	PROPN
ap-6106	41	14	by	by	ADP
ap-6106	41	15	separators	separator	NOUN
ap-6106	41	16	,	,	PUNCT
ap-6106	41	17	which	which	PRON
ap-6106	41	18	are	be	AUX
ap-6106	41	19	the	the	DET
ap-6106	41	20	segments	segment	NOUN
ap-6106	41	21	connecting	connect	VERB
ap-6106	41	22	the	the	DET
ap-6106	41	23	cell	cell	NOUN
ap-6106	41	24	center	center	NOUN
ap-6106	41	25	to	to	ADP
ap-6106	41	26	the	the	DET
ap-6106	41	27	edge	edge	NOUN
ap-6106	41	28	midpoints	midpoint	NOUN
ap-6106	41	29	.	.	PUNCT
ap-6106	42	1	the	the	DET
ap-6106	42	2	edge	edge	NOUN
ap-6106	42	3	e(ca	e(ca	NOUN
ap-6106	42	4	)	)	PUNCT
ap-6106	42	5	separates	separate	VERB
ap-6106	42	6	cells	cell	NOUN
ap-6106	42	7	c	c	PROPN
ap-6106	42	8	and	and	CCONJ
ap-6106	42	9	a.	a.	NOUN
ap-6106	42	10	the	the	DET
ap-6106	42	11	outer	outer	ADJ
ap-6106	42	12	normal	normal	ADJ
ap-6106	42	13	to	to	ADP
ap-6106	42	14	the	the	DET
ap-6106	42	15	edge	edge	NOUN
ap-6106	42	16	e(ca	e(ca	NOUN
ap-6106	42	17	)	)	PUNCT
ap-6106	42	18	(	(	PUNCT
ap-6106	42	19	w.r.t	w.r.t	NOUN
ap-6106	42	20	.	.	PUNCT
ap-6106	43	1	the	the	DET
ap-6106	43	2	cell	cell	NOUN
ap-6106	43	3	c	c	NOUN
ap-6106	43	4	)	)	PUNCT
ap-6106	43	5	is	be	AUX
ap-6106	43	6	denoted	denote	VERB
ap-6106	43	7	by	by	ADP
ap-6106	43	8	ne(ca	ne(ca	NOUN
ap-6106	43	9	)	)	PUNCT
ap-6106	43	10	and	and	CCONJ
ap-6106	43	11	its	its	PRON
ap-6106	43	12	length	length	NOUN
ap-6106	43	13	is	be	AUX
ap-6106	43	14	equal	equal	ADJ
ap-6106	43	15	to	to	ADP
ap-6106	43	16	the	the	DET
ap-6106	43	17	length	length	NOUN
ap-6106	43	18	of	of	ADP
ap-6106	43	19	the	the	DET
ap-6106	43	20	edge	edge	NOUN
ap-6106	43	21	e(ca	e(ca	NOUN
ap-6106	43	22	)	)	PUNCT
ap-6106	43	23	.	.	PUNCT
ap-6106	44	1	around	around	ADP
ap-6106	44	2	each	each	DET
ap-6106	44	3	node	node	NOUN
ap-6106	44	4	p	p	NOUN
ap-6106	44	5	,	,	PUNCT
ap-6106	44	6	we	we	PRON
ap-6106	44	7	construct	construct	VERB
ap-6106	44	8	a	a	DET
ap-6106	44	9	dual	dual	ADJ
ap-6106	44	10	cell	cell	NOUN
ap-6106	44	11	as	as	ADP
ap-6106	44	12	the	the	DET
ap-6106	44	13	union	union	NOUN
ap-6106	44	14	of	of	ADP
ap-6106	44	15	the	the	DET
ap-6106	44	16	subcells	subcell	NOUN
ap-6106	44	17	spc	spc	PROPN
ap-6106	44	18	of	of	ADP
ap-6106	44	19	all	all	DET
ap-6106	44	20	cells	cell	NOUN
ap-6106	44	21	attached	attach	VERB
ap-6106	44	22	to	to	ADP
ap-6106	44	23	vertex	vertex	NOUN
ap-6106	44	24	p.	p.	NOUN
ap-6106	45	1	the	the	DET
ap-6106	45	2	edges	edge	NOUN
ap-6106	45	3	of	of	ADP
ap-6106	45	4	the	the	DET
ap-6106	45	5	dual	dual	ADJ
ap-6106	45	6	cell	cell	NOUN
ap-6106	45	7	p	p	X
ap-6106	45	8	which	which	PRON
ap-6106	45	9	connect	connect	VERB
ap-6106	45	10	the	the	DET
ap-6106	45	11	cell	cell	NOUN
ap-6106	45	12	center	center	NOUN
ap-6106	45	13	and	and	CCONJ
ap-6106	45	14	the	the	DET
ap-6106	45	15	edge	edge	NOUN
ap-6106	45	16	centers	center	NOUN
ap-6106	45	17	are	be	AUX
ap-6106	45	18	the	the	DET
ap-6106	45	19	separators	separator	NOUN
ap-6106	45	20	spc±.	spc±.	VERB
ap-6106	45	21	the	the	DET
ap-6106	45	22	outer	outer	ADJ
ap-6106	45	23	normals	normal	NOUN
ap-6106	45	24	nspc±	nspc±	NOUN
ap-6106	45	25	to	to	ADP
ap-6106	45	26	the	the	DET
ap-6106	45	27	separators	separator	NOUN
ap-6106	45	28	spc±	spc±	VERB
ap-6106	45	29	have	have	VERB
ap-6106	45	30	the	the	DET
ap-6106	45	31	same	same	ADJ
ap-6106	45	32	length	length	NOUN
ap-6106	45	33	as	as	SCONJ
ap-6106	45	34	the	the	DET
ap-6106	45	35	separators	separator	NOUN
ap-6106	45	36	spc±	spc±	VERB
ap-6106	45	37	,	,	PUNCT
ap-6106	45	38	see	see	VERB
ap-6106	45	39	fig	fig	NOUN
ap-6106	45	40	.	.	PUNCT
ap-6106	46	1	1	1	X
ap-6106	46	2	.	.	X
ap-6106	46	3	the	the	DET
ap-6106	46	4	corner	corner	NOUN
ap-6106	46	5	vector	vector	NOUN
ap-6106	46	6	npc	npc	NOUN
ap-6106	46	7	=	=	SYM
ap-6106	46	8	ne(ca	ne(ca	PROPN
ap-6106	46	9	)	)	PUNCT
ap-6106	47	1	+	+	CCONJ
ap-6106	47	2	ne(cb	ne(cb	ADJ
ap-6106	47	3	)	)	PUNCT
ap-6106	47	4	2	2	NUM
ap-6106	47	5	=	=	SYM
ap-6106	47	6	−(nspc+	−(nspc+	PROPN
ap-6106	47	7	+	+	NUM
ap-6106	47	8	nspc−	nspc−	NOUN
ap-6106	47	9	)	)	PUNCT
ap-6106	47	10	(	(	PUNCT
ap-6106	47	11	6	6	NUM
ap-6106	47	12	)	)	PUNCT
ap-6106	47	13	is	be	AUX
ap-6106	47	14	the	the	DET
ap-6106	47	15	average	average	NOUN
ap-6106	47	16	of	of	ADP
ap-6106	47	17	two	two	NUM
ap-6106	47	18	neighboring	neighboring	NOUN
ap-6106	47	19	edge	edge	NOUN
ap-6106	47	20	normals	normal	NOUN
ap-6106	47	21	ne(ca	ne(ca	NOUN
ap-6106	47	22	)	)	PUNCT
ap-6106	47	23	and	and	CCONJ
ap-6106	47	24	ne(cb	ne(cb	PROPN
ap-6106	47	25	)	)	PUNCT
ap-6106	47	26	(	(	PUNCT
ap-6106	47	27	see	see	VERB
ap-6106	47	28	fig	fig	NOUN
ap-6106	47	29	.	.	PUNCT
ap-6106	48	1	2	2	NUM
ap-6106	48	2	)	)	PUNCT
ap-6106	49	1	and	and	CCONJ
ap-6106	49	2	is	be	AUX
ap-6106	49	3	equal	equal	ADJ
ap-6106	49	4	to	to	ADP
ap-6106	49	5	minus	minus	ADP
ap-6106	49	6	the	the	DET
ap-6106	49	7	sum	sum	NOUN
ap-6106	49	8	of	of	ADP
ap-6106	49	9	separator	separator	NOUN
ap-6106	49	10	normals	normal	NOUN
ap-6106	49	11	nspc+	nspc+	PRON
ap-6106	49	12	and	and	CCONJ
ap-6106	49	13	nspc−	nspc−	NOUN
ap-6106	49	14	of	of	ADP
ap-6106	49	15	the	the	DET
ap-6106	49	16	corresponding	corresponding	PROPN
ap-6106	49	17	subcell	subcell	PROPN
ap-6106	49	18	spc	spc	PROPN
ap-6106	49	19	.	.	PUNCT
ap-6106	50	1	we	we	PRON
ap-6106	50	2	define	define	VERB
ap-6106	50	3	the	the	DET
ap-6106	50	4	cell	cell	NOUN
ap-6106	50	5	center	center	NOUN
ap-6106	50	6	xc	xc	PROPN
ap-6106	51	1	=	=	PRON
ap-6106	51	2	(	(	PUNCT
ap-6106	51	3	xc	xc	PROPN
ap-6106	51	4	,	,	PUNCT
ap-6106	51	5	yc	yc	PROPN
ap-6106	51	6	)	)	PUNCT
ap-6106	51	7	as	as	SCONJ
ap-6106	51	8	the	the	DET
ap-6106	51	9	arithmetic	arithmetic	ADJ
ap-6106	51	10	average	average	NOUN
ap-6106	51	11	of	of	ADP
ap-6106	51	12	the	the	DET
ap-6106	51	13	cell	cell	NOUN
ap-6106	51	14	nodes	nod	VERB
ap-6106	51	15	positions	position	NOUN
ap-6106	51	16	xp	xp	INTJ
ap-6106	51	17	.	.	PUNCT
ap-6106	52	1	each	each	DET
ap-6106	52	2	subcell	subcell	PROPN
ap-6106	52	3	spc	spc	PROPN
ap-6106	52	4	is	be	AUX
ap-6106	52	5	a	a	DET
ap-6106	52	6	quadrilateral	quadrilateral	NOUN
ap-6106	52	7	with	with	ADP
ap-6106	52	8	volume	volume	NOUN
ap-6106	52	9	(	(	PUNCT
ap-6106	52	10	area	area	NOUN
ap-6106	52	11	)	)	PUNCT
ap-6106	52	12	vpc	vpc	NOUN
ap-6106	52	13	=	=	SYM
ap-6106	52	14	1	1	NUM
ap-6106	52	15	2	2	NUM
ap-6106	52	16	4∑	4∑	NUM
ap-6106	52	17	i=1	i=1	PROPN
ap-6106	53	1	(	(	PUNCT
ap-6106	53	2	yi+1	yi+1	NOUN
ap-6106	53	3	−	−	PROPN
ap-6106	53	4	yi)(xi+1	yi)(xi+1	PROPN
ap-6106	54	1	+	+	CCONJ
ap-6106	54	2	xi	xi	NOUN
ap-6106	54	3	)	)	PUNCT
ap-6106	54	4	,	,	PUNCT
ap-6106	55	1	where	where	SCONJ
ap-6106	55	2	the	the	DET
ap-6106	55	3	subscript	subscript	NOUN
ap-6106	55	4	i	i	PRON
ap-6106	55	5	denotes	denote	VERB
ap-6106	55	6	four	four	NUM
ap-6106	55	7	nodes	node	NOUN
ap-6106	55	8	of	of	ADP
ap-6106	55	9	subcell	subcell	NOUN
ap-6106	55	10	spc	spc	PROPN
ap-6106	55	11	and	and	CCONJ
ap-6106	55	12	x5	x5	PROPN
ap-6106	55	13	≡	≡	PROPN
ap-6106	55	14	x1	x1	PROPN
ap-6106	55	15	.	.	PUNCT
ap-6106	56	1	the	the	DET
ap-6106	56	2	nodal	nodal	NOUN
ap-6106	56	3	volume	volume	NOUN
ap-6106	56	4	vp	vp	PROPN
ap-6106	56	5	and	and	CCONJ
ap-6106	56	6	the	the	DET
ap-6106	56	7	cell	cell	NOUN
ap-6106	56	8	volume	volume	NOUN
ap-6106	56	9	vc	vc	PROPN
ap-6106	56	10	are	be	AUX
ap-6106	56	11	given	give	VERB
ap-6106	56	12	by	by	ADP
ap-6106	56	13	sums	sum	NOUN
ap-6106	56	14	of	of	ADP
ap-6106	56	15	subcells	subcell	NOUN
ap-6106	56	16	having	have	VERB
ap-6106	56	17	node	node	ADJ
ap-6106	56	18	p	p	NOUN
ap-6106	56	19	or	or	CCONJ
ap-6106	56	20	cell	cell	NOUN
ap-6106	56	21	center	center	NOUN
ap-6106	56	22	c	c	NOUN
ap-6106	56	23	as	as	ADP
ap-6106	56	24	their	their	PRON
ap-6106	56	25	vertex	vertex	NOUN
ap-6106	56	26	,	,	PUNCT
ap-6106	56	27	respectively	respectively	ADV
ap-6106	56	28	:	:	PUNCT
ap-6106	56	29	vp	vp	PROPN
ap-6106	56	30	=	=	SYM
ap-6106	56	31	∑	∑	PUNCT
ap-6106	56	32	c(p	c(p	PROPN
ap-6106	56	33	)	)	PUNCT
ap-6106	56	34	vpc	vpc	NOUN
ap-6106	56	35	,	,	PUNCT
ap-6106	56	36	vc	vc	PROPN
ap-6106	56	37	=	=	SYM
ap-6106	56	38	∑	∑	PUNCT
ap-6106	56	39	p(c	p(c	NOUN
ap-6106	56	40	)	)	PUNCT
ap-6106	56	41	vpc	vpc	NOUN
ap-6106	56	42	.	.	PUNCT
ap-6106	57	1	the	the	DET
ap-6106	57	2	subzonal	subzonal	PROPN
ap-6106	57	3	mass	mass	PROPN
ap-6106	57	4	mpc	mpc	PROPN
ap-6106	57	5	is	be	AUX
ap-6106	57	6	defined	define	VERB
ap-6106	57	7	by	by	ADP
ap-6106	57	8	mpc	mpc	NOUN
ap-6106	57	9	=	=	PROPN
ap-6106	57	10	ρcvpc	ρcvpc	NOUN
ap-6106	57	11	.	.	PUNCT
ap-6106	58	1	the	the	DET
ap-6106	58	2	mass	mass	NOUN
ap-6106	58	3	of	of	ADP
ap-6106	58	4	primary	primary	ADJ
ap-6106	58	5	cell	cell	NOUN
ap-6106	58	6	mc	mc	PROPN
ap-6106	58	7	and	and	CCONJ
ap-6106	58	8	the	the	DET
ap-6106	58	9	mass	mass	NOUN
ap-6106	58	10	of	of	ADP
ap-6106	58	11	dual	dual	ADJ
ap-6106	58	12	cell	cell	NOUN
ap-6106	58	13	mp	mp	PROPN
ap-6106	58	14	are	be	AUX
ap-6106	58	15	defined	define	VERB
ap-6106	58	16	similarly	similarly	ADV
ap-6106	58	17	as	as	ADP
ap-6106	58	18	volumes	volume	NOUN
ap-6106	58	19	:	:	PUNCT
ap-6106	58	20	mc	mc	PROPN
ap-6106	58	21	=	=	PUNCT
ap-6106	58	22	∑	∑	PUNCT
ap-6106	58	23	p(c	p(c	PROPN
ap-6106	58	24	)	)	PUNCT
ap-6106	58	25	mpc	mpc	PROPN
ap-6106	58	26	,	,	PUNCT
ap-6106	58	27	mp	mp	PROPN
ap-6106	58	28	=	=	SYM
ap-6106	58	29	∑	∑	PUNCT
ap-6106	58	30	c(p	c(p	PROPN
ap-6106	58	31	)	)	PUNCT
ap-6106	58	32	mpc	mpc	PROPN
ap-6106	58	33	.	.	PUNCT
ap-6106	59	1	the	the	DET
ap-6106	59	2	lagrangian	lagrangian	ADJ
ap-6106	59	3	approach	approach	NOUN
ap-6106	59	4	assumes	assume	VERB
ap-6106	59	5	no	no	DET
ap-6106	59	6	mass	mass	NOUN
ap-6106	59	7	flux	flux	NOUN
ap-6106	59	8	between	between	ADP
ap-6106	59	9	subcells	subcell	NOUN
ap-6106	59	10	.	.	PUNCT
ap-6106	60	1	thus	thus	ADV
ap-6106	60	2	the	the	DET
ap-6106	60	3	subzonal	subzonal	ADJ
ap-6106	60	4	masses	masse	NOUN
ap-6106	60	5	,	,	PUNCT
ap-6106	60	6	as	as	ADV
ap-6106	60	7	well	well	ADV
ap-6106	60	8	as	as	ADP
ap-6106	60	9	cell	cell	NOUN
ap-6106	60	10	and	and	CCONJ
ap-6106	60	11	nodal	nodal	ADJ
ap-6106	60	12	masses	masse	NOUN
ap-6106	60	13	,	,	PUNCT
ap-6106	60	14	remain	remain	VERB
ap-6106	60	15	constant	constant	ADJ
ap-6106	60	16	.	.	PUNCT
ap-6106	61	1	4	4	X
ap-6106	61	2	.	.	PUNCT
ap-6106	61	3	schemes	scheme	NOUN
ap-6106	61	4	we	we	PRON
ap-6106	61	5	employ	employ	VERB
ap-6106	61	6	richtmyer	richtmyer	NOUN
ap-6106	61	7	’s	’s	PART
ap-6106	61	8	finite	finite	PROPN
ap-6106	61	9	volume	volume	NOUN
ap-6106	61	10	formulation	formulation	NOUN
ap-6106	62	1	[	[	X
ap-6106	62	2	16	16	NUM
ap-6106	62	3	]	]	PUNCT
ap-6106	62	4	of	of	ADP
ap-6106	62	5	the	the	DET
ap-6106	62	6	lax	lax	ADJ
ap-6106	62	7	-	-	PUNCT
ap-6106	62	8	wendroff	wendroff	NOUN
ap-6106	62	9	method	method	NOUN
ap-6106	62	10	.	.	PUNCT
ap-6106	63	1	each	each	DET
ap-6106	63	2	step	step	NOUN
ap-6106	63	3	of	of	ADP
ap-6106	63	4	the	the	DET
ap-6106	63	5	method	method	NOUN
ap-6106	63	6	consists	consist	VERB
ap-6106	63	7	of	of	ADP
ap-6106	63	8	a	a	DET
ap-6106	63	9	predictor	predictor	NOUN
ap-6106	63	10	and	and	CCONJ
ap-6106	63	11	a	a	DET
ap-6106	63	12	corrector	corrector	NOUN
ap-6106	63	13	.	.	PUNCT
ap-6106	64	1	4.1	4.1	NUM
ap-6106	64	2	.	.	PUNCT
ap-6106	64	3	predictor	predictor	VERB
ap-6106	64	4	the	the	DET
ap-6106	64	5	predictor	predictor	NOUN
ap-6106	64	6	computes	compute	VERB
ap-6106	64	7	the	the	DET
ap-6106	64	8	nodal	nodal	NOUN
ap-6106	64	9	estimates	estimate	NOUN
ap-6106	64	10	of	of	ADP
ap-6106	64	11	conserved	conserve	VERB
ap-6106	64	12	quantities	quantity	NOUN
ap-6106	64	13	at	at	ADP
ap-6106	64	14	time	time	NOUN
ap-6106	64	15	level	level	NOUN
ap-6106	64	16	n	n	NOUN
ap-6106	64	17	+	+	CCONJ
ap-6106	64	18	1	1	NUM
ap-6106	64	19	2	2	NUM
ap-6106	64	20	from	from	ADP
ap-6106	64	21	cellular	cellular	ADJ
ap-6106	64	22	quantities	quantity	NOUN
ap-6106	64	23	at	at	ADP
ap-6106	64	24	time	time	NOUN
ap-6106	64	25	level	level	NOUN
ap-6106	64	26	n	n	CCONJ
ap-6106	64	27	wn+	wn+	VERB
ap-6106	64	28	1	1	NUM
ap-6106	64	29	2	2	NUM
ap-6106	64	30	p	p	NOUN
ap-6106	64	31	=	=	PUNCT
ap-6106	64	32	∑	∑	PUNCT
ap-6106	64	33	c(p	c(p	NOUN
ap-6106	64	34	)	)	PUNCT
ap-6106	64	35	wn	wn	PROPN
ap-6106	64	36	c	c	PROPN
ap-6106	64	37	/vpc∑	/vpc∑	PROPN
ap-6106	65	1	c(p	c(p	NOUN
ap-6106	65	2	)	)	PUNCT
ap-6106	65	3	1	1	NUM
ap-6106	65	4	/	/	SYM
ap-6106	65	5	vpc	vpc	NOUN
ap-6106	65	6	+	+	CCONJ
ap-6106	65	7	∆t	∆t	PROPN
ap-6106	65	8	2mp	2mp	ADJ
ap-6106	65	9	∑	∑	SYM
ap-6106	65	10	c(p	c(p	NOUN
ap-6106	65	11	)	)	PUNCT
ap-6106	65	12	fnc	fnc	PROPN
ap-6106	65	13	·	·	PUNCT
ap-6106	65	14	(	(	PUNCT
ap-6106	65	15	nnspc++nnspc−	nnspc++nnspc−	PROPN
ap-6106	65	16	)	)	PUNCT
ap-6106	65	17	,	,	PUNCT
ap-6106	65	18	(	(	PUNCT
ap-6106	65	19	7	7	X
ap-6106	65	20	)	)	PUNCT
ap-6106	65	21	where	where	SCONJ
ap-6106	65	22	the	the	DET
ap-6106	65	23	summation	summation	NOUN
ap-6106	65	24	goes	go	VERB
ap-6106	65	25	over	over	ADP
ap-6106	65	26	c(p	c(p	NOUN
ap-6106	65	27	)	)	PUNCT
ap-6106	65	28	,	,	PUNCT
ap-6106	65	29	which	which	PRON
ap-6106	65	30	is	be	AUX
ap-6106	65	31	the	the	DET
ap-6106	65	32	set	set	NOUN
ap-6106	65	33	of	of	ADP
ap-6106	65	34	all	all	DET
ap-6106	65	35	cells	cell	NOUN
ap-6106	65	36	sharing	share	VERB
ap-6106	65	37	the	the	DET
ap-6106	65	38	vertex	vertex	NOUN
ap-6106	65	39	p.	p.	NOUN
ap-6106	65	40	in	in	ADP
ap-6106	65	41	the	the	DET
ap-6106	65	42	original	original	ADJ
ap-6106	65	43	paper	paper	NOUN
ap-6106	65	44	[	[	X
ap-6106	65	45	13	13	NUM
ap-6106	65	46	]	]	PUNCT
ap-6106	65	47	the	the	DET
ap-6106	65	48	conservative	conservative	ADJ
ap-6106	65	49	cell	cell	NOUN
ap-6106	65	50	quantities	quantity	NOUN
ap-6106	65	51	in	in	ADP
ap-6106	65	52	the	the	DET
ap-6106	65	53	first	first	ADJ
ap-6106	65	54	term	term	NOUN
ap-6106	65	55	on	on	ADP
ap-6106	65	56	the	the	DET
ap-6106	65	57	right	right	ADJ
ap-6106	65	58	hand	hand	NOUN
ap-6106	65	59	side	side	NOUN
ap-6106	65	60	of	of	ADP
ap-6106	65	61	(	(	PUNCT
ap-6106	65	62	7	7	NUM
ap-6106	65	63	)	)	PUNCT
ap-6106	65	64	were	be	AUX
ap-6106	65	65	weighted	weight	VERB
ap-6106	65	66	by	by	ADP
ap-6106	65	67	the	the	DET
ap-6106	65	68	cartesian	cartesian	ADJ
ap-6106	65	69	subzonal	subzonal	ADJ
ap-6106	65	70	masses	masse	NOUN
ap-6106	65	71	mpc	mpc	NOUN
ap-6106	65	72	,	,	PUNCT
ap-6106	65	73	giving	give	VERB
ap-6106	65	74	the	the	DET
ap-6106	65	75	standard	standard	ADJ
ap-6106	65	76	lax	lax	NOUN
ap-6106	65	77	-	-	PUNCT
ap-6106	65	78	friedrichs	friedrich	NOUN
ap-6106	65	79	(	(	PUNCT
ap-6106	65	80	lf	lf	NOUN
ap-6106	65	81	)	)	PUNCT
ap-6106	65	82	approximation	approximation	NOUN
ap-6106	65	83	.	.	PUNCT
ap-6106	66	1	here	here	ADV
ap-6106	66	2	,	,	PUNCT
ap-6106	66	3	being	be	AUX
ap-6106	66	4	inspired	inspire	VERB
ap-6106	66	5	by	by	ADP
ap-6106	66	6	wendroff	wendroff	NOUN
ap-6106	66	7	and	and	CCONJ
ap-6106	66	8	white	white	ADJ
ap-6106	66	9	[	[	X
ap-6106	66	10	17	17	NUM
ap-6106	66	11	]	]	PUNCT
ap-6106	66	12	,	,	PUNCT
ap-6106	66	13	we	we	PRON
ap-6106	66	14	weight	weight	VERB
ap-6106	66	15	them	they	PRON
ap-6106	66	16	by	by	ADP
ap-6106	66	17	the	the	DET
ap-6106	66	18	inverses	inverse	NOUN
ap-6106	66	19	of	of	ADP
ap-6106	66	20	the	the	DET
ap-6106	66	21	subzonal	subzonal	ADJ
ap-6106	66	22	volumes	volume	NOUN
ap-6106	66	23	1	1	NUM
ap-6106	66	24	/	/	SYM
ap-6106	66	25	vpc	vpc	NOUN
ap-6106	66	26	.	.	PUNCT
ap-6106	67	1	the	the	DET
ap-6106	67	2	standard	standard	ADJ
ap-6106	67	3	lf	lf	ADP
ap-6106	67	4	weighting	weighting	NOUN
ap-6106	67	5	on	on	ADP
ap-6106	67	6	a	a	DET
ap-6106	67	7	1d	1d	NUM
ap-6106	67	8	non	non	ADJ
ap-6106	67	9	-	-	ADJ
ap-6106	67	10	uniform	uniform	ADJ
ap-6106	67	11	eulerian	eulerian	ADJ
ap-6106	67	12	mesh	mesh	NOUN
ap-6106	67	13	looks	look	VERB
ap-6106	67	14	like	like	ADP
ap-6106	67	15	(	(	PUNCT
ap-6106	67	16	∆xjwj	∆xjwj	NUM
ap-6106	67	17	+	+	NUM
ap-6106	67	18	∆xj+1wj+1)/(∆xj	∆xj+1wj+1)/(∆xj	NOUN
ap-6106	67	19	+	+	CCONJ
ap-6106	67	20	∆xj+1	∆xj+1	NUM
ap-6106	67	21	)	)	PUNCT
ap-6106	67	22	,	,	PUNCT
ap-6106	67	23	while	while	SCONJ
ap-6106	67	24	wendroff	wendroff	NOUN
ap-6106	67	25	and	and	CCONJ
ap-6106	67	26	white	white	ADJ
ap-6106	67	27	[	[	X
ap-6106	67	28	17	17	NUM
ap-6106	67	29	]	]	PUNCT
ap-6106	67	30	proposed	propose	VERB
ap-6106	67	31	to	to	PART
ap-6106	67	32	use	use	VERB
ap-6106	67	33	(	(	PUNCT
ap-6106	67	34	∆xj+1wj	∆xj+1wj	PROPN
ap-6106	67	35	+	+	CCONJ
ap-6106	67	36	∆xjwj+1)/(∆xj	∆xjwj+1)/(∆xj	PROPN
ap-6106	67	37	+	+	CCONJ
ap-6106	67	38	∆xj+1	∆xj+1	NUM
ap-6106	67	39	)	)	PUNCT
ap-6106	67	40	,	,	PUNCT
ap-6106	67	41	which	which	PRON
ap-6106	67	42	is	be	AUX
ap-6106	67	43	the	the	DET
ap-6106	67	44	same	same	ADJ
ap-6106	67	45	as	as	ADP
ap-6106	67	46	the	the	DET
ap-6106	67	47	linear	linear	ADJ
ap-6106	67	48	interpolation	interpolation	NOUN
ap-6106	67	49	from	from	ADP
ap-6106	67	50	cell	cell	NOUN
ap-6106	67	51	centers	center	NOUN
ap-6106	67	52	to	to	ADP
ap-6106	67	53	the	the	DET
ap-6106	67	54	nodes	node	NOUN
ap-6106	67	55	.	.	PUNCT
ap-6106	68	1	we	we	PRON
ap-6106	68	2	call	call	VERB
ap-6106	68	3	this	this	DET
ap-6106	68	4	weighting	weighting	NOUN
ap-6106	68	5	wendroffwhite	wendroffwhite	NOUN
ap-6106	68	6	(	(	PUNCT
ap-6106	68	7	ww	ww	PROPN
ap-6106	68	8	)	)	PUNCT
ap-6106	68	9	weighting	weighting	NOUN
ap-6106	68	10	.	.	PUNCT
ap-6106	69	1	on	on	ADP
ap-6106	69	2	a	a	DET
ap-6106	69	3	2d	2d	NUM
ap-6106	69	4	orthogonal	orthogonal	ADJ
ap-6106	69	5	mesh	mesh	NOUN
ap-6106	69	6	the	the	DET
ap-6106	69	7	ww	ww	PROPN
ap-6106	69	8	weighting	weighting	NOUN
ap-6106	69	9	can	can	AUX
ap-6106	69	10	be	be	AUX
ap-6106	69	11	generalized	generalize	VERB
ap-6106	69	12	to	to	ADP
ap-6106	69	13	the	the	DET
ap-6106	69	14	weighting	weighting	NOUN
ap-6106	69	15	by	by	ADP
ap-6106	69	16	the	the	DET
ap-6106	69	17	inverses	inverse	NOUN
ap-6106	69	18	of	of	ADP
ap-6106	69	19	subzonal	subzonal	ADJ
ap-6106	69	20	volumes	volume	NOUN
ap-6106	69	21	,	,	PUNCT
ap-6106	69	22	which	which	PRON
ap-6106	69	23	is	be	AUX
ap-6106	69	24	the	the	DET
ap-6106	69	25	same	same	ADJ
ap-6106	69	26	as	as	ADP
ap-6106	69	27	the	the	DET
ap-6106	69	28	bi	bi	ADJ
ap-6106	69	29	-	-	ADJ
ap-6106	69	30	linear	linear	ADJ
ap-6106	69	31	interpolation	interpolation	NOUN
ap-6106	69	32	from	from	ADP
ap-6106	69	33	cell	cell	NOUN
ap-6106	69	34	centers	center	NOUN
ap-6106	69	35	to	to	ADP
ap-6106	69	36	nodes	node	NOUN
ap-6106	69	37	.	.	PUNCT
ap-6106	70	1	in	in	ADP
ap-6106	70	2	(	(	PUNCT
ap-6106	70	3	7	7	X
ap-6106	70	4	)	)	PUNCT
ap-6106	70	5	we	we	PRON
ap-6106	70	6	apply	apply	VERB
ap-6106	70	7	the	the	DET
ap-6106	70	8	same	same	ADJ
ap-6106	70	9	weighting	weighting	NOUN
ap-6106	70	10	to	to	ADP
ap-6106	70	11	general	general	ADJ
ap-6106	70	12	lagrangian	lagrangian	ADJ
ap-6106	70	13	meshes	mesh	NOUN
ap-6106	70	14	.	.	PUNCT
ap-6106	71	1	4.2	4.2	NUM
ap-6106	71	2	.	.	PUNCT
ap-6106	72	1	corrector	corrector	VERB
ap-6106	72	2	the	the	DET
ap-6106	72	3	nodal	nodal	NOUN
ap-6106	72	4	estimates	estimate	NOUN
ap-6106	72	5	from	from	ADP
ap-6106	72	6	the	the	DET
ap-6106	72	7	predictor	predictor	NOUN
ap-6106	72	8	(	(	PUNCT
ap-6106	72	9	7	7	X
ap-6106	72	10	)	)	PUNCT
ap-6106	72	11	are	be	AUX
ap-6106	72	12	used	use	VERB
ap-6106	72	13	to	to	PART
ap-6106	72	14	compute	compute	VERB
ap-6106	72	15	the	the	DET
ap-6106	72	16	final	final	ADJ
ap-6106	72	17	lw	lw	NOUN
ap-6106	72	18	cell	cell	NOUN
ap-6106	72	19	values	value	NOUN
ap-6106	72	20	at	at	ADP
ap-6106	72	21	time	time	NOUN
ap-6106	72	22	level	level	NOUN
ap-6106	72	23	n+	n+	ADP
ap-6106	72	24	1	1	NUM
ap-6106	72	25	mcwn+1	mcwn+1	PROPN
ap-6106	72	26	c	c	NOUN
ap-6106	72	27	=	=	PUNCT
ap-6106	72	28	mcwn	mcwn	PROPN
ap-6106	72	29	c	c	NOUN
ap-6106	72	30	+	+	CCONJ
ap-6106	72	31	∆t	∆t	VERB
ap-6106	72	32	∑	∑	PUNCT
ap-6106	72	33	e(ca	e(ca	NOUN
ap-6106	72	34	)	)	PUNCT
ap-6106	72	35	fn+	fn+	NOUN
ap-6106	72	36	1	1	NUM
ap-6106	72	37	2	2	NUM
ap-6106	72	38	e(ca	e(ca	NOUN
ap-6106	72	39	)	)	PUNCT
ap-6106	72	40	·	·	PUNCT
ap-6106	73	1	n	n	X
ap-6106	73	2	n+	n+	NUM
ap-6106	73	3	1	1	NUM
ap-6106	73	4	2	2	NUM
ap-6106	73	5	e(ca	e(ca	NOUN
ap-6106	73	6	)	)	PUNCT
ap-6106	73	7	,	,	PUNCT
ap-6106	73	8	(	(	PUNCT
ap-6106	73	9	8)	8)	NUM
ap-6106	73	10	where	where	SCONJ
ap-6106	73	11	the	the	DET
ap-6106	73	12	summation	summation	NOUN
ap-6106	73	13	goes	go	VERB
ap-6106	73	14	over	over	ADP
ap-6106	73	15	e(c	e(c	NOUN
ap-6106	73	16	)	)	PUNCT
ap-6106	73	17	which	which	PRON
ap-6106	73	18	is	be	AUX
ap-6106	73	19	the	the	DET
ap-6106	73	20	set	set	NOUN
ap-6106	73	21	of	of	ADP
ap-6106	73	22	all	all	DET
ap-6106	73	23	edges	edge	NOUN
ap-6106	73	24	of	of	ADP
ap-6106	73	25	cell	cell	NOUN
ap-6106	73	26	c	c	NOUN
ap-6106	73	27	,	,	PUNCT
ap-6106	73	28	the	the	DET
ap-6106	73	29	edge	edge	NOUN
ap-6106	73	30	e(ca	e(ca	NOUN
ap-6106	73	31	)	)	PUNCT
ap-6106	73	32	is	be	AUX
ap-6106	73	33	the	the	DET
ap-6106	73	34	edge	edge	NOUN
ap-6106	73	35	between	between	ADP
ap-6106	73	36	cells	cell	NOUN
ap-6106	73	37	c	c	PROPN
ap-6106	73	38	and	and	CCONJ
ap-6106	73	39	a	a	PRON
ap-6106	73	40	,	,	PUNCT
ap-6106	73	41	and	and	CCONJ
ap-6106	73	42	where	where	SCONJ
ap-6106	73	43	fn+	fn+	NOUN
ap-6106	73	44	1	1	NUM
ap-6106	73	45	2	2	NUM
ap-6106	73	46	e(ca	e(ca	NOUN
ap-6106	73	47	)	)	PUNCT
ap-6106	73	48	is	be	AUX
ap-6106	73	49	the	the	DET
ap-6106	73	50	average	average	NOUN
ap-6106	73	51	of	of	ADP
ap-6106	73	52	the	the	DET
ap-6106	73	53	two	two	NUM
ap-6106	73	54	nodal	nodal	ADJ
ap-6106	73	55	fluxes	flux	NOUN
ap-6106	73	56	at	at	ADP
ap-6106	73	57	the	the	DET
ap-6106	73	58	endpoints	endpoint	NOUN
ap-6106	73	59	of	of	ADP
ap-6106	73	60	the	the	DET
ap-6106	73	61	edge	edge	NOUN
ap-6106	73	62	e(ca	e(ca	NOUN
ap-6106	73	63	)	)	PUNCT
ap-6106	73	64	fn+	fn+	NOUN
ap-6106	73	65	1	1	NUM
ap-6106	73	66	2	2	NUM
ap-6106	73	67	e(ca	e(ca	NOUN
ap-6106	73	68	)	)	PUNCT
ap-6106	74	1	=	=	SYM
ap-6106	74	2	fn+	fn+	NOUN
ap-6106	74	3	1	1	NUM
ap-6106	74	4	2	2	NUM
ap-6106	74	5	pe(ca)+	pe(ca)+	NOUN
ap-6106	74	6	+	+	CCONJ
ap-6106	74	7	fn+	fn+	NOUN
ap-6106	74	8	1	1	NUM
ap-6106	74	9	2	2	NUM
ap-6106	74	10	pe(ca)−	pe(ca)−	NOUN
ap-6106	74	11	2	2	NUM
ap-6106	74	12	.	.	PUNCT
ap-6106	75	1	the	the	DET
ap-6106	75	2	corrector	corrector	NOUN
ap-6106	75	3	(	(	PUNCT
ap-6106	75	4	8)	8)	NUM
ap-6106	75	5	can	can	AUX
ap-6106	75	6	be	be	AUX
ap-6106	75	7	rewritten	rewrite	VERB
ap-6106	75	8	as	as	ADP
ap-6106	75	9	mcwn+1	mcwn+1	NOUN
ap-6106	75	10	c	c	NOUN
ap-6106	75	11	=	=	PUNCT
ap-6106	75	12	mcwn	mcwn	PROPN
ap-6106	75	13	c	c	NOUN
ap-6106	75	14	+	+	CCONJ
ap-6106	75	15	∆t	∆t	VERB
ap-6106	75	16	∑	∑	PUNCT
ap-6106	75	17	p(c	p(c	NOUN
ap-6106	75	18	)	)	PUNCT
ap-6106	75	19	fn+	fn+	NOUN
ap-6106	75	20	1	1	NUM
ap-6106	75	21	2	2	NUM
ap-6106	75	22	p	p	NOUN
ap-6106	75	23	·	·	PUNCT
ap-6106	75	24	nn+	nn+	NOUN
ap-6106	75	25	1	1	NUM
ap-6106	75	26	2	2	NUM
ap-6106	75	27	pc	pc	NOUN
ap-6106	75	28	(	(	PUNCT
ap-6106	75	29	9	9	NUM
ap-6106	75	30	)	)	PUNCT
ap-6106	75	31	using	use	VERB
ap-6106	75	32	the	the	DET
ap-6106	75	33	summation	summation	NOUN
ap-6106	75	34	over	over	ADP
ap-6106	75	35	p(c	p(c	PROPN
ap-6106	75	36	)	)	PUNCT
ap-6106	75	37	,	,	PUNCT
ap-6106	75	38	which	which	PRON
ap-6106	75	39	is	be	AUX
ap-6106	75	40	the	the	DET
ap-6106	75	41	set	set	NOUN
ap-6106	75	42	of	of	ADP
ap-6106	75	43	all	all	DET
ap-6106	75	44	points	point	NOUN
ap-6106	75	45	,	,	PUNCT
ap-6106	75	46	i.e.	i.e.	X
ap-6106	75	47	vertices	vertex	NOUN
ap-6106	75	48	,	,	PUNCT
ap-6106	75	49	of	of	ADP
ap-6106	75	50	cell	cell	NOUN
ap-6106	75	51	c	c	NOUN
ap-6106	75	52	and	and	CCONJ
ap-6106	75	53	the	the	DET
ap-6106	75	54	corner	corner	NOUN
ap-6106	75	55	vectors	vector	NOUN
ap-6106	75	56	nn+	nn+	VERB
ap-6106	75	57	1	1	NUM
ap-6106	75	58	2	2	NUM
ap-6106	75	59	pc	pc	NOUN
ap-6106	75	60	.	.	PUNCT
ap-6106	76	1	69	69	NUM
ap-6106	76	2	d.	d.	PROPN
ap-6106	76	3	fridrich	fridrich	PROPN
ap-6106	76	4	,	,	PUNCT
ap-6106	76	5	r.	r.	PROPN
ap-6106	76	6	liska	liska	PROPN
ap-6106	76	7	,	,	PUNCT
ap-6106	76	8	i.	i.	PROPN
ap-6106	76	9	tarant	tarant	PROPN
ap-6106	76	10	et	et	PROPN
ap-6106	76	11	al	al	PROPN
ap-6106	76	12	.	.	PROPN
ap-6106	76	13	acta	acta	PROPN
ap-6106	76	14	polytechnica	polytechnica	PROPN
ap-6106	76	15	figure	figure	NOUN
ap-6106	76	16	1	1	NUM
ap-6106	76	17	.	.	PUNCT
ap-6106	77	1	the	the	DET
ap-6106	77	2	primary	primary	NOUN
ap-6106	77	3	(	(	PUNCT
ap-6106	77	4	here	here	ADV
ap-6106	77	5	triangular	triangular	NOUN
ap-6106	77	6	)	)	PUNCT
ap-6106	77	7	mesh	mesh	NOUN
ap-6106	77	8	drawn	draw	VERB
ap-6106	77	9	by	by	ADP
ap-6106	77	10	solid	solid	ADJ
ap-6106	77	11	segments	segment	NOUN
ap-6106	77	12	with	with	ADP
ap-6106	77	13	an	an	DET
ap-6106	77	14	edge	edge	NOUN
ap-6106	77	15	normal	normal	ADJ
ap-6106	77	16	to	to	ADP
ap-6106	77	17	the	the	DET
ap-6106	77	18	primary	primary	ADJ
ap-6106	77	19	edge	edge	NOUN
ap-6106	77	20	eca	eca	NOUN
ap-6106	77	21	and	and	CCONJ
ap-6106	77	22	one	one	NUM
ap-6106	77	23	dual	dual	ADJ
ap-6106	77	24	cell	cell	NOUN
ap-6106	77	25	delineated	delineate	VERB
ap-6106	77	26	by	by	ADP
ap-6106	77	27	the	the	DET
ap-6106	77	28	separators	separator	NOUN
ap-6106	77	29	(	(	PUNCT
ap-6106	77	30	dotted	dotted	ADJ
ap-6106	77	31	segments	segment	NOUN
ap-6106	77	32	)	)	PUNCT
ap-6106	77	33	,	,	PUNCT
ap-6106	77	34	shown	show	VERB
ap-6106	77	35	along	along	ADP
ap-6106	77	36	with	with	ADP
ap-6106	77	37	their	their	PRON
ap-6106	77	38	normals	normal	NOUN
ap-6106	77	39	.	.	PUNCT
ap-6106	78	1	figure	figure	NOUN
ap-6106	78	2	2	2	NUM
ap-6106	78	3	.	.	X
ap-6106	79	1	averaging	average	VERB
ap-6106	79	2	of	of	ADP
ap-6106	79	3	the	the	DET
ap-6106	79	4	edge	edge	NOUN
ap-6106	79	5	normals	normal	NOUN
ap-6106	79	6	ne(ca	ne(ca	NOUN
ap-6106	79	7	)	)	PUNCT
ap-6106	79	8	and	and	CCONJ
ap-6106	79	9	ne(cb	ne(cb	PROPN
ap-6106	79	10	)	)	PUNCT
ap-6106	79	11	of	of	ADP
ap-6106	79	12	the	the	DET
ap-6106	79	13	cell	cell	NOUN
ap-6106	79	14	c	c	VERB
ap-6106	79	15	to	to	PART
ap-6106	79	16	define	define	VERB
ap-6106	79	17	the	the	DET
ap-6106	79	18	corner	corner	NOUN
ap-6106	79	19	vector	vector	NOUN
ap-6106	79	20	npc	npc	NOUN
ap-6106	79	21	.	.	PUNCT
ap-6106	80	1	70	70	NUM
ap-6106	80	2	vol	vol	NOUN
ap-6106	80	3	.	.	PUNCT
ap-6106	81	1	61	61	NUM
ap-6106	81	2	special	special	ADJ
ap-6106	81	3	issue/2021	issue/2021	NOUN
ap-6106	81	4	lagrangian	lagrangian	ADJ
ap-6106	81	5	lax	lax	PROPN
ap-6106	81	6	-	-	PUNCT
ap-6106	81	7	wendroff	wendroff	NOUN
ap-6106	81	8	hll	hll	PROPN
ap-6106	81	9	scheme	scheme	PROPN
ap-6106	81	10	4.3	4.3	NUM
ap-6106	81	11	.	.	PUNCT
ap-6106	82	1	mesh	mesh	NOUN
ap-6106	82	2	positions	position	NOUN
ap-6106	82	3	update	update	VERB
ap-6106	82	4	the	the	DET
ap-6106	82	5	node	node	ADJ
ap-6106	82	6	positions	position	NOUN
ap-6106	82	7	are	be	AUX
ap-6106	82	8	updated	update	VERB
ap-6106	82	9	using	use	VERB
ap-6106	82	10	the	the	DET
ap-6106	82	11	nodal	nodal	NOUN
ap-6106	82	12	velocity	velocity	NOUN
ap-6106	82	13	estimates	estimate	NOUN
ap-6106	82	14	from	from	ADP
ap-6106	82	15	the	the	DET
ap-6106	82	16	predictor	predictor	NOUN
ap-6106	82	17	:	:	PUNCT
ap-6106	82	18	xn+1	xn+1	NUM
ap-6106	83	1	p	p	X
ap-6106	84	1	=	=	PUNCT
ap-6106	85	1	xn	xn	PROPN
ap-6106	86	1	p	p	NOUN
ap-6106	87	1	+	+	X
ap-6106	87	2	∆tun+	∆tun+	PROPN
ap-6106	87	3	1	1	NUM
ap-6106	87	4	2	2	NUM
ap-6106	87	5	p	p	NOUN
ap-6106	87	6	,	,	PUNCT
ap-6106	87	7	xn+	xn+	PROPN
ap-6106	87	8	1	1	NUM
ap-6106	87	9	2	2	NUM
ap-6106	87	10	p	p	NOUN
ap-6106	87	11	=	=	PUNCT
ap-6106	87	12	(	(	PUNCT
ap-6106	87	13	xn+1	xn+1	PROPN
ap-6106	87	14	p	p	X
ap-6106	88	1	+	+	NOUN
ap-6106	88	2	xn	xn	PROPN
ap-6106	88	3	p	p	NOUN
ap-6106	88	4	)	)	PUNCT
ap-6106	88	5	/2	/2	PROPN
ap-6106	89	1	4.4	4.4	NUM
ap-6106	89	2	.	.	PUNCT
ap-6106	90	1	artificial	artificial	ADJ
ap-6106	90	2	dissipation	dissipation	NOUN
ap-6106	90	3	the	the	DET
ap-6106	90	4	dissipative	dissipative	ADJ
ap-6106	90	5	terms	term	NOUN
ap-6106	90	6	dc	dc	PROPN
ap-6106	90	7	are	be	AUX
ap-6106	90	8	added	add	VERB
ap-6106	90	9	to	to	ADP
ap-6106	90	10	the	the	DET
ap-6106	90	11	corrector	corrector	NOUN
ap-6106	90	12	(	(	PUNCT
ap-6106	90	13	8)	8)	NUM
ap-6106	90	14	mc	mc	PROPN
ap-6106	90	15	wn+1	wn+1	NOUN
ap-6106	90	16	c	c	PROPN
ap-6106	90	17	−wn	−wn	NOUN
ap-6106	90	18	c	c	X
ap-6106	90	19	∆t	∆t	NOUN
ap-6106	90	20	=	=	SYM
ap-6106	90	21	∑	∑	PART
ap-6106	90	22	e(ca	e(ca	X
ap-6106	90	23	)	)	PUNCT
ap-6106	90	24	fn+	fn+	NOUN
ap-6106	90	25	1	1	NUM
ap-6106	90	26	2	2	NUM
ap-6106	90	27	e(ca	e(ca	NOUN
ap-6106	90	28	)	)	PUNCT
ap-6106	90	29	·	·	PUNCT
ap-6106	91	1	n	n	X
ap-6106	91	2	n+	n+	NUM
ap-6106	91	3	1	1	NUM
ap-6106	91	4	2	2	NUM
ap-6106	91	5	e(ca	e(ca	NOUN
ap-6106	91	6	)	)	PUNCT
ap-6106	91	7	+	+	CCONJ
ap-6106	91	8	dc	dc	PROPN
ap-6106	91	9	,	,	PUNCT
ap-6106	91	10	so	so	SCONJ
ap-6106	91	11	that	that	SCONJ
ap-6106	91	12	the	the	DET
ap-6106	91	13	scheme	scheme	NOUN
ap-6106	91	14	can	can	AUX
ap-6106	91	15	compute	compute	VERB
ap-6106	91	16	shock	shock	NOUN
ap-6106	91	17	waves	wave	NOUN
ap-6106	91	18	.	.	PUNCT
ap-6106	92	1	we	we	PRON
ap-6106	92	2	use	use	VERB
ap-6106	92	3	the	the	DET
ap-6106	92	4	dissipative	dissipative	ADJ
ap-6106	92	5	parts	part	NOUN
ap-6106	92	6	of	of	ADP
ap-6106	92	7	the	the	DET
ap-6106	92	8	hll	hll	PROPN
ap-6106	92	9	approximate	approximate	PROPN
ap-6106	92	10	riemann	riemann	PROPN
ap-6106	92	11	solver	solver	PROPN
ap-6106	92	12	fluxes	flux	NOUN
ap-6106	92	13	[	[	X
ap-6106	92	14	14	14	NUM
ap-6106	92	15	]	]	PUNCT
ap-6106	92	16	as	as	SCONJ
ap-6106	92	17	the	the	DET
ap-6106	92	18	artificial	artificial	ADJ
ap-6106	92	19	dissipation	dissipation	NOUN
ap-6106	92	20	terms	term	VERB
ap-6106	92	21	dc	dc	PROPN
ap-6106	92	22	=	=	SYM
ap-6106	92	23	dτ	dτ	PROPN
ap-6106	92	24	·	·	PUNCT
ap-6106	92	25	∑	∑	SYM
ap-6106	92	26	e(c	e(c	NUM
ap-6106	92	27	)	)	PUNCT
ap-6106	92	28	σcaσac	σcaσac	VERB
ap-6106	92	29	σca	σca	PRON
ap-6106	92	30	+	+	CCONJ
ap-6106	92	31	σac	σac	AUX
ap-6106	92	32	|nne(ca)|(wn	|nne(ca)|(wn	VERB
ap-6106	92	33	a	a	DET
ap-6106	92	34	−wn	−wn	NOUN
ap-6106	92	35	c	c	NOUN
ap-6106	92	36	)	)	PUNCT
ap-6106	92	37	,	,	PUNCT
ap-6106	92	38	(	(	PUNCT
ap-6106	92	39	10	10	NUM
ap-6106	92	40	)	)	PUNCT
ap-6106	92	41	where	where	SCONJ
ap-6106	92	42	the	the	DET
ap-6106	92	43	modified	modify	VERB
ap-6106	92	44	signal	signal	NOUN
ap-6106	92	45	velocity	velocity	NOUN
ap-6106	92	46	is	be	AUX
ap-6106	92	47	defined	define	VERB
ap-6106	92	48	by	by	ADP
ap-6106	92	49	σca	σca	NOUN
ap-6106	92	50	=	=	SYM
ap-6106	92	51	ρnc	ρnc	X
ap-6106	92	52	(	(	PUNCT
ap-6106	92	53	cs	cs	PROPN
ap-6106	92	54	,	,	PUNCT
ap-6106	92	55	nc	nc	PROPN
ap-6106	92	56	+	+	NOUN
ap-6106	92	57	|(unc	|(unc	NUM
ap-6106	92	58	−	−	PROPN
ap-6106	92	59	una	una	PROPN
ap-6106	92	60	)	)	PUNCT
ap-6106	92	61	·	·	PUNCT
ap-6106	92	62	nne(ca)|	nne(ca)|	X
ap-6106	92	63	|nne(ca)|	|nne(ca)|	PROPN
ap-6106	92	64	)	)	PUNCT
ap-6106	92	65	,	,	PUNCT
ap-6106	92	66	and	and	CCONJ
ap-6106	92	67	dτ	dτ	NOUN
ap-6106	92	68	=	=	SYM
ap-6106	92	69			PROPN
ap-6106	92	70	τη	τη	VERB
ap-6106	92	71	0	0	NUM
ap-6106	92	72	0	0	NUM
ap-6106	92	73	0	0	NUM
ap-6106	92	74	0	0	NUM
ap-6106	92	75	τu	τu	ADP
ap-6106	92	76	0	0	NUM
ap-6106	92	77	0	0	NUM
ap-6106	92	78	0	0	NUM
ap-6106	92	79	0	0	NUM
ap-6106	92	80	τu	τu	ADP
ap-6106	92	81	0	0	NUM
ap-6106	92	82	0	0	NUM
ap-6106	92	83	0	0	NUM
ap-6106	92	84	0	0	NUM
ap-6106	92	85	τe	τe	DET
ap-6106	92	86			NOUN
ap-6106	92	87	(	(	PUNCT
ap-6106	92	88	11	11	NUM
ap-6106	92	89	)	)	PUNCT
ap-6106	92	90	is	be	AUX
ap-6106	92	91	the	the	DET
ap-6106	92	92	diagonal	diagonal	ADJ
ap-6106	92	93	matrix	matrix	NOUN
ap-6106	92	94	of	of	ADP
ap-6106	92	95	dimensionless	dimensionless	NOUN
ap-6106	92	96	coefficients	coefficient	NOUN
ap-6106	92	97	,	,	PUNCT
ap-6106	92	98	which	which	PRON
ap-6106	92	99	control	control	VERB
ap-6106	92	100	how	how	SCONJ
ap-6106	92	101	much	much	ADJ
ap-6106	92	102	artificial	artificial	ADJ
ap-6106	92	103	dissipation	dissipation	NOUN
ap-6106	92	104	is	be	AUX
ap-6106	92	105	added	add	VERB
ap-6106	92	106	.	.	PUNCT
ap-6106	93	1	we	we	PRON
ap-6106	93	2	employ	employ	VERB
ap-6106	93	3	the	the	DET
ap-6106	93	4	method	method	NOUN
ap-6106	93	5	with	with	ADP
ap-6106	93	6	τη	τη	ADP
ap-6106	93	7	=	=	SYM
ap-6106	93	8	0	0	PROPN
ap-6106	93	9	,	,	PUNCT
ap-6106	93	10	which	which	PRON
ap-6106	93	11	we	we	PRON
ap-6106	93	12	call	call	VERB
ap-6106	93	13	lw+2	lw+2	PROPN
ap-6106	93	14	and	and	CCONJ
ap-6106	93	15	which	which	PRON
ap-6106	93	16	satisfies	satisfy	VERB
ap-6106	93	17	the	the	DET
ap-6106	93	18	geometric	geometric	ADJ
ap-6106	93	19	conservation	conservation	NOUN
ap-6106	93	20	law	law	NOUN
ap-6106	93	21	[	[	X
ap-6106	93	22	13	13	NUM
ap-6106	93	23	]	]	PUNCT
ap-6106	93	24	.	.	PUNCT
ap-6106	94	1	in	in	ADP
ap-6106	94	2	all	all	DET
ap-6106	94	3	these	these	DET
ap-6106	94	4	tests	test	NOUN
ap-6106	94	5	we	we	PRON
ap-6106	94	6	use	use	VERB
ap-6106	94	7	τη	τη	VERB
ap-6106	94	8	=	=	SYM
ap-6106	94	9	0	0	PROPN
ap-6106	94	10	and	and	CCONJ
ap-6106	94	11	τu	τu	ADP
ap-6106	94	12	=	=	PUNCT
ap-6106	94	13	τe	τe	ADP
ap-6106	95	1	=	=	SYM
ap-6106	95	2	τ	τ	PROPN
ap-6106	95	3	.	.	PUNCT
ap-6106	96	1	in	in	ADP
ap-6106	96	2	[	[	X
ap-6106	96	3	13	13	NUM
ap-6106	96	4	]	]	PUNCT
ap-6106	96	5	we	we	PRON
ap-6106	96	6	have	have	AUX
ap-6106	96	7	used	use	VERB
ap-6106	96	8	also	also	ADV
ap-6106	96	9	the	the	DET
ap-6106	96	10	scheme	scheme	NOUN
ap-6106	96	11	lw+3	lw+3	NOUN
ap-6106	96	12	with	with	ADP
ap-6106	96	13	τη	τη	NUM
ap-6106	96	14	6=	6=	ADP
ap-6106	96	15	0	0	NUM
ap-6106	96	16	.	.	PROPN
ap-6106	97	1	5	5	NUM
ap-6106	97	2	.	.	X
ap-6106	97	3	numerical	numerical	ADJ
ap-6106	97	4	results	result	NOUN
ap-6106	97	5	in	in	ADP
ap-6106	97	6	the	the	DET
ap-6106	97	7	original	original	ADJ
ap-6106	97	8	paper	paper	NOUN
ap-6106	98	1	[	[	X
ap-6106	98	2	13	13	NUM
ap-6106	98	3	]	]	PUNCT
ap-6106	98	4	,	,	PUNCT
ap-6106	98	5	all	all	DET
ap-6106	98	6	2d	2d	NUM
ap-6106	98	7	numerical	numerical	ADJ
ap-6106	98	8	results	result	NOUN
ap-6106	98	9	were	be	AUX
ap-6106	98	10	shown	show	VERB
ap-6106	98	11	on	on	ADP
ap-6106	98	12	a	a	DET
ap-6106	98	13	structured	structured	ADJ
ap-6106	98	14	quadrilateral	quadrilateral	ADJ
ap-6106	98	15	mesh	mesh	NOUN
ap-6106	98	16	,	,	PUNCT
ap-6106	98	17	i.e.	i.e.	X
ap-6106	98	18	,	,	PUNCT
ap-6106	98	19	a	a	DET
ap-6106	98	20	logically	logically	ADV
ap-6106	98	21	rectangular	rectangular	ADJ
ap-6106	98	22	(	(	PUNCT
ap-6106	98	23	cartesian	cartesian	ADJ
ap-6106	98	24	)	)	PUNCT
ap-6106	98	25	grid	grid	NOUN
ap-6106	98	26	,	,	PUNCT
ap-6106	98	27	although	although	SCONJ
ap-6106	98	28	the	the	DET
ap-6106	98	29	actual	actual	ADJ
ap-6106	98	30	method	method	NOUN
ap-6106	98	31	was	be	AUX
ap-6106	98	32	already	already	ADV
ap-6106	98	33	formulated	formulate	VERB
ap-6106	98	34	for	for	ADP
ap-6106	98	35	general	general	ADJ
ap-6106	98	36	polygonal	polygonal	ADJ
ap-6106	98	37	meshes	mesh	NOUN
ap-6106	98	38	,	,	PUNCT
ap-6106	98	39	using	use	VERB
ap-6106	98	40	the	the	DET
ap-6106	98	41	p	p	PROPN
ap-6106	98	42	-	-	PUNCT
ap-6106	98	43	c	c	NOUN
ap-6106	98	44	notation	notation	NOUN
ap-6106	98	45	.	.	PUNCT
ap-6106	99	1	here	here	ADV
ap-6106	99	2	we	we	PRON
ap-6106	99	3	present	present	VERB
ap-6106	99	4	the	the	DET
ap-6106	99	5	results	result	NOUN
ap-6106	99	6	on	on	ADP
ap-6106	99	7	a	a	DET
ap-6106	99	8	variety	variety	NOUN
ap-6106	99	9	of	of	ADP
ap-6106	99	10	general	general	ADJ
ap-6106	99	11	meshes	mesh	NOUN
ap-6106	99	12	.	.	PUNCT
ap-6106	100	1	in	in	ADP
ap-6106	100	2	particular	particular	ADJ
ap-6106	100	3	,	,	PUNCT
ap-6106	100	4	the	the	DET
ap-6106	100	5	following	follow	VERB
ap-6106	100	6	topologies	topology	NOUN
ap-6106	100	7	are	be	AUX
ap-6106	100	8	used	use	VERB
ap-6106	100	9	:	:	PUNCT
ap-6106	100	10	first	first	ADV
ap-6106	100	11	,	,	PUNCT
ap-6106	100	12	we	we	PRON
ap-6106	100	13	consider	consider	VERB
ap-6106	100	14	a	a	DET
ap-6106	100	15	honeycomb	honeycomb	NOUN
ap-6106	100	16	mesh	mesh	NOUN
ap-6106	100	17	,	,	PUNCT
ap-6106	100	18	that	that	ADV
ap-6106	100	19	is	is	ADV
ap-6106	100	20	,	,	PUNCT
ap-6106	100	21	a	a	DET
ap-6106	100	22	tessellation	tessellation	NOUN
ap-6106	100	23	of	of	ADP
ap-6106	100	24	the	the	DET
ap-6106	100	25	computational	computational	ADJ
ap-6106	100	26	domain	domain	NOUN
ap-6106	100	27	by	by	ADP
ap-6106	100	28	regular	regular	ADJ
ap-6106	100	29	hexagons	hexagon	NOUN
ap-6106	100	30	.	.	PUNCT
ap-6106	101	1	the	the	DET
ap-6106	101	2	boundary	boundary	ADJ
ap-6106	101	3	cells	cell	NOUN
ap-6106	101	4	are	be	AUX
ap-6106	101	5	trimmed	trim	VERB
ap-6106	101	6	accordingly	accordingly	ADV
ap-6106	101	7	to	to	PART
ap-6106	101	8	preserve	preserve	VERB
ap-6106	101	9	the	the	DET
ap-6106	101	10	straight	straight	ADJ
ap-6106	101	11	domain	domain	NOUN
ap-6106	101	12	boundaries	boundary	NOUN
ap-6106	101	13	,	,	PUNCT
ap-6106	101	14	which	which	PRON
ap-6106	101	15	makes	make	VERB
ap-6106	101	16	them	they	PRON
ap-6106	101	17	non	non	ADJ
ap-6106	101	18	-	-	ADJ
ap-6106	101	19	hexagonal	hexagonal	ADJ
ap-6106	101	20	.	.	PUNCT
ap-6106	102	1	below	below	ADV
ap-6106	102	2	,	,	PUNCT
ap-6106	102	3	we	we	PRON
ap-6106	102	4	call	call	VERB
ap-6106	102	5	this	this	PRON
ap-6106	102	6	a	a	DET
ap-6106	102	7	regular	regular	ADJ
ap-6106	102	8	hexagonal	hexagonal	ADJ
ap-6106	102	9	mesh	mesh	NOUN
ap-6106	102	10	.	.	PUNCT
ap-6106	103	1	splitting	split	VERB
ap-6106	103	2	each	each	DET
ap-6106	103	3	hexagon	hexagon	NOUN
ap-6106	103	4	into	into	ADP
ap-6106	103	5	six	six	NUM
ap-6106	103	6	triangles	triangle	NOUN
ap-6106	103	7	meeting	meeting	NOUN
ap-6106	103	8	at	at	ADP
ap-6106	103	9	the	the	DET
ap-6106	103	10	hexagon	hexagon	NOUN
ap-6106	103	11	’s	’s	PART
ap-6106	103	12	center	center	NOUN
ap-6106	103	13	,	,	PUNCT
ap-6106	103	14	and	and	CCONJ
ap-6106	103	15	similarly	similarly	ADV
ap-6106	103	16	splitting	split	VERB
ap-6106	103	17	the	the	DET
ap-6106	103	18	boundary	boundary	ADJ
ap-6106	103	19	cells	cell	NOUN
ap-6106	103	20	,	,	PUNCT
ap-6106	103	21	we	we	PRON
ap-6106	103	22	obtain	obtain	VERB
ap-6106	103	23	a	a	DET
ap-6106	103	24	structure	structure	NOUN
ap-6106	103	25	which	which	PRON
ap-6106	103	26	we	we	PRON
ap-6106	103	27	will	will	AUX
ap-6106	103	28	refer	refer	VERB
ap-6106	103	29	to	to	ADP
ap-6106	103	30	as	as	ADP
ap-6106	103	31	a	a	DET
ap-6106	103	32	regular	regular	ADJ
ap-6106	103	33	triangular	triangular	NOUN
ap-6106	103	34	mesh	mesh	NOUN
ap-6106	103	35	.	.	PUNCT
ap-6106	104	1	note	note	VERB
ap-6106	104	2	that	that	SCONJ
ap-6106	104	3	the	the	DET
ap-6106	104	4	regular	regular	ADJ
ap-6106	104	5	hexagonal	hexagonal	ADJ
ap-6106	104	6	(	(	PUNCT
ap-6106	104	7	honeycomb	honeycomb	NOUN
ap-6106	104	8	)	)	PUNCT
ap-6106	104	9	mesh	mesh	NOUN
ap-6106	104	10	can	can	AUX
ap-6106	104	11	be	be	AUX
ap-6106	104	12	seen	see	VERB
ap-6106	104	13	as	as	ADP
ap-6106	104	14	a	a	DET
ap-6106	104	15	voronoi	voronoi	ADJ
ap-6106	104	16	tessellation	tessellation	NOUN
ap-6106	104	17	with	with	ADP
ap-6106	104	18	regularly	regularly	ADV
ap-6106	104	19	distributed	distribute	VERB
ap-6106	104	20	generators	generator	NOUN
ap-6106	104	21	.	.	PUNCT
ap-6106	105	1	perturbing	perturb	VERB
ap-6106	105	2	the	the	DET
ap-6106	105	3	positions	position	NOUN
ap-6106	105	4	of	of	ADP
ap-6106	105	5	these	these	DET
ap-6106	105	6	generators	generator	NOUN
ap-6106	105	7	and	and	CCONJ
ap-6106	105	8	generating	generate	VERB
ap-6106	105	9	a	a	DET
ap-6106	105	10	new	new	ADJ
ap-6106	105	11	voronoi	voronoi	NOUN
ap-6106	105	12	tessellation	tessellation	NOUN
ap-6106	105	13	,	,	PUNCT
ap-6106	105	14	we	we	PRON
ap-6106	105	15	obtain	obtain	VERB
ap-6106	105	16	a	a	DET
ap-6106	105	17	mesh	mesh	NOUN
ap-6106	105	18	with	with	ADP
ap-6106	105	19	cells	cell	NOUN
ap-6106	105	20	being	be	AUX
ap-6106	105	21	generally	generally	ADV
ap-6106	105	22	convex	convex	ADJ
ap-6106	105	23	polygons	polygon	NOUN
ap-6106	105	24	.	.	PUNCT
ap-6106	106	1	at	at	ADP
ap-6106	106	2	this	this	DET
ap-6106	106	3	point	point	NOUN
ap-6106	106	4	,	,	PUNCT
ap-6106	106	5	the	the	DET
ap-6106	106	6	mesh	mesh	NOUN
ap-6106	106	7	may	may	AUX
ap-6106	106	8	need	need	VERB
ap-6106	106	9	cleaning	clean	VERB
ap-6106	106	10	from	from	ADP
ap-6106	106	11	too	too	ADV
ap-6106	106	12	short	short	ADJ
ap-6106	106	13	edges	edge	NOUN
ap-6106	106	14	and	and	CCONJ
ap-6106	106	15	similar	similar	ADJ
ap-6106	106	16	degeneracies	degeneracy	NOUN
ap-6106	106	17	.	.	PUNCT
ap-6106	107	1	finally	finally	ADV
ap-6106	107	2	,	,	PUNCT
ap-6106	107	3	splitting	split	VERB
ap-6106	107	4	each	each	PRON
ap-6106	107	5	of	of	ADP
ap-6106	107	6	these	these	DET
ap-6106	107	7	polygons	polygon	NOUN
ap-6106	107	8	of	of	ADP
ap-6106	107	9	n	n	PRON
ap-6106	107	10	vertices	vertex	NOUN
ap-6106	107	11	into	into	ADP
ap-6106	107	12	n	n	NOUN
ap-6106	107	13	triangles	triangle	NOUN
ap-6106	107	14	meeting	meeting	NOUN
ap-6106	107	15	at	at	ADP
ap-6106	107	16	the	the	DET
ap-6106	107	17	polygon	polygon	PROPN
ap-6106	107	18	’s	’s	PART
ap-6106	107	19	center	center	NOUN
ap-6106	107	20	,	,	PUNCT
ap-6106	107	21	we	we	PRON
ap-6106	107	22	obtain	obtain	VERB
ap-6106	107	23	an	an	DET
ap-6106	107	24	irregular	irregular	ADJ
ap-6106	107	25	triangular	triangular	NOUN
ap-6106	107	26	grid	grid	NOUN
ap-6106	107	27	.	.	PUNCT
ap-6106	108	1	note	note	VERB
ap-6106	108	2	that	that	SCONJ
ap-6106	108	3	while	while	SCONJ
ap-6106	108	4	in	in	ADP
ap-6106	108	5	the	the	DET
ap-6106	108	6	regular	regular	ADJ
ap-6106	108	7	triangular	triangular	NOUN
ap-6106	108	8	grid	grid	NOUN
ap-6106	108	9	each	each	PRON
ap-6106	108	10	of	of	ADP
ap-6106	108	11	the	the	DET
ap-6106	108	12	interior	interior	ADJ
ap-6106	108	13	nodes	node	NOUN
ap-6106	108	14	was	be	AUX
ap-6106	108	15	connected	connect	VERB
ap-6106	108	16	to	to	ADP
ap-6106	108	17	six	six	NUM
ap-6106	108	18	neighbors	neighbor	NOUN
ap-6106	108	19	,	,	PUNCT
ap-6106	108	20	now	now	ADV
ap-6106	108	21	the	the	DET
ap-6106	108	22	connectivity	connectivity	NOUN
ap-6106	108	23	varies	vary	VERB
ap-6106	108	24	and	and	CCONJ
ap-6106	108	25	thus	thus	ADV
ap-6106	108	26	we	we	PRON
ap-6106	108	27	have	have	VERB
ap-6106	108	28	an	an	DET
ap-6106	108	29	unstructured	unstructured	ADJ
ap-6106	108	30	triangular	triangular	NOUN
ap-6106	108	31	mesh	mesh	NOUN
ap-6106	108	32	.	.	PUNCT
ap-6106	109	1	in	in	ADP
ap-6106	109	2	the	the	DET
ap-6106	109	3	process	process	NOUN
ap-6106	109	4	of	of	ADP
ap-6106	109	5	generating	generate	VERB
ap-6106	109	6	these	these	DET
ap-6106	109	7	test	test	NOUN
ap-6106	109	8	grids	grid	NOUN
ap-6106	109	9	,	,	PUNCT
ap-6106	109	10	we	we	PRON
ap-6106	109	11	utilized	utilize	VERB
ap-6106	109	12	the	the	DET
ap-6106	109	13	voronoi	voronoi	PROPN
ap-6106	109	14	tessellator	tessellator	NOUN
ap-6106	109	15	shapo	shapo	NOUN
ap-6106	110	1	[	[	X
ap-6106	110	2	18	18	NUM
ap-6106	110	3	]	]	PUNCT
ap-6106	110	4	and	and	CCONJ
ap-6106	110	5	its	its	PRON
ap-6106	110	6	advanced	advanced	ADJ
ap-6106	110	7	tools	tool	NOUN
ap-6106	110	8	.	.	PUNCT
ap-6106	111	1	5.1	5.1	NUM
ap-6106	111	2	.	.	NOUN
ap-6106	111	3	time	time	NOUN
ap-6106	111	4	step	step	NOUN
ap-6106	111	5	control	control	NOUN
ap-6106	111	6	the	the	DET
ap-6106	111	7	time	time	NOUN
ap-6106	111	8	step	step	NOUN
ap-6106	111	9	∆t	∆t	PROPN
ap-6106	111	10	is	be	AUX
ap-6106	111	11	adaptively	adaptively	ADV
ap-6106	111	12	controlled	control	VERB
ap-6106	111	13	by	by	ADP
ap-6106	111	14	the	the	DET
ap-6106	111	15	cfl	cfl	NOUN
ap-6106	111	16	condition	condition	NOUN
ap-6106	111	17	and	and	CCONJ
ap-6106	111	18	limited	limit	VERB
ap-6106	111	19	by	by	ADP
ap-6106	111	20	the	the	DET
ap-6106	111	21	multiple	multiple	NOUN
ap-6106	111	22	of	of	ADP
ap-6106	111	23	the	the	DET
ap-6106	111	24	previous	previous	ADJ
ap-6106	111	25	time	time	NOUN
ap-6106	111	26	step	step	NOUN
ap-6106	111	27	,	,	PUNCT
ap-6106	111	28	so	so	SCONJ
ap-6106	111	29	that	that	SCONJ
ap-6106	111	30	it	it	PRON
ap-6106	111	31	does	do	AUX
ap-6106	111	32	not	not	PART
ap-6106	111	33	grow	grow	VERB
ap-6106	111	34	too	too	ADV
ap-6106	111	35	fast	fast	ADV
ap-6106	111	36	.	.	PUNCT
ap-6106	112	1	at	at	ADP
ap-6106	112	2	time	time	NOUN
ap-6106	112	3	level	level	NOUN
ap-6106	112	4	n	n	CCONJ
ap-6106	112	5	we	we	PRON
ap-6106	112	6	set	set	VERB
ap-6106	112	7	∆tn	∆tn	PROPN
ap-6106	113	1	=	=	SYM
ap-6106	113	2	min	min	PROPN
ap-6106	113	3	(	(	PUNCT
ap-6106	113	4	ccfl	ccfl	NOUN
ap-6106	113	5	min	min	PROPN
ap-6106	114	1	c	c	PROPN
ap-6106	114	2	√	√	PROPN
ap-6106	114	3	v	v	PROPN
ap-6106	114	4	nc	nc	PROPN
ap-6106	114	5	cs	cs	PROPN
ap-6106	114	6	,	,	PUNCT
ap-6106	114	7	nc	nc	PROPN
ap-6106	114	8	,	,	PUNCT
ap-6106	114	9	cg∆tn−1	cg∆tn−1	PROPN
ap-6106	114	10	)	)	PUNCT
ap-6106	114	11	,	,	PUNCT
ap-6106	114	12	(	(	PUNCT
ap-6106	114	13	12	12	NUM
ap-6106	114	14	)	)	PUNCT
ap-6106	114	15	where	where	SCONJ
ap-6106	114	16	cs	cs	PROPN
ap-6106	114	17	,	,	PUNCT
ap-6106	114	18	nc	nc	PROPN
ap-6106	114	19	is	be	AUX
ap-6106	114	20	the	the	DET
ap-6106	114	21	sound	sound	ADJ
ap-6106	114	22	speed	speed	NOUN
ap-6106	114	23	and	and	CCONJ
ap-6106	114	24	we	we	PRON
ap-6106	114	25	use	use	VERB
ap-6106	114	26	cg	cg	NOUN
ap-6106	114	27	=	=	NOUN
ap-6106	114	28	1.05	1.05	NUM
ap-6106	114	29	to	to	PART
ap-6106	114	30	limit	limit	VERB
ap-6106	114	31	the	the	DET
ap-6106	114	32	time	time	NOUN
ap-6106	114	33	step	step	NOUN
ap-6106	114	34	growth	growth	NOUN
ap-6106	114	35	.	.	PUNCT
ap-6106	115	1	in	in	ADP
ap-6106	115	2	the	the	DET
ap-6106	115	3	numerical	numerical	ADJ
ap-6106	115	4	tests	test	NOUN
ap-6106	115	5	we	we	PRON
ap-6106	115	6	set	set	VERB
ap-6106	115	7	ccfl	ccfl	NOUN
ap-6106	115	8	=	=	PUNCT
ap-6106	115	9	0.15	0.15	NUM
ap-6106	115	10	.	.	PUNCT
ap-6106	116	1	the	the	DET
ap-6106	116	2	noh	noh	PROPN
ap-6106	116	3	problem	problem	NOUN
ap-6106	116	4	on	on	ADP
ap-6106	116	5	the	the	DET
ap-6106	116	6	triangular	triangular	NOUN
ap-6106	116	7	mesh	mesh	NOUN
ap-6106	116	8	with	with	ADP
ap-6106	116	9	ccfl	ccfl	NOUN
ap-6106	116	10	=	=	SYM
ap-6106	116	11	0.5	0.5	NUM
ap-6106	116	12	generated	generate	VERB
ap-6106	116	13	small	small	ADJ
ap-6106	116	14	oscillations	oscillation	NOUN
ap-6106	116	15	on	on	ADP
ap-6106	116	16	the	the	DET
ap-6106	116	17	plateau	plateau	NOUN
ap-6106	116	18	of	of	ADP
ap-6106	116	19	the	the	DET
ap-6106	116	20	solution	solution	NOUN
ap-6106	116	21	.	.	PUNCT
ap-6106	117	1	the	the	DET
ap-6106	117	2	time	time	NOUN
ap-6106	117	3	step	step	NOUN
ap-6106	117	4	is	be	AUX
ap-6106	117	5	further	far	ADV
ap-6106	117	6	constrained	constrain	VERB
ap-6106	117	7	by	by	ADP
ap-6106	117	8	the	the	DET
ap-6106	117	9	requirement	requirement	NOUN
ap-6106	117	10	that	that	SCONJ
ap-6106	117	11	the	the	DET
ap-6106	117	12	cell	cell	NOUN
ap-6106	117	13	volumes	volume	NOUN
ap-6106	117	14	do	do	AUX
ap-6106	117	15	not	not	PART
ap-6106	117	16	change	change	VERB
ap-6106	117	17	much	much	ADV
ap-6106	117	18	during	during	ADP
ap-6106	117	19	one	one	NUM
ap-6106	117	20	time	time	NOUN
ap-6106	117	21	step	step	NOUN
ap-6106	117	22	.	.	PUNCT
ap-6106	118	1	if	if	SCONJ
ap-6106	118	2	|v	|v	PROPN
ap-6106	118	3	n+1	n+1	PROPN
ap-6106	118	4	c	c	PROPN
ap-6106	118	5	/v	/v	PUNCT
ap-6106	118	6	nc	nc	PROPN
ap-6106	118	7	−1|	−1|	PROPN
ap-6106	118	8	>	>	X
ap-6106	118	9	cv	cv	PROPN
ap-6106	118	10	for	for	ADP
ap-6106	118	11	some	some	DET
ap-6106	118	12	cell	cell	NOUN
ap-6106	118	13	c	c	NOUN
ap-6106	118	14	,	,	PUNCT
ap-6106	118	15	then	then	ADV
ap-6106	118	16	the	the	DET
ap-6106	118	17	time	time	NOUN
ap-6106	118	18	step	step	NOUN
ap-6106	118	19	is	be	AUX
ap-6106	118	20	reduced	reduce	VERB
ap-6106	118	21	to	to	ADP
ap-6106	118	22	a	a	DET
ap-6106	118	23	half	half	NOUN
ap-6106	118	24	∆tn	∆tn	VERB
ap-6106	119	1	=	=	NOUN
ap-6106	119	2	∆tn/2	∆tn/2	NOUN
ap-6106	119	3	and	and	CCONJ
ap-6106	119	4	recomputed	recompute	VERB
ap-6106	119	5	.	.	PUNCT
ap-6106	120	1	in	in	ADP
ap-6106	120	2	the	the	DET
ap-6106	120	3	tests	test	NOUN
ap-6106	120	4	we	we	PRON
ap-6106	120	5	set	set	VERB
ap-6106	120	6	cv	cv	PROPN
ap-6106	120	7	=	=	NOUN
ap-6106	120	8	0.1	0.1	NUM
ap-6106	120	9	.	.	PUNCT
ap-6106	121	1	5.2	5.2	NUM
ap-6106	121	2	.	.	PUNCT
ap-6106	122	1	noh	noh	PROPN
ap-6106	122	2	problem	problem	VERB
ap-6106	122	3	the	the	DET
ap-6106	122	4	noh	noh	PROPN
ap-6106	122	5	implosion	implosion	PROPN
ap-6106	122	6	test	test	NOUN
ap-6106	122	7	problem	problem	NOUN
ap-6106	123	1	[	[	X
ap-6106	123	2	19	19	NUM
ap-6106	123	3	]	]	PUNCT
ap-6106	123	4	is	be	AUX
ap-6106	123	5	a	a	DET
ap-6106	123	6	spherical	spherical	ADJ
ap-6106	123	7	infinite	infinite	NOUN
ap-6106	123	8	strength	strength	NOUN
ap-6106	123	9	shock	shock	NOUN
ap-6106	123	10	propagating	propagate	VERB
ap-6106	123	11	out	out	ADP
ap-6106	123	12	from	from	ADP
ap-6106	123	13	the	the	DET
ap-6106	123	14	origin	origin	NOUN
ap-6106	123	15	.	.	PUNCT
ap-6106	124	1	its	its	PRON
ap-6106	124	2	cylindrical	cylindrical	ADJ
ap-6106	124	3	version	version	NOUN
ap-6106	124	4	is	be	AUX
ap-6106	124	5	modeled	model	VERB
ap-6106	124	6	in	in	ADP
ap-6106	124	7	the	the	DET
ap-6106	124	8	cartesian	cartesian	ADJ
ap-6106	124	9	(	(	PUNCT
ap-6106	124	10	x	x	NOUN
ap-6106	124	11	,	,	PUNCT
ap-6106	124	12	y	y	NOUN
ap-6106	124	13	)	)	PUNCT
ap-6106	124	14	plane	plane	NOUN
ap-6106	124	15	as	as	SCONJ
ap-6106	124	16	follows	follow	VERB
ap-6106	124	17	.	.	PUNCT
ap-6106	125	1	initially	initially	ADV
ap-6106	125	2	,	,	PUNCT
ap-6106	125	3	the	the	DET
ap-6106	125	4	density	density	NOUN
ap-6106	125	5	is	be	AUX
ap-6106	125	6	set	set	VERB
ap-6106	125	7	to	to	ADP
ap-6106	125	8	unity	unity	NOUN
ap-6106	125	9	and	and	CCONJ
ap-6106	125	10	the	the	DET
ap-6106	125	11	pressure	pressure	NOUN
ap-6106	125	12	to	to	ADP
ap-6106	125	13	zero	zero	NUM
ap-6106	125	14	everywhere	everywhere	ADV
ap-6106	125	15	,	,	PUNCT
ap-6106	125	16	the	the	DET
ap-6106	125	17	velocity	velocity	NOUN
ap-6106	125	18	has	have	VERB
ap-6106	125	19	a	a	DET
ap-6106	125	20	magnitude	magnitude	NOUN
ap-6106	125	21	of	of	ADP
ap-6106	125	22	1	1	NUM
ap-6106	125	23	and	and	CCONJ
ap-6106	125	24	is	be	AUX
ap-6106	125	25	directed	direct	VERB
ap-6106	125	26	toward	toward	ADP
ap-6106	125	27	the	the	DET
ap-6106	125	28	origin	origin	NOUN
ap-6106	125	29	,	,	PUNCT
ap-6106	125	30	that	that	ADV
ap-6106	125	31	is	is	ADV
ap-6106	125	32	,	,	PUNCT
ap-6106	125	33	u	u	PROPN
ap-6106	125	34	=	=	SYM
ap-6106	125	35	−x/|x|	−x/|x|	PROPN
ap-6106	125	36	,	,	PUNCT
ap-6106	125	37	and	and	CCONJ
ap-6106	125	38	the	the	DET
ap-6106	125	39	ideal	ideal	ADJ
ap-6106	125	40	polytropic	polytropic	ADJ
ap-6106	125	41	gas	gas	NOUN
ap-6106	125	42	equation	equation	NOUN
ap-6106	125	43	of	of	ADP
ap-6106	125	44	a	a	DET
ap-6106	125	45	state	state	NOUN
ap-6106	125	46	with	with	ADP
ap-6106	125	47	adiabatic	adiabatic	ADJ
ap-6106	125	48	index	index	NOUN
ap-6106	125	49	γ	γ	NOUN
ap-6106	125	50	=	=	SYM
ap-6106	125	51	5/3	5/3	NUM
ap-6106	125	52	is	be	AUX
ap-6106	125	53	used	use	VERB
ap-6106	125	54	.	.	PUNCT
ap-6106	126	1	the	the	DET
ap-6106	126	2	exact	exact	ADJ
ap-6106	126	3	solution	solution	NOUN
ap-6106	126	4	at	at	ADP
ap-6106	126	5	time	time	NOUN
ap-6106	126	6	t	t	PROPN
ap-6106	126	7	inside	inside	ADP
ap-6106	126	8	the	the	DET
ap-6106	126	9	shocked	shocked	ADJ
ap-6106	126	10	region	region	NOUN
ap-6106	126	11	(	(	PUNCT
ap-6106	126	12	|x|	|x|	PROPN
ap-6106	126	13	≤	≤	NOUN
ap-6106	126	14	t/3	t/3	NUM
ap-6106	126	15	)	)	PUNCT
ap-6106	126	16	is	be	AUX
ap-6106	126	17	density	density	NOUN
ap-6106	126	18	ρ	ρ	PROPN
ap-6106	126	19	=	=	SYM
ap-6106	126	20	16	16	NUM
ap-6106	126	21	,	,	PUNCT
ap-6106	126	22	pressure	pressure	NOUN
ap-6106	126	23	p	p	NOUN
ap-6106	126	24	=	=	NOUN
ap-6106	126	25	16/3	16/3	NOUN
ap-6106	126	26	,	,	PUNCT
ap-6106	126	27	zero	zero	NUM
ap-6106	126	28	velocity	velocity	NOUN
ap-6106	126	29	,	,	PUNCT
ap-6106	126	30	while	while	SCONJ
ap-6106	126	31	outside	outside	ADP
ap-6106	126	32	the	the	DET
ap-6106	126	33	shock	shock	NOUN
ap-6106	126	34	(	(	PUNCT
ap-6106	126	35	|x|	|x|	PROPN
ap-6106	126	36	>	>	SYM
ap-6106	126	37	t/3	t/3	NOUN
ap-6106	126	38	)	)	PUNCT
ap-6106	126	39	we	we	PRON
ap-6106	126	40	should	should	AUX
ap-6106	126	41	have	have	VERB
ap-6106	126	42	the	the	DET
ap-6106	126	43	exact	exact	ADJ
ap-6106	126	44	density	density	NOUN
ap-6106	126	45	ρ	ρ	NOUN
ap-6106	126	46	=	=	SYM
ap-6106	126	47	1	1	NUM
ap-6106	126	48	+	+	NUM
ap-6106	126	49	t/|x|	t/|x|	NOUN
ap-6106	126	50	,	,	PUNCT
ap-6106	126	51	zero	zero	NUM
ap-6106	126	52	pressure	pressure	NOUN
ap-6106	126	53	and	and	CCONJ
ap-6106	126	54	the	the	DET
ap-6106	126	55	velocity	velocity	NOUN
ap-6106	126	56	should	should	AUX
ap-6106	126	57	remain	remain	VERB
ap-6106	126	58	u	u	NOUN
ap-6106	126	59	=	=	SYM
ap-6106	126	60	−x/|x|	−x/|x|	PROPN
ap-6106	126	61	.	.	PUNCT
ap-6106	127	1	in	in	ADP
ap-6106	127	2	our	our	PRON
ap-6106	127	3	simulations	simulation	NOUN
ap-6106	127	4	,	,	PUNCT
ap-6106	127	5	we	we	PRON
ap-6106	127	6	approximate	approximate	VERB
ap-6106	127	7	the	the	DET
ap-6106	127	8	zero	zero	NUM
ap-6106	127	9	initial	initial	ADJ
ap-6106	127	10	pressure	pressure	NOUN
ap-6106	127	11	by	by	ADP
ap-6106	127	12	p	p	NOUN
ap-6106	127	13	=	=	SYM
ap-6106	127	14	10−6	10−6	NUM
ap-6106	127	15	.	.	PUNCT
ap-6106	128	1	the	the	DET
ap-6106	128	2	results	result	NOUN
ap-6106	128	3	are	be	AUX
ap-6106	128	4	shown	show	VERB
ap-6106	128	5	at	at	ADP
ap-6106	128	6	the	the	DET
ap-6106	128	7	usual	usual	ADJ
ap-6106	128	8	final	final	ADJ
ap-6106	128	9	time	time	NOUN
ap-6106	128	10	tfinal	tfinal	ADJ
ap-6106	128	11	=	=	ADJ
ap-6106	128	12	0.6	0.6	NUM
ap-6106	128	13	.	.	PUNCT
ap-6106	129	1	figures	figure	NOUN
ap-6106	129	2	3	3	NUM
ap-6106	129	3	and	and	CCONJ
ap-6106	129	4	4	4	NUM
ap-6106	129	5	show	show	VERB
ap-6106	129	6	the	the	DET
ap-6106	129	7	density	density	NOUN
ap-6106	129	8	color	color	NOUN
ap-6106	129	9	maps	map	NOUN
ap-6106	129	10	resulting	result	VERB
ap-6106	129	11	from	from	ADP
ap-6106	129	12	calculations	calculation	NOUN
ap-6106	129	13	,	,	PUNCT
ap-6106	129	14	where	where	SCONJ
ap-6106	129	15	the	the	DET
ap-6106	129	16	initial	initial	ADJ
ap-6106	129	17	computational	computational	ADJ
ap-6106	129	18	domain	domain	NOUN
ap-6106	129	19	[	[	X
ap-6106	129	20	−1	−1	NOUN
ap-6106	129	21	,	,	PUNCT
ap-6106	129	22	1]×	1]×	NUM
ap-6106	130	1	[	[	X
ap-6106	130	2	−1	−1	NOUN
ap-6106	130	3	,	,	PUNCT
ap-6106	130	4	1	1	NUM
ap-6106	130	5	]	]	PUNCT
ap-6106	130	6	was	be	AUX
ap-6106	130	7	covered	cover	VERB
ap-6106	130	8	by	by	ADP
ap-6106	130	9	a	a	DET
ap-6106	130	10	regular	regular	ADJ
ap-6106	130	11	triangular	triangular	NOUN
ap-6106	130	12	mesh	mesh	NOUN
ap-6106	130	13	(	(	PUNCT
ap-6106	130	14	described	describe	VERB
ap-6106	130	15	above	above	ADV
ap-6106	130	16	)	)	PUNCT
ap-6106	130	17	consisting	consist	VERB
ap-6106	130	18	of	of	ADP
ap-6106	130	19	10,108	10,108	NUM
ap-6106	130	20	cells	cell	NOUN
ap-6106	130	21	,	,	PUNCT
ap-6106	130	22	resp	resp	NOUN
ap-6106	130	23	.	.	PUNCT
ap-6106	131	1	by	by	ADP
ap-6106	131	2	a	a	DET
ap-6106	131	3	regular	regular	ADJ
ap-6106	131	4	hexagonal	hexagonal	ADJ
ap-6106	131	5	mesh	mesh	NOUN
ap-6106	131	6	of	of	ADP
ap-6106	131	7	10,083	10,083	NUM
ap-6106	131	8	cells	cell	NOUN
ap-6106	131	9	.	.	PUNCT
ap-6106	132	1	these	these	DET
ap-6106	132	2	meshes	mesh	NOUN
ap-6106	132	3	have	have	VERB
ap-6106	132	4	a	a	DET
ap-6106	132	5	comparable	comparable	ADJ
ap-6106	132	6	numbers	number	NOUN
ap-6106	132	7	of	of	ADP
ap-6106	132	8	cells	cell	NOUN
ap-6106	132	9	and	and	CCONJ
ap-6106	132	10	both	both	PRON
ap-6106	132	11	will	will	AUX
ap-6106	132	12	be	be	AUX
ap-6106	132	13	further	far	ADV
ap-6106	132	14	referred	refer	VERB
ap-6106	132	15	to	to	ADP
ap-6106	132	16	as	as	ADP
ap-6106	132	17	“	"	PUNCT
ap-6106	132	18	coarse	coarse	NOUN
ap-6106	132	19	”	"	PUNCT
ap-6106	132	20	.	.	PUNCT
ap-6106	133	1	71	71	NUM
ap-6106	133	2	d.	d.	PROPN
ap-6106	133	3	fridrich	fridrich	PROPN
ap-6106	133	4	,	,	PUNCT
ap-6106	133	5	r.	r.	PROPN
ap-6106	133	6	liska	liska	PROPN
ap-6106	133	7	,	,	PUNCT
ap-6106	133	8	i.	i.	PROPN
ap-6106	133	9	tarant	tarant	PROPN
ap-6106	133	10	et	et	PROPN
ap-6106	133	11	al	al	PROPN
ap-6106	133	12	.	.	PROPN
ap-6106	133	13	acta	acta	PROPN
ap-6106	133	14	polytechnica	polytechnica	PROPN
ap-6106	133	15	0.0	0.0	NUM
ap-6106	133	16	0.2	0.2	NUM
ap-6106	133	17	0.4	0.4	NUM
ap-6106	133	18	0.0	0.0	NUM
ap-6106	133	19	0.2	0.2	NUM
ap-6106	133	20	0.4	0.4	NUM
ap-6106	133	21	0	0	NUM
ap-6106	133	22	2	2	NUM
ap-6106	133	23	4	4	NUM
ap-6106	133	24	6	6	NUM
ap-6106	133	25	8	8	NUM
ap-6106	133	26	10	10	NUM
ap-6106	133	27	12	12	NUM
ap-6106	133	28	14	14	NUM
ap-6106	133	29	16	16	NUM
ap-6106	133	30	18	18	NUM
ap-6106	133	31	figure	figure	NOUN
ap-6106	133	32	3	3	NUM
ap-6106	133	33	.	.	PUNCT
ap-6106	133	34	density	density	NOUN
ap-6106	133	35	and	and	CCONJ
ap-6106	133	36	mesh	mesh	NOUN
ap-6106	133	37	for	for	ADP
ap-6106	133	38	noh	noh	PROPN
ap-6106	133	39	problem	problem	NOUN
ap-6106	133	40	on	on	ADP
ap-6106	133	41	coarse	coarse	ADV
ap-6106	133	42	(	(	PUNCT
ap-6106	133	43	10108	10108	NUM
ap-6106	133	44	-	-	PUNCT
ap-6106	133	45	cell	cell	NOUN
ap-6106	133	46	)	)	PUNCT
ap-6106	133	47	regular	regular	ADJ
ap-6106	133	48	triangular	triangular	NOUN
ap-6106	133	49	mesh	mesh	NOUN
ap-6106	133	50	with	with	ADP
ap-6106	133	51	τ	τ	PROPN
ap-6106	133	52	=	=	SYM
ap-6106	133	53	2	2	NUM
ap-6106	133	54	.	.	NOUN
ap-6106	133	55	0.0	0.0	NUM
ap-6106	133	56	0.2	0.2	NUM
ap-6106	133	57	0.4	0.4	NUM
ap-6106	133	58	0.0	0.0	NUM
ap-6106	133	59	0.2	0.2	NUM
ap-6106	133	60	0.4	0.4	NUM
ap-6106	133	61	0	0	NUM
ap-6106	133	62	2	2	NUM
ap-6106	133	63	4	4	NUM
ap-6106	133	64	6	6	NUM
ap-6106	133	65	8	8	NUM
ap-6106	133	66	10	10	NUM
ap-6106	133	67	12	12	NUM
ap-6106	133	68	14	14	NUM
ap-6106	133	69	16	16	NUM
ap-6106	133	70	18	18	NUM
ap-6106	133	71	figure	figure	NOUN
ap-6106	133	72	4	4	NUM
ap-6106	133	73	.	.	PUNCT
ap-6106	133	74	density	density	NOUN
ap-6106	133	75	and	and	CCONJ
ap-6106	133	76	mesh	mesh	NOUN
ap-6106	133	77	for	for	ADP
ap-6106	133	78	noh	noh	PROPN
ap-6106	133	79	problem	problem	NOUN
ap-6106	133	80	on	on	ADP
ap-6106	133	81	coarse	coarse	ADV
ap-6106	133	82	(	(	PUNCT
ap-6106	133	83	10083	10083	NUM
ap-6106	133	84	-	-	PUNCT
ap-6106	133	85	cell	cell	NOUN
ap-6106	133	86	)	)	PUNCT
ap-6106	133	87	regular	regular	ADJ
ap-6106	133	88	hexagonal	hexagonal	ADJ
ap-6106	133	89	mesh	mesh	NOUN
ap-6106	133	90	with	with	ADP
ap-6106	133	91	τ	τ	PROPN
ap-6106	133	92	=	=	SYM
ap-6106	133	93	1.25	1.25	NUM
ap-6106	133	94	.	.	PUNCT
ap-6106	133	95	note	note	VERB
ap-6106	133	96	that	that	SCONJ
ap-6106	133	97	for	for	ADP
ap-6106	133	98	each	each	DET
ap-6106	133	99	mesh	mesh	NOUN
ap-6106	133	100	we	we	PRON
ap-6106	133	101	are	be	AUX
ap-6106	133	102	showing	show	VERB
ap-6106	133	103	the	the	DET
ap-6106	133	104	results	result	NOUN
ap-6106	133	105	with	with	ADP
ap-6106	133	106	a	a	DET
ap-6106	133	107	different	different	ADJ
ap-6106	133	108	dissipation	dissipation	NOUN
ap-6106	133	109	parameter	parameter	NOUN
ap-6106	133	110	τ	τ	PROPN
ap-6106	133	111	.	.	PUNCT
ap-6106	134	1	indeed	indeed	ADV
ap-6106	134	2	,	,	PUNCT
ap-6106	134	3	as	as	SCONJ
ap-6106	134	4	we	we	PRON
ap-6106	134	5	can	can	AUX
ap-6106	134	6	see	see	VERB
ap-6106	134	7	in	in	ADP
ap-6106	134	8	figs	fig	NOUN
ap-6106	134	9	.	.	PUNCT
ap-6106	135	1	5	5	NUM
ap-6106	135	2	and	and	CCONJ
ap-6106	135	3	6	6	NUM
ap-6106	135	4	,	,	PUNCT
ap-6106	135	5	the	the	DET
ap-6106	135	6	optimal	optimal	ADJ
ap-6106	135	7	dissipation	dissipation	NOUN
ap-6106	135	8	coefficient	coefficient	NOUN
ap-6106	135	9	,	,	PUNCT
ap-6106	135	10	which	which	PRON
ap-6106	135	11	prevents	prevent	VERB
ap-6106	135	12	the	the	DET
ap-6106	135	13	oscillation	oscillation	NOUN
ap-6106	135	14	near	near	ADP
ap-6106	135	15	the	the	DET
ap-6106	135	16	shock	shock	NOUN
ap-6106	135	17	but	but	CCONJ
ap-6106	135	18	still	still	ADV
ap-6106	135	19	does	do	AUX
ap-6106	135	20	not	not	PART
ap-6106	135	21	smooth	smooth	VERB
ap-6106	135	22	it	it	PRON
ap-6106	135	23	too	too	ADV
ap-6106	135	24	much	much	ADV
ap-6106	135	25	,	,	PUNCT
ap-6106	135	26	seems	seem	VERB
ap-6106	135	27	to	to	PART
ap-6106	135	28	depend	depend	VERB
ap-6106	135	29	on	on	ADP
ap-6106	135	30	the	the	DET
ap-6106	135	31	mesh	mesh	NOUN
ap-6106	135	32	topology	topology	NOUN
ap-6106	135	33	.	.	PUNCT
ap-6106	136	1	for	for	ADP
ap-6106	136	2	the	the	DET
ap-6106	136	3	regular	regular	ADJ
ap-6106	136	4	triangular	triangular	NOUN
ap-6106	136	5	mesh	mesh	NOUN
ap-6106	136	6	a	a	DET
ap-6106	136	7	reasonable	reasonable	ADJ
ap-6106	136	8	choice	choice	NOUN
ap-6106	136	9	seems	seem	VERB
ap-6106	136	10	to	to	PART
ap-6106	136	11	be	be	AUX
ap-6106	136	12	around	around	ADP
ap-6106	136	13	τ	τ	X
ap-6106	136	14	=	=	SYM
ap-6106	136	15	2	2	NUM
ap-6106	136	16	,	,	PUNCT
ap-6106	136	17	while	while	SCONJ
ap-6106	136	18	for	for	ADP
ap-6106	136	19	hexagons	hexagon	NOUN
ap-6106	136	20	it	it	PRON
ap-6106	136	21	is	be	AUX
ap-6106	136	22	about	about	ADP
ap-6106	136	23	τ	τ	X
ap-6106	136	24	=	=	SYM
ap-6106	136	25	1.25	1.25	NUM
ap-6106	136	26	.	.	PUNCT
ap-6106	137	1	let	let	VERB
ap-6106	137	2	us	we	PRON
ap-6106	137	3	remark	remark	VERB
ap-6106	137	4	,	,	PUNCT
ap-6106	137	5	that	that	SCONJ
ap-6106	137	6	for	for	ADP
ap-6106	137	7	a	a	DET
ap-6106	137	8	regular	regular	ADJ
ap-6106	137	9	quadrilateral	quadrilateral	ADJ
ap-6106	137	10	grid	grid	NOUN
ap-6106	137	11	,	,	PUNCT
ap-6106	137	12	which	which	PRON
ap-6106	137	13	is	be	AUX
ap-6106	137	14	not	not	PART
ap-6106	137	15	shown	show	VERB
ap-6106	137	16	here	here	ADV
ap-6106	137	17	,	,	PUNCT
ap-6106	137	18	the	the	DET
ap-6106	137	19	optimum	optimum	NOUN
ap-6106	137	20	is	be	AUX
ap-6106	137	21	about	about	ADV
ap-6106	137	22	τ	τ	X
ap-6106	137	23	=	=	SYM
ap-6106	137	24	1.5	1.5	NUM
ap-6106	137	25	.	.	PUNCT
ap-6106	138	1	this	this	PRON
ap-6106	138	2	is	be	AUX
ap-6106	138	3	in	in	ADP
ap-6106	138	4	good	good	ADJ
ap-6106	138	5	agreement	agreement	NOUN
ap-6106	138	6	with	with	ADP
ap-6106	138	7	the	the	DET
ap-6106	138	8	results	result	NOUN
ap-6106	138	9	shown	show	VERB
ap-6106	138	10	in	in	ADP
ap-6106	138	11	[	[	X
ap-6106	138	12	13	13	NUM
ap-6106	138	13	]	]	PUNCT
ap-6106	138	14	,	,	PUNCT
ap-6106	138	15	which	which	PRON
ap-6106	138	16	however	however	ADV
ap-6106	138	17	used	use	VERB
ap-6106	138	18	the	the	DET
ap-6106	138	19	default	default	NOUN
ap-6106	138	20	lf	lf	ADP
ap-6106	138	21	mass	mass	ADJ
ap-6106	138	22	weighting	weighting	NOUN
ap-6106	138	23	in	in	ADP
ap-6106	138	24	the	the	DET
ap-6106	138	25	predictor	predictor	NOUN
ap-6106	138	26	instead	instead	ADV
ap-6106	138	27	of	of	ADP
ap-6106	138	28	(	(	PUNCT
ap-6106	138	29	7	7	NUM
ap-6106	138	30	)	)	PUNCT
ap-6106	138	31	.	.	PUNCT
ap-6106	139	1	this	this	DET
ap-6106	139	2	mesh	mesh	ADJ
ap-6106	139	3	dependence	dependence	NOUN
ap-6106	139	4	of	of	ADP
ap-6106	139	5	the	the	DET
ap-6106	139	6	optimal	optimal	ADJ
ap-6106	139	7	dissipation	dissipation	NOUN
ap-6106	139	8	parameter	parameter	NOUN
ap-6106	139	9	deserves	deserve	VERB
ap-6106	139	10	further	further	ADJ
ap-6106	139	11	study	study	NOUN
ap-6106	139	12	.	.	PUNCT
ap-6106	140	1	0	0	NUM
ap-6106	141	1	0.05	0.05	NUM
ap-6106	141	2	0.1	0.1	NUM
ap-6106	141	3	0.15	0.15	NUM
ap-6106	141	4	0.2	0.2	NUM
ap-6106	141	5	0.25	0.25	NUM
ap-6106	141	6	0.3	0.3	NUM
ap-6106	141	7	0.35	0.35	NUM
ap-6106	141	8	0.4	0.4	NUM
ap-6106	141	9	2	2	NUM
ap-6106	141	10	4	4	NUM
ap-6106	141	11	6	6	NUM
ap-6106	141	12	8	8	NUM
ap-6106	141	13	10	10	NUM
ap-6106	141	14	12	12	NUM
ap-6106	141	15	14	14	NUM
ap-6106	141	16	16	16	NUM
ap-6106	141	17	figure	figure	NOUN
ap-6106	141	18	5	5	NUM
ap-6106	141	19	.	.	PUNCT
ap-6106	141	20	scatter	scatter	NOUN
ap-6106	141	21	plot	plot	NOUN
ap-6106	141	22	of	of	ADP
ap-6106	141	23	density	density	NOUN
ap-6106	141	24	for	for	ADP
ap-6106	141	25	noh	noh	PROPN
ap-6106	141	26	problem	problem	NOUN
ap-6106	141	27	on	on	ADP
ap-6106	141	28	coarse	coarse	ADJ
ap-6106	141	29	regular	regular	ADJ
ap-6106	141	30	triangular	triangular	NOUN
ap-6106	141	31	mesh	mesh	NOUN
ap-6106	141	32	with	with	ADP
ap-6106	141	33	different	different	ADJ
ap-6106	141	34	values	value	NOUN
ap-6106	141	35	of	of	ADP
ap-6106	141	36	dissipation	dissipation	NOUN
ap-6106	141	37	parameter	parameter	NOUN
ap-6106	141	38	τ	τ	PROPN
ap-6106	141	39	.	.	PUNCT
ap-6106	141	40	0	0	NUM
ap-6106	142	1	0.05	0.05	NUM
ap-6106	142	2	0.1	0.1	NUM
ap-6106	142	3	0.15	0.15	NUM
ap-6106	142	4	0.2	0.2	NUM
ap-6106	142	5	0.25	0.25	NUM
ap-6106	142	6	0.3	0.3	NUM
ap-6106	142	7	0.35	0.35	NUM
ap-6106	142	8	0.4	0.4	NUM
ap-6106	142	9	2	2	NUM
ap-6106	142	10	4	4	NUM
ap-6106	142	11	6	6	NUM
ap-6106	142	12	8	8	NUM
ap-6106	142	13	10	10	NUM
ap-6106	142	14	12	12	NUM
ap-6106	142	15	14	14	NUM
ap-6106	142	16	16	16	NUM
ap-6106	142	17	figure	figure	NOUN
ap-6106	142	18	6	6	NUM
ap-6106	142	19	.	.	PUNCT
ap-6106	142	20	scatter	scatter	NOUN
ap-6106	142	21	plot	plot	NOUN
ap-6106	142	22	of	of	ADP
ap-6106	142	23	density	density	NOUN
ap-6106	142	24	for	for	ADP
ap-6106	142	25	noh	noh	PROPN
ap-6106	142	26	problem	problem	NOUN
ap-6106	142	27	on	on	ADP
ap-6106	142	28	coarse	coarse	ADJ
ap-6106	142	29	regular	regular	ADJ
ap-6106	142	30	hexagonal	hexagonal	ADJ
ap-6106	142	31	mesh	mesh	NOUN
ap-6106	142	32	with	with	ADP
ap-6106	142	33	different	different	ADJ
ap-6106	142	34	values	value	NOUN
ap-6106	142	35	of	of	ADP
ap-6106	142	36	dissipation	dissipation	NOUN
ap-6106	142	37	parameter	parameter	NOUN
ap-6106	142	38	τ	τ	PROPN
ap-6106	142	39	.	.	PUNCT
ap-6106	143	1	as	as	ADP
ap-6106	143	2	for	for	ADP
ap-6106	143	3	the	the	DET
ap-6106	143	4	symmetry	symmetry	NOUN
ap-6106	143	5	and	and	CCONJ
ap-6106	143	6	value	value	NOUN
ap-6106	143	7	of	of	ADP
ap-6106	143	8	density	density	NOUN
ap-6106	143	9	on	on	ADP
ap-6106	143	10	the	the	DET
ap-6106	143	11	plateau	plateau	NOUN
ap-6106	143	12	(	(	PUNCT
ap-6106	143	13	inside	inside	ADP
ap-6106	143	14	the	the	DET
ap-6106	143	15	shocked	shocked	ADJ
ap-6106	143	16	region	region	NOUN
ap-6106	143	17	)	)	PUNCT
ap-6106	143	18	,	,	PUNCT
ap-6106	143	19	the	the	DET
ap-6106	143	20	contour	contour	NOUN
ap-6106	143	21	plots	plot	NOUN
ap-6106	143	22	suggest	suggest	VERB
ap-6106	143	23	that	that	SCONJ
ap-6106	143	24	the	the	DET
ap-6106	143	25	regular	regular	ADJ
ap-6106	143	26	hexagons	hexagon	NOUN
ap-6106	143	27	in	in	ADP
ap-6106	143	28	fig	fig	NOUN
ap-6106	143	29	.	.	PUNCT
ap-6106	144	1	8	8	NUM
ap-6106	144	2	do	do	VERB
ap-6106	144	3	better	well	ADJ
ap-6106	144	4	than	than	ADP
ap-6106	144	5	regular	regular	ADJ
ap-6106	144	6	triangles	triangle	NOUN
ap-6106	144	7	in	in	ADP
ap-6106	144	8	fig	fig	NOUN
ap-6106	144	9	.	.	PUNCT
ap-6106	145	1	7	7	X
ap-6106	145	2	.	.	PUNCT
ap-6106	145	3	the	the	DET
ap-6106	145	4	comparison	comparison	NOUN
ap-6106	145	5	of	of	ADP
ap-6106	145	6	results	result	NOUN
ap-6106	145	7	of	of	ADP
ap-6106	145	8	our	our	PRON
ap-6106	145	9	lw+2	lw+2	ADJ
ap-6106	145	10	method	method	NOUN
ap-6106	145	11	and	and	CCONJ
ap-6106	145	12	the	the	DET
ap-6106	145	13	standard	standard	ADJ
ap-6106	145	14	staggered	staggered	ADJ
ap-6106	145	15	method	method	NOUN
ap-6106	145	16	with	with	ADP
ap-6106	145	17	tensor	tensor	NOUN
ap-6106	145	18	artificial	artificial	ADJ
ap-6106	145	19	viscosity	viscosity	NOUN
ap-6106	145	20	on	on	ADP
ap-6106	145	21	logical	logical	ADJ
ap-6106	145	22	72	72	NUM
ap-6106	145	23	vol	vol	NOUN
ap-6106	145	24	.	.	PUNCT
ap-6106	146	1	61	61	NUM
ap-6106	146	2	special	special	ADJ
ap-6106	146	3	issue/2021	issue/2021	NOUN
ap-6106	146	4	lagrangian	lagrangian	ADJ
ap-6106	146	5	lax	lax	PROPN
ap-6106	146	6	-	-	PUNCT
ap-6106	146	7	wendroff	wendroff	NOUN
ap-6106	146	8	hll	hll	PROPN
ap-6106	146	9	scheme	scheme	NOUN
ap-6106	146	10	0.00	0.00	NUM
ap-6106	146	11	0.05	0.05	NUM
ap-6106	146	12	0.10	0.10	NUM
ap-6106	146	13	0.15	0.15	NUM
ap-6106	146	14	0.20	0.20	NUM
ap-6106	146	15	0.00	0.00	NUM
ap-6106	146	16	0.05	0.05	NUM
ap-6106	146	17	0.10	0.10	NUM
ap-6106	146	18	0.15	0.15	NUM
ap-6106	146	19	0.20	0.20	NUM
ap-6106	146	20	12.0	12.0	NUM
ap-6106	146	21	12.4	12.4	NUM
ap-6106	146	22	12.7	12.7	NUM
ap-6106	146	23	13.1	13.1	NUM
ap-6106	146	24	13.5	13.5	NUM
ap-6106	146	25	13.8	13.8	NUM
ap-6106	146	26	14.2	14.2	NUM
ap-6106	146	27	14.5	14.5	NUM
ap-6106	146	28	14.9	14.9	NUM
ap-6106	146	29	15.3	15.3	NUM
ap-6106	146	30	15.6	15.6	NUM
ap-6106	146	31	16.0	16.0	NUM
ap-6106	146	32	figure	figure	NOUN
ap-6106	146	33	7	7	NUM
ap-6106	146	34	.	.	PUNCT
ap-6106	146	35	contour	contour	NOUN
ap-6106	146	36	plot	plot	NOUN
ap-6106	146	37	of	of	ADP
ap-6106	146	38	density	density	NOUN
ap-6106	146	39	for	for	ADP
ap-6106	146	40	noh	noh	PROPN
ap-6106	146	41	problem	problem	NOUN
ap-6106	146	42	on	on	ADP
ap-6106	146	43	coarse	coarse	ADJ
ap-6106	146	44	regular	regular	ADJ
ap-6106	146	45	triangular	triangular	NOUN
ap-6106	146	46	mesh	mesh	NOUN
ap-6106	146	47	with	with	ADP
ap-6106	146	48	τ	τ	PROPN
ap-6106	146	49	=	=	SYM
ap-6106	146	50	2	2	NUM
ap-6106	146	51	.	.	NOUN
ap-6106	146	52	0.00	0.00	NUM
ap-6106	146	53	0.05	0.05	NUM
ap-6106	146	54	0.10	0.10	NUM
ap-6106	146	55	0.15	0.15	NUM
ap-6106	146	56	0.20	0.20	NUM
ap-6106	146	57	0.00	0.00	NUM
ap-6106	146	58	0.05	0.05	NUM
ap-6106	146	59	0.10	0.10	NUM
ap-6106	146	60	0.15	0.15	NUM
ap-6106	146	61	0.20	0.20	NUM
ap-6106	146	62	12.0	12.0	NUM
ap-6106	146	63	12.4	12.4	NUM
ap-6106	146	64	12.7	12.7	NUM
ap-6106	146	65	13.1	13.1	NUM
ap-6106	146	66	13.5	13.5	NUM
ap-6106	146	67	13.8	13.8	NUM
ap-6106	146	68	14.2	14.2	NUM
ap-6106	146	69	14.5	14.5	NUM
ap-6106	146	70	14.9	14.9	NUM
ap-6106	146	71	15.3	15.3	NUM
ap-6106	146	72	15.6	15.6	NUM
ap-6106	146	73	16.0	16.0	NUM
ap-6106	146	74	figure	figure	NOUN
ap-6106	146	75	8	8	NUM
ap-6106	146	76	.	.	PUNCT
ap-6106	147	1	contour	contour	NOUN
ap-6106	147	2	plot	plot	NOUN
ap-6106	147	3	of	of	ADP
ap-6106	147	4	density	density	NOUN
ap-6106	147	5	for	for	ADP
ap-6106	147	6	noh	noh	PROPN
ap-6106	147	7	problem	problem	NOUN
ap-6106	147	8	on	on	ADP
ap-6106	147	9	coarse	coarse	ADJ
ap-6106	147	10	regular	regular	ADJ
ap-6106	147	11	hexagonal	hexagonal	ADJ
ap-6106	147	12	mesh	mesh	NOUN
ap-6106	147	13	with	with	ADP
ap-6106	147	14	τ	τ	PROPN
ap-6106	147	15	=	=	SYM
ap-6106	147	16	1.25	1.25	NUM
ap-6106	147	17	.	.	PUNCT
ap-6106	148	1	rectangular	rectangular	ADJ
ap-6106	148	2	quadrilateral	quadrilateral	ADJ
ap-6106	148	3	mesh	mesh	NOUN
ap-6106	148	4	in	in	ADP
ap-6106	148	5	[	[	X
ap-6106	148	6	13	13	NUM
ap-6106	148	7	]	]	PUNCT
ap-6106	148	8	shows	show	VERB
ap-6106	148	9	that	that	SCONJ
ap-6106	148	10	our	our	PRON
ap-6106	148	11	method	method	NOUN
ap-6106	148	12	preserves	preserve	VERB
ap-6106	148	13	polar	polar	ADJ
ap-6106	148	14	symmetry	symmetry	NOUN
ap-6106	148	15	much	much	ADV
ap-6106	148	16	better	well	ADV
ap-6106	148	17	.	.	PUNCT
ap-6106	149	1	finally	finally	ADV
ap-6106	149	2	,	,	PUNCT
ap-6106	149	3	to	to	PART
ap-6106	149	4	demonstrate	demonstrate	VERB
ap-6106	149	5	the	the	DET
ap-6106	149	6	numerical	numerical	ADJ
ap-6106	149	7	convergence	convergence	NOUN
ap-6106	149	8	,	,	PUNCT
ap-6106	149	9	we	we	PRON
ap-6106	149	10	show	show	VERB
ap-6106	149	11	the	the	DET
ap-6106	149	12	sequence	sequence	NOUN
ap-6106	149	13	of	of	ADP
ap-6106	149	14	density	density	NOUN
ap-6106	149	15	scatter	scatter	NOUN
ap-6106	149	16	plots	plot	VERB
ap-6106	149	17	on	on	ADP
ap-6106	149	18	meshes	mesh	NOUN
ap-6106	149	19	with	with	ADP
ap-6106	149	20	the	the	DET
ap-6106	149	21	same	same	ADJ
ap-6106	149	22	topology	topology	NOUN
ap-6106	149	23	and	and	CCONJ
ap-6106	149	24	different	different	ADJ
ap-6106	149	25	resolutions	resolution	NOUN
ap-6106	149	26	,	,	PUNCT
ap-6106	149	27	referred	refer	VERB
ap-6106	149	28	to	to	ADP
ap-6106	149	29	as	as	ADP
ap-6106	149	30	“	"	PUNCT
ap-6106	149	31	coarse	coarse	NOUN
ap-6106	149	32	”	"	PUNCT
ap-6106	149	33	,	,	PUNCT
ap-6106	149	34	“	"	PUNCT
ap-6106	149	35	medium	medium	ADJ
ap-6106	149	36	”	"	PUNCT
ap-6106	149	37	and	and	CCONJ
ap-6106	149	38	“	"	PUNCT
ap-6106	149	39	fine	fine	ADJ
ap-6106	149	40	”	"	PUNCT
ap-6106	149	41	,	,	PUNCT
ap-6106	149	42	namely	namely	ADV
ap-6106	149	43	in	in	ADP
ap-6106	149	44	fig	fig	NOUN
ap-6106	149	45	.	.	PUNCT
ap-6106	150	1	9	9	NUM
ap-6106	150	2	for	for	ADP
ap-6106	150	3	the	the	DET
ap-6106	150	4	regular	regular	ADJ
ap-6106	150	5	grid	grid	NOUN
ap-6106	150	6	of	of	ADP
ap-6106	150	7	10,108	10,108	NUM
ap-6106	150	8	,	,	PUNCT
ap-6106	150	9	40,280	40,280	NUM
ap-6106	150	10	and	and	CCONJ
ap-6106	150	11	160,816	160,816	NUM
ap-6106	150	12	triangles	triangle	NOUN
ap-6106	150	13	and	and	CCONJ
ap-6106	150	14	in	in	ADP
ap-6106	150	15	fig	fig	NOUN
ap-6106	150	16	.	.	PUNCT
ap-6106	151	1	10	10	NUM
ap-6106	151	2	for	for	ADP
ap-6106	151	3	the	the	DET
ap-6106	151	4	regular	regular	ADJ
ap-6106	151	5	hexagonal	hexagonal	ADJ
ap-6106	151	6	grid	grid	NOUN
ap-6106	151	7	of	of	ADP
ap-6106	151	8	10,083	10,083	NUM
ap-6106	151	9	,	,	PUNCT
ap-6106	151	10	40,037	40,037	NUM
ap-6106	151	11	and	and	CCONJ
ap-6106	151	12	159,561	159,561	NUM
ap-6106	151	13	cells	cell	NOUN
ap-6106	151	14	.	.	PUNCT
ap-6106	152	1	the	the	DET
ap-6106	152	2	mesh	mesh	NOUN
ap-6106	152	3	resolutions	resolution	NOUN
ap-6106	152	4	in	in	ADP
ap-6106	152	5	both	both	DET
ap-6106	152	6	cases	case	NOUN
ap-6106	152	7	are	be	AUX
ap-6106	152	8	chosen	choose	VERB
ap-6106	152	9	so	so	SCONJ
ap-6106	152	10	that	that	SCONJ
ap-6106	152	11	the	the	DET
ap-6106	152	12	cell	cell	NOUN
ap-6106	152	13	numbers	number	NOUN
ap-6106	152	14	approximately	approximately	ADV
ap-6106	152	15	correspond	correspond	VERB
ap-6106	152	16	to	to	ADP
ap-6106	152	17	those	those	PRON
ap-6106	152	18	of	of	ADP
ap-6106	152	19	regular	regular	ADJ
ap-6106	152	20	quadrilateral	quadrilateral	ADJ
ap-6106	152	21	meshes	mesh	NOUN
ap-6106	152	22	of	of	ADP
ap-6106	152	23	50×50	50×50	NUM
ap-6106	152	24	,	,	PUNCT
ap-6106	152	25	100×100	100×100	NUM
ap-6106	152	26	,	,	PUNCT
ap-6106	152	27	resp	resp	NOUN
ap-6106	152	28	.	.	PUNCT
ap-6106	153	1	200×200	200×200	NUM
ap-6106	153	2	initally	initally	ADV
ap-6106	153	3	square	square	ADJ
ap-6106	153	4	cells	cell	NOUN
ap-6106	153	5	per	per	ADP
ap-6106	153	6	quadrant	quadrant	NOUN
ap-6106	153	7	,	,	PUNCT
ap-6106	153	8	shown	show	VERB
ap-6106	153	9	in	in	ADP
ap-6106	153	10	the	the	DET
ap-6106	153	11	original	original	ADJ
ap-6106	153	12	paper	paper	NOUN
ap-6106	153	13	[	[	X
ap-6106	153	14	13	13	NUM
ap-6106	153	15	]	]	PUNCT
ap-6106	153	16	.	.	PUNCT
ap-6106	154	1	(	(	PUNCT
ap-6106	154	2	but	but	CCONJ
ap-6106	154	3	again	again	ADV
ap-6106	154	4	,	,	PUNCT
ap-6106	154	5	keep	keep	VERB
ap-6106	154	6	in	in	ADP
ap-6106	154	7	mind	mind	NOUN
ap-6106	154	8	that	that	SCONJ
ap-6106	154	9	the	the	DET
ap-6106	154	10	results	result	NOUN
ap-6106	154	11	shown	show	VERB
ap-6106	154	12	there	there	PRON
ap-6106	154	13	use	use	VERB
ap-6106	154	14	the	the	DET
ap-6106	154	15	standard	standard	ADJ
ap-6106	154	16	lf	lf	ADP
ap-6106	154	17	weighting	weighting	NOUN
ap-6106	154	18	.	.	PUNCT
ap-6106	154	19	)	)	PUNCT
ap-6106	155	1	a	a	DET
ap-6106	155	2	more	more	ADV
ap-6106	155	3	thorough	thorough	ADJ
ap-6106	155	4	test	test	NOUN
ap-6106	155	5	of	of	ADP
ap-6106	155	6	convergence	convergence	NOUN
ap-6106	155	7	will	will	AUX
ap-6106	155	8	be	be	AUX
ap-6106	155	9	presented	present	VERB
ap-6106	155	10	in	in	ADP
ap-6106	155	11	sec	sec	PROPN
ap-6106	155	12	.	.	PROPN
ap-6106	156	1	5.4	5.4	NUM
ap-6106	156	2	.	.	PUNCT
ap-6106	157	1	note	note	VERB
ap-6106	157	2	that	that	SCONJ
ap-6106	157	3	we	we	PRON
ap-6106	157	4	obtain	obtain	VERB
ap-6106	157	5	decent	decent	ADJ
ap-6106	157	6	results	result	NOUN
ap-6106	157	7	also	also	ADV
ap-6106	157	8	on	on	ADP
ap-6106	157	9	unstructured	unstructured	ADJ
ap-6106	157	10	meshes	mesh	NOUN
ap-6106	157	11	of	of	ADP
ap-6106	157	12	9,914	9,914	NUM
ap-6106	157	13	triangles	triangle	NOUN
ap-6106	157	14	in	in	ADP
ap-6106	157	15	fig	fig	NOUN
ap-6106	157	16	.	.	PUNCT
ap-6106	158	1	11	11	NUM
ap-6106	158	2	and	and	CCONJ
ap-6106	158	3	of	of	ADP
ap-6106	158	4	10,083	10,083	NUM
ap-6106	158	5	figure	figure	NOUN
ap-6106	158	6	9	9	NUM
ap-6106	158	7	.	.	PUNCT
ap-6106	158	8	convergence	convergence	NOUN
ap-6106	158	9	of	of	ADP
ap-6106	158	10	scatter	scatter	NOUN
ap-6106	158	11	plots	plot	NOUN
ap-6106	158	12	of	of	ADP
ap-6106	158	13	density	density	NOUN
ap-6106	158	14	for	for	ADP
ap-6106	158	15	noh	noh	PROPN
ap-6106	158	16	problem	problem	NOUN
ap-6106	158	17	on	on	ADP
ap-6106	158	18	regular	regular	ADJ
ap-6106	158	19	triangular	triangular	NOUN
ap-6106	158	20	mesh	mesh	NOUN
ap-6106	158	21	with	with	ADP
ap-6106	158	22	τ	τ	PROPN
ap-6106	158	23	=	=	SYM
ap-6106	158	24	2	2	X
ap-6106	158	25	.	.	X
ap-6106	158	26	figure	figure	NOUN
ap-6106	158	27	10	10	NUM
ap-6106	158	28	.	.	PUNCT
ap-6106	159	1	convergence	convergence	NOUN
ap-6106	159	2	of	of	ADP
ap-6106	159	3	scatter	scatter	NOUN
ap-6106	159	4	plots	plot	NOUN
ap-6106	159	5	of	of	ADP
ap-6106	159	6	density	density	NOUN
ap-6106	159	7	for	for	ADP
ap-6106	159	8	noh	noh	PROPN
ap-6106	159	9	problem	problem	NOUN
ap-6106	159	10	on	on	ADP
ap-6106	159	11	regular	regular	ADJ
ap-6106	159	12	hexagonal	hexagonal	ADJ
ap-6106	159	13	mesh	mesh	NOUN
ap-6106	159	14	with	with	ADP
ap-6106	159	15	τ	τ	PROPN
ap-6106	159	16	=	=	SYM
ap-6106	159	17	1.25	1.25	NUM
ap-6106	159	18	.	.	PUNCT
ap-6106	160	1	general	general	ADJ
ap-6106	160	2	polygons	polygon	NOUN
ap-6106	160	3	(	(	PUNCT
ap-6106	160	4	ranging	range	VERB
ap-6106	160	5	from	from	ADP
ap-6106	160	6	triangles	triangle	NOUN
ap-6106	160	7	to	to	ADP
ap-6106	160	8	nonagons	nonagon	NOUN
ap-6106	160	9	)	)	PUNCT
ap-6106	160	10	in	in	ADP
ap-6106	160	11	fig	fig	NOUN
ap-6106	160	12	.	.	PUNCT
ap-6106	161	1	12	12	NUM
ap-6106	161	2	.	.	X
ap-6106	162	1	5.3	5.3	NUM
ap-6106	162	2	.	.	PUNCT
ap-6106	163	1	sedov	sedov	PROPN
ap-6106	163	2	problem	problem	VERB
ap-6106	163	3	the	the	DET
ap-6106	163	4	sedov	sedov	PROPN
ap-6106	163	5	blast	blast	NOUN
ap-6106	163	6	wave	wave	NOUN
ap-6106	163	7	test	test	NOUN
ap-6106	163	8	problem	problem	NOUN
ap-6106	164	1	[	[	X
ap-6106	164	2	20	20	NUM
ap-6106	164	3	]	]	PUNCT
ap-6106	164	4	describes	describe	VERB
ap-6106	164	5	the	the	DET
ap-6106	164	6	evolution	evolution	NOUN
ap-6106	164	7	of	of	ADP
ap-6106	164	8	a	a	DET
ap-6106	164	9	blast	blast	NOUN
ap-6106	164	10	wave	wave	NOUN
ap-6106	164	11	in	in	ADP
ap-6106	164	12	a	a	DET
ap-6106	164	13	point	point	NOUN
ap-6106	164	14	-	-	PUNCT
ap-6106	164	15	symmetric	symmetric	ADJ
ap-6106	164	16	explosion	explosion	NOUN
ap-6106	164	17	.	.	PUNCT
ap-6106	165	1	again	again	ADV
ap-6106	165	2	,	,	PUNCT
ap-6106	165	3	we	we	PRON
ap-6106	165	4	consider	consider	VERB
ap-6106	165	5	its	its	PRON
ap-6106	165	6	cylindrical	cylindrical	ADJ
ap-6106	165	7	version	version	NOUN
ap-6106	165	8	in	in	ADP
ap-6106	165	9	cartesian	cartesian	ADJ
ap-6106	165	10	geometry	geometry	NOUN
ap-6106	165	11	.	.	PUNCT
ap-6106	166	1	the	the	DET
ap-6106	166	2	ideal	ideal	ADJ
ap-6106	166	3	polytropic	polytropic	ADJ
ap-6106	166	4	gas	gas	NOUN
ap-6106	166	5	,	,	PUNCT
ap-6106	166	6	this	this	DET
ap-6106	166	7	time	time	NOUN
ap-6106	166	8	with	with	ADP
ap-6106	166	9	the	the	DET
ap-6106	166	10	adiabatic	adiabatic	ADJ
ap-6106	166	11	index	index	NOUN
ap-6106	166	12	γ	γ	NOUN
ap-6106	166	13	=	=	SYM
ap-6106	166	14	7/5	7/5	NUM
ap-6106	166	15	,	,	PUNCT
ap-6106	166	16	is	be	AUX
ap-6106	166	17	initially	initially	ADV
ap-6106	166	18	at	at	ADP
ap-6106	166	19	73	73	NUM
ap-6106	166	20	d.	d.	PROPN
ap-6106	166	21	fridrich	fridrich	PROPN
ap-6106	166	22	,	,	PUNCT
ap-6106	166	23	r.	r.	PROPN
ap-6106	166	24	liska	liska	PROPN
ap-6106	166	25	,	,	PUNCT
ap-6106	166	26	i.	i.	PROPN
ap-6106	166	27	tarant	tarant	PROPN
ap-6106	166	28	et	et	PROPN
ap-6106	167	1	al	al	PROPN
ap-6106	167	2	.	.	PROPN
ap-6106	167	3	acta	acta	PROPN
ap-6106	167	4	polytechnica	polytechnica	PROPN
ap-6106	167	5	0.0	0.0	NUM
ap-6106	167	6	0.2	0.2	NUM
ap-6106	167	7	0.4	0.4	NUM
ap-6106	167	8	0.0	0.0	NUM
ap-6106	167	9	0.2	0.2	NUM
ap-6106	167	10	0.4	0.4	NUM
ap-6106	167	11	0	0	NUM
ap-6106	167	12	2	2	NUM
ap-6106	167	13	4	4	NUM
ap-6106	167	14	6	6	NUM
ap-6106	167	15	8	8	NUM
ap-6106	167	16	10	10	NUM
ap-6106	167	17	12	12	NUM
ap-6106	167	18	14	14	NUM
ap-6106	167	19	16	16	NUM
ap-6106	167	20	18	18	NUM
ap-6106	167	21	figure	figure	NOUN
ap-6106	167	22	11	11	NUM
ap-6106	167	23	.	.	PUNCT
ap-6106	168	1	density	density	NOUN
ap-6106	168	2	and	and	CCONJ
ap-6106	168	3	mesh	mesh	NOUN
ap-6106	168	4	for	for	ADP
ap-6106	168	5	noh	noh	PROPN
ap-6106	168	6	problem	problem	NOUN
ap-6106	168	7	on	on	ADP
ap-6106	168	8	irregular	irregular	ADJ
ap-6106	168	9	triangular	triangular	NOUN
ap-6106	168	10	mesh	mesh	NOUN
ap-6106	168	11	of	of	ADP
ap-6106	168	12	9914	9914	NUM
ap-6106	168	13	cells	cell	NOUN
ap-6106	168	14	with	with	ADP
ap-6106	168	15	τ	τ	PROPN
ap-6106	168	16	=	=	SYM
ap-6106	168	17	2	2	NUM
ap-6106	168	18	.	.	NOUN
ap-6106	168	19	0.0	0.0	NUM
ap-6106	168	20	0.2	0.2	NUM
ap-6106	168	21	0.4	0.4	NUM
ap-6106	168	22	0.0	0.0	NUM
ap-6106	168	23	0.2	0.2	NUM
ap-6106	168	24	0.4	0.4	NUM
ap-6106	168	25	0	0	NUM
ap-6106	168	26	2	2	NUM
ap-6106	168	27	4	4	NUM
ap-6106	168	28	6	6	NUM
ap-6106	168	29	8	8	NUM
ap-6106	168	30	10	10	NUM
ap-6106	168	31	12	12	NUM
ap-6106	168	32	14	14	NUM
ap-6106	168	33	16	16	NUM
ap-6106	168	34	18	18	NUM
ap-6106	168	35	figure	figure	NOUN
ap-6106	168	36	12	12	NUM
ap-6106	168	37	.	.	PUNCT
ap-6106	169	1	density	density	NOUN
ap-6106	169	2	and	and	CCONJ
ap-6106	169	3	mesh	mesh	NOUN
ap-6106	169	4	for	for	ADP
ap-6106	169	5	noh	noh	PROPN
ap-6106	169	6	problem	problem	NOUN
ap-6106	169	7	on	on	ADP
ap-6106	169	8	irregular	irregular	ADJ
ap-6106	169	9	polygonal	polygonal	ADJ
ap-6106	169	10	mesh	mesh	NOUN
ap-6106	169	11	of	of	ADP
ap-6106	169	12	10083	10083	NUM
ap-6106	169	13	cells	cell	NOUN
ap-6106	169	14	with	with	ADP
ap-6106	169	15	τ	τ	PROPN
ap-6106	169	16	=	=	SYM
ap-6106	169	17	1.25	1.25	NUM
ap-6106	169	18	.	.	PUNCT
ap-6106	170	1	rest	rest	NOUN
ap-6106	170	2	,	,	PUNCT
ap-6106	170	3	its	its	PRON
ap-6106	170	4	density	density	NOUN
ap-6106	170	5	is	be	AUX
ap-6106	170	6	set	set	VERB
ap-6106	170	7	to	to	ADP
ap-6106	170	8	1	1	NUM
ap-6106	170	9	everywhere	everywhere	ADV
ap-6106	170	10	and	and	CCONJ
ap-6106	170	11	the	the	DET
ap-6106	170	12	total	total	ADJ
ap-6106	170	13	energy	energy	NOUN
ap-6106	170	14	e	e	NOUN
ap-6106	170	15	=	=	NOUN
ap-6106	170	16	0.979264	0.979264	NUM
ap-6106	170	17	is	be	AUX
ap-6106	170	18	stored	store	VERB
ap-6106	170	19	at	at	ADP
ap-6106	170	20	the	the	DET
ap-6106	170	21	origin	origin	NOUN
ap-6106	170	22	in	in	ADP
ap-6106	170	23	the	the	DET
ap-6106	170	24	form	form	NOUN
ap-6106	170	25	of	of	ADP
ap-6106	170	26	internal	internal	ADJ
ap-6106	170	27	energy	energy	NOUN
ap-6106	170	28	.	.	PUNCT
ap-6106	171	1	at	at	ADP
ap-6106	171	2	the	the	DET
ap-6106	171	3	final	final	ADJ
ap-6106	171	4	time	time	NOUN
ap-6106	171	5	tfinal	tfinal	NOUN
ap-6106	171	6	=	=	PUNCT
ap-6106	171	7	1.0	1.0	NUM
ap-6106	171	8	the	the	DET
ap-6106	171	9	exact	exact	ADJ
ap-6106	171	10	solution	solution	NOUN
ap-6106	171	11	is	be	AUX
ap-6106	171	12	a	a	DET
ap-6106	171	13	point	point	NOUN
ap-6106	171	14	-	-	PUNCT
ap-6106	171	15	symmetric	symmetric	ADJ
ap-6106	171	16	diverging	diverge	VERB
ap-6106	171	17	shock	shock	NOUN
ap-6106	171	18	whose	whose	DET
ap-6106	171	19	front	front	NOUN
ap-6106	171	20	is	be	AUX
ap-6106	171	21	at	at	ADP
ap-6106	171	22	radius	radius	NOUN
ap-6106	171	23	|x|	|x|	PROPN
ap-6106	171	24	=	=	SYM
ap-6106	171	25	1	1	NUM
ap-6106	171	26	and	and	CCONJ
ap-6106	171	27	has	have	VERB
ap-6106	171	28	a	a	DET
ap-6106	171	29	density	density	NOUN
ap-6106	171	30	peak	peak	NOUN
ap-6106	171	31	ρ	ρ	NOUN
ap-6106	171	32	=	=	SYM
ap-6106	171	33	6	6	NUM
ap-6106	171	34	.	.	PUNCT
ap-6106	172	1	the	the	DET
ap-6106	172	2	exact	exact	ADJ
ap-6106	172	3	solution	solution	NOUN
ap-6106	172	4	shown	show	VERB
ap-6106	172	5	in	in	ADP
ap-6106	172	6	the	the	DET
ap-6106	172	7	scatter	scatter	NOUN
ap-6106	172	8	plots	plot	NOUN
ap-6106	172	9	as	as	SCONJ
ap-6106	172	10	a	a	DET
ap-6106	172	11	reference	reference	NOUN
ap-6106	172	12	was	be	AUX
ap-6106	172	13	obtained	obtain	VERB
ap-6106	172	14	by	by	ADP
ap-6106	172	15	the	the	DET
ap-6106	172	16	code	code	NOUN
ap-6106	172	17	cococubed	cococube	VERB
ap-6106	172	18	[	[	X
ap-6106	172	19	21	21	NUM
ap-6106	172	20	]	]	PUNCT
ap-6106	172	21	.	.	PUNCT
ap-6106	173	1	note	note	VERB
ap-6106	173	2	that	that	SCONJ
ap-6106	173	3	while	while	SCONJ
ap-6106	173	4	we	we	PRON
ap-6106	173	5	are	be	AUX
ap-6106	173	6	only	only	ADV
ap-6106	173	7	showing	show	VERB
ap-6106	173	8	one	one	NUM
ap-6106	173	9	quadrant	quadrant	NOUN
ap-6106	173	10	of	of	ADP
ap-6106	173	11	the	the	DET
ap-6106	173	12	computational	computational	ADJ
ap-6106	173	13	domain	domain	NOUN
ap-6106	173	14	,	,	PUNCT
ap-6106	173	15	the	the	DET
ap-6106	173	16	calculation	calculation	NOUN
ap-6106	173	17	is	be	AUX
ap-6106	173	18	performed	perform	VERB
ap-6106	173	19	on	on	ADP
ap-6106	173	20	the	the	DET
ap-6106	173	21	entire	entire	ADJ
ap-6106	173	22	domain	domain	NOUN
ap-6106	173	23	.	.	PUNCT
ap-6106	174	1	this	this	PRON
ap-6106	174	2	allows	allow	VERB
ap-6106	174	3	us	we	PRON
ap-6106	174	4	to	to	PART
ap-6106	174	5	use	use	VERB
ap-6106	174	6	a	a	DET
ap-6106	174	7	general	general	ADJ
ap-6106	174	8	polygonal	polygonal	ADJ
ap-6106	174	9	mesh	mesh	NOUN
ap-6106	174	10	which	which	PRON
ap-6106	174	11	is	be	AUX
ap-6106	174	12	,	,	PUNCT
ap-6106	174	13	unlike	unlike	ADP
ap-6106	174	14	the	the	DET
ap-6106	174	15	regular	regular	ADJ
ap-6106	174	16	meshes	mesh	NOUN
ap-6106	174	17	,	,	PUNCT
ap-6106	174	18	non	non	ADJ
ap-6106	174	19	-	-	ADJ
ap-6106	174	20	symmetric	symmetric	ADJ
ap-6106	174	21	.	.	PUNCT
ap-6106	175	1	in	in	ADP
ap-6106	175	2	the	the	DET
ap-6106	175	3	literature	literature	NOUN
ap-6106	175	4	,	,	PUNCT
ap-6106	175	5	one	one	PRON
ap-6106	175	6	often	often	ADV
ap-6106	175	7	encounters	encounter	VERB
ap-6106	175	8	this	this	DET
ap-6106	175	9	test	test	NOUN
ap-6106	175	10	set	set	VERB
ap-6106	175	11	up	up	ADP
ap-6106	175	12	on	on	ADP
ap-6106	175	13	a	a	DET
ap-6106	175	14	quadrilateral	quadrilateral	ADJ
ap-6106	175	15	mesh	mesh	NOUN
ap-6106	175	16	with	with	ADP
ap-6106	175	17	the	the	DET
ap-6106	175	18	calculation	calculation	NOUN
ap-6106	175	19	performed	perform	VERB
ap-6106	175	20	only	only	ADV
ap-6106	175	21	on	on	ADP
ap-6106	175	22	one	one	NUM
ap-6106	175	23	quadrant	quadrant	NOUN
ap-6106	175	24	,	,	PUNCT
ap-6106	175	25	so	so	SCONJ
ap-6106	175	26	that	that	SCONJ
ap-6106	175	27	the	the	DET
ap-6106	175	28	total	total	ADJ
ap-6106	175	29	energy	energy	NOUN
ap-6106	175	30	e	e	NOUN
ap-6106	175	31	=	=	SYM
ap-6106	175	32	0.244816	0.244816	NUM
ap-6106	175	33	,	,	PUNCT
ap-6106	175	34	one	one	NUM
ap-6106	175	35	quarter	quarter	NOUN
ap-6106	175	36	of	of	ADP
ap-6106	175	37	ours	our	NOUN
ap-6106	175	38	,	,	PUNCT
ap-6106	175	39	is	be	AUX
ap-6106	175	40	stored	store	VERB
ap-6106	175	41	in	in	ADP
ap-6106	175	42	a	a	DET
ap-6106	175	43	single	single	ADJ
ap-6106	175	44	corner	corner	NOUN
ap-6106	175	45	cell	cell	NOUN
ap-6106	175	46	.	.	PUNCT
ap-6106	176	1	in	in	ADP
ap-6106	176	2	our	our	PRON
ap-6106	176	3	im0.0	im0.0	NUM
ap-6106	176	4	0.2	0.2	NUM
ap-6106	176	5	0.4	0.4	NUM
ap-6106	176	6	0.6	0.6	NUM
ap-6106	176	7	0.8	0.8	NUM
ap-6106	176	8	1.0	1.0	NUM
ap-6106	176	9	1.2	1.2	NUM
ap-6106	176	10	0.0	0.0	NUM
ap-6106	176	11	0.2	0.2	NUM
ap-6106	176	12	0.4	0.4	NUM
ap-6106	176	13	0.6	0.6	NUM
ap-6106	176	14	0.8	0.8	NUM
ap-6106	176	15	1.0	1.0	NUM
ap-6106	176	16	1.2	1.2	NUM
ap-6106	176	17	0	0	NUM
ap-6106	176	18	1	1	NUM
ap-6106	176	19	2	2	NUM
ap-6106	176	20	3	3	NUM
ap-6106	176	21	4	4	NUM
ap-6106	176	22	5	5	NUM
ap-6106	176	23	6	6	NUM
ap-6106	176	24	figure	figure	NOUN
ap-6106	176	25	13	13	NUM
ap-6106	176	26	.	.	PUNCT
ap-6106	176	27	density	density	NOUN
ap-6106	176	28	and	and	CCONJ
ap-6106	176	29	mesh	mesh	NOUN
ap-6106	176	30	for	for	ADP
ap-6106	176	31	sedov	sedov	PROPN
ap-6106	176	32	problem	problem	NOUN
ap-6106	176	33	on	on	ADP
ap-6106	176	34	regular	regular	ADJ
ap-6106	176	35	triangular	triangular	NOUN
ap-6106	176	36	mesh	mesh	NOUN
ap-6106	176	37	of	of	ADP
ap-6106	176	38	10108	10108	NUM
ap-6106	176	39	cells	cell	NOUN
ap-6106	176	40	with	with	ADP
ap-6106	176	41	τ	τ	PROPN
ap-6106	176	42	=	=	SYM
ap-6106	176	43	2	2	X
ap-6106	176	44	.	.	PUNCT
ap-6106	176	45	plementation	plementation	NOUN
ap-6106	176	46	,	,	PUNCT
ap-6106	176	47	all	all	PRON
ap-6106	176	48	of	of	ADP
ap-6106	176	49	the	the	DET
ap-6106	176	50	initial	initial	ADJ
ap-6106	176	51	energy	energy	NOUN
ap-6106	176	52	is	be	AUX
ap-6106	176	53	stored	store	VERB
ap-6106	176	54	is	be	AUX
ap-6106	176	55	one	one	NUM
ap-6106	176	56	regular	regular	ADJ
ap-6106	176	57	hexahedral	hexahedral	ADJ
ap-6106	176	58	cell	cell	NOUN
ap-6106	176	59	centered	center	VERB
ap-6106	176	60	at	at	ADP
ap-6106	176	61	(	(	PUNCT
ap-6106	176	62	0	0	NUM
ap-6106	176	63	,	,	PUNCT
ap-6106	176	64	0	0	NUM
ap-6106	176	65	)	)	PUNCT
ap-6106	176	66	in	in	ADP
ap-6106	176	67	the	the	DET
ap-6106	176	68	case	case	NOUN
ap-6106	176	69	of	of	ADP
ap-6106	176	70	the	the	DET
ap-6106	176	71	honeycomb	honeycomb	NOUN
ap-6106	176	72	and	and	CCONJ
ap-6106	176	73	general	general	ADJ
ap-6106	176	74	polygonal	polygonal	ADJ
ap-6106	176	75	meshes	mesh	NOUN
ap-6106	176	76	.	.	PUNCT
ap-6106	177	1	six	six	NUM
ap-6106	177	2	triangular	triangular	NOUN
ap-6106	177	3	cells	cell	NOUN
ap-6106	177	4	are	be	AUX
ap-6106	177	5	created	create	VERB
ap-6106	177	6	by	by	ADP
ap-6106	177	7	its	its	PRON
ap-6106	177	8	subdivision	subdivision	NOUN
ap-6106	177	9	for	for	ADP
ap-6106	177	10	the	the	DET
ap-6106	177	11	structured	structured	ADJ
ap-6106	177	12	and	and	CCONJ
ap-6106	177	13	unstructured	unstructured	ADJ
ap-6106	177	14	triangular	triangular	NOUN
ap-6106	177	15	meshes	mesh	NOUN
ap-6106	177	16	.	.	PUNCT
ap-6106	178	1	the	the	DET
ap-6106	178	2	initial	initial	ADJ
ap-6106	178	3	computational	computational	ADJ
ap-6106	178	4	domain	domain	NOUN
ap-6106	178	5	[	[	X
ap-6106	178	6	−1.2	−1.2	PROPN
ap-6106	178	7	,	,	PUNCT
ap-6106	178	8	1.2	1.2	NUM
ap-6106	178	9	]	]	SYM
ap-6106	178	10	×	×	NOUN
ap-6106	178	11	[	[	X
ap-6106	178	12	−1.2	−1.2	PROPN
ap-6106	178	13	,	,	PUNCT
ap-6106	178	14	1.2	1.2	NUM
ap-6106	178	15	]	]	PUNCT
ap-6106	178	16	was	be	AUX
ap-6106	178	17	covered	cover	VERB
ap-6106	178	18	by	by	ADP
ap-6106	178	19	the	the	DET
ap-6106	178	20	same	same	ADJ
ap-6106	178	21	meshes	mesh	NOUN
ap-6106	178	22	as	as	ADP
ap-6106	178	23	earlier	early	ADV
ap-6106	178	24	for	for	ADP
ap-6106	178	25	the	the	DET
ap-6106	178	26	noh	noh	PROPN
ap-6106	178	27	test	test	NOUN
ap-6106	178	28	,	,	PUNCT
ap-6106	178	29	just	just	ADV
ap-6106	178	30	now	now	ADV
ap-6106	178	31	scaled	scale	VERB
ap-6106	178	32	to	to	ADP
ap-6106	178	33	this	this	DET
ap-6106	178	34	bigger	big	ADJ
ap-6106	178	35	domain	domain	NOUN
ap-6106	178	36	.	.	PUNCT
ap-6106	179	1	in	in	ADP
ap-6106	179	2	fig	fig	NOUN
ap-6106	179	3	.	.	PUNCT
ap-6106	180	1	13	13	NUM
ap-6106	180	2	we	we	PRON
ap-6106	180	3	see	see	VERB
ap-6106	180	4	the	the	DET
ap-6106	180	5	density	density	NOUN
ap-6106	180	6	color	color	NOUN
ap-6106	180	7	map	map	NOUN
ap-6106	180	8	on	on	ADP
ap-6106	180	9	the	the	DET
ap-6106	180	10	coarse	coarse	ADJ
ap-6106	180	11	regular	regular	ADJ
ap-6106	180	12	triangular	triangular	NOUN
ap-6106	180	13	mesh	mesh	NOUN
ap-6106	180	14	,	,	PUNCT
ap-6106	180	15	in	in	ADP
ap-6106	180	16	fig	fig	NOUN
ap-6106	180	17	.	.	PUNCT
ap-6106	181	1	14	14	NUM
ap-6106	181	2	on	on	ADP
ap-6106	181	3	the	the	DET
ap-6106	181	4	coarse	coarse	ADJ
ap-6106	181	5	regular	regular	ADJ
ap-6106	181	6	hexagonal	hexagonal	ADJ
ap-6106	181	7	grid	grid	NOUN
ap-6106	181	8	,	,	PUNCT
ap-6106	181	9	and	and	CCONJ
ap-6106	181	10	in	in	ADP
ap-6106	181	11	fig	fig	NOUN
ap-6106	181	12	.	.	PUNCT
ap-6106	182	1	17	17	NUM
ap-6106	182	2	on	on	ADP
ap-6106	182	3	the	the	DET
ap-6106	182	4	same	same	ADJ
ap-6106	182	5	number	number	NOUN
ap-6106	182	6	of	of	ADP
ap-6106	182	7	general	general	ADJ
ap-6106	182	8	polygons	polygon	NOUN
ap-6106	182	9	.	.	PUNCT
ap-6106	183	1	the	the	DET
ap-6106	183	2	scatter	scatter	NOUN
ap-6106	183	3	plots	plot	VERB
ap-6106	183	4	in	in	ADP
ap-6106	183	5	fig	fig	NOUN
ap-6106	183	6	.	.	PUNCT
ap-6106	184	1	15	15	NUM
ap-6106	184	2	show	show	VERB
ap-6106	184	3	that	that	SCONJ
ap-6106	184	4	with	with	ADP
ap-6106	184	5	increasing	increase	VERB
ap-6106	184	6	resolution	resolution	NOUN
ap-6106	184	7	on	on	ADP
ap-6106	184	8	regular	regular	ADJ
ap-6106	184	9	triangles	triangle	NOUN
ap-6106	184	10	(	(	PUNCT
ap-6106	184	11	coarse	coarse	ADJ
ap-6106	184	12	mesh	mesh	NOUN
ap-6106	184	13	at	at	ADP
ap-6106	184	14	left	left	ADJ
ap-6106	184	15	and	and	CCONJ
ap-6106	184	16	fine	fine	ADJ
ap-6106	184	17	at	at	ADP
ap-6106	184	18	right	right	NOUN
ap-6106	184	19	)	)	PUNCT
ap-6106	184	20	we	we	PRON
ap-6106	184	21	approach	approach	VERB
ap-6106	184	22	to	to	ADP
ap-6106	184	23	the	the	DET
ap-6106	184	24	correct	correct	ADJ
ap-6106	184	25	diverging	diverge	VERB
ap-6106	184	26	shock	shock	NOUN
ap-6106	184	27	with	with	ADP
ap-6106	184	28	the	the	DET
ap-6106	184	29	front	front	NOUN
ap-6106	184	30	at	at	ADP
ap-6106	184	31	radius	radius	NOUN
ap-6106	184	32	|x|	|x|	PROPN
ap-6106	184	33	=	=	SYM
ap-6106	184	34	1	1	NUM
ap-6106	184	35	and	and	CCONJ
ap-6106	184	36	a	a	DET
ap-6106	184	37	density	density	NOUN
ap-6106	184	38	peak	peak	NOUN
ap-6106	184	39	ρ	ρ	PROPN
ap-6106	184	40	=	=	PROPN
ap-6106	184	41	6	6	NUM
ap-6106	184	42	and	and	CCONJ
ap-6106	184	43	to	to	PART
ap-6106	184	44	correct	correct	VERB
ap-6106	184	45	low	low	ADJ
ap-6106	184	46	density	density	NOUN
ap-6106	184	47	around	around	ADP
ap-6106	184	48	the	the	DET
ap-6106	184	49	origin	origin	NOUN
ap-6106	184	50	.	.	PUNCT
ap-6106	185	1	similarly	similarly	ADV
ap-6106	185	2	in	in	ADP
ap-6106	185	3	fig	fig	NOUN
ap-6106	185	4	.	.	PUNCT
ap-6106	186	1	16	16	NUM
ap-6106	186	2	we	we	PRON
ap-6106	186	3	again	again	ADV
ap-6106	186	4	compare	compare	VERB
ap-6106	186	5	the	the	DET
ap-6106	186	6	solutions	solution	NOUN
ap-6106	186	7	of	of	ADP
ap-6106	186	8	sedov	sedov	PROPN
ap-6106	186	9	problem	problem	NOUN
ap-6106	186	10	on	on	ADP
ap-6106	186	11	the	the	DET
ap-6106	186	12	lowest	low	ADJ
ap-6106	186	13	and	and	CCONJ
ap-6106	186	14	highest	high	ADJ
ap-6106	186	15	resolution	resolution	NOUN
ap-6106	186	16	meshes	mesh	NOUN
ap-6106	186	17	of	of	ADP
ap-6106	186	18	regular	regular	ADJ
ap-6106	186	19	hexagons	hexagon	NOUN
ap-6106	186	20	introduced	introduce	VERB
ap-6106	186	21	earlier	early	ADV
ap-6106	186	22	for	for	ADP
ap-6106	186	23	the	the	DET
ap-6106	186	24	noh	noh	PROPN
ap-6106	186	25	test	test	NOUN
ap-6106	186	26	.	.	PUNCT
ap-6106	187	1	5.4	5.4	NUM
ap-6106	187	2	.	.	PUNCT
ap-6106	187	3	smooth	smooth	ADJ
ap-6106	187	4	expansion	expansion	NOUN
ap-6106	187	5	problem	problem	NOUN
ap-6106	187	6	to	to	PART
ap-6106	187	7	check	check	VERB
ap-6106	187	8	the	the	DET
ap-6106	187	9	numerical	numerical	ADJ
ap-6106	187	10	order	order	NOUN
ap-6106	187	11	of	of	ADP
ap-6106	187	12	accuracy	accuracy	NOUN
ap-6106	187	13	of	of	ADP
ap-6106	187	14	the	the	DET
ap-6106	187	15	lw	lw	PROPN
ap-6106	187	16	scheme	scheme	NOUN
ap-6106	187	17	we	we	PRON
ap-6106	187	18	define	define	VERB
ap-6106	187	19	a	a	DET
ap-6106	187	20	smooth	smooth	ADJ
ap-6106	187	21	,	,	PUNCT
ap-6106	187	22	radially	radially	ADV
ap-6106	187	23	symmetric	symmetric	ADJ
ap-6106	187	24	,	,	PUNCT
ap-6106	187	25	expansion	expansion	NOUN
ap-6106	187	26	problem	problem	NOUN
ap-6106	187	27	for	for	ADP
ap-6106	187	28	a	a	DET
ap-6106	187	29	gas	gas	NOUN
ap-6106	187	30	with	with	ADP
ap-6106	187	31	γ	γ	X
ap-6106	187	32	=	=	SYM
ap-6106	187	33	5/3	5/3	NUM
ap-6106	187	34	on	on	ADP
ap-6106	187	35	the	the	DET
ap-6106	187	36	circular	circular	ADJ
ap-6106	187	37	domain	domain	NOUN
ap-6106	187	38	with	with	ADP
ap-6106	187	39	the	the	DET
ap-6106	187	40	initial	initial	ADJ
ap-6106	187	41	radius	radius	NOUN
ap-6106	187	42	3	3	NUM
ap-6106	187	43	,	,	PUNCT
ap-6106	187	44	centered	center	VERB
ap-6106	187	45	at	at	ADP
ap-6106	187	46	the	the	DET
ap-6106	187	47	origin	origin	NOUN
ap-6106	187	48	.	.	PUNCT
ap-6106	188	1	the	the	DET
ap-6106	188	2	initial	initial	ADJ
ap-6106	188	3	density	density	NOUN
ap-6106	188	4	has	have	VERB
ap-6106	188	5	gaussian	gaussian	ADJ
ap-6106	188	6	profile	profile	NOUN
ap-6106	188	7	ρ0	ρ0	PROPN
ap-6106	188	8	=	=	SYM
ap-6106	188	9	exp(−|x|2	exp(−|x|2	NUM
ap-6106	188	10	)	)	PUNCT
ap-6106	188	11	,	,	PUNCT
ap-6106	188	12	the	the	DET
ap-6106	188	13	initial	initial	ADJ
ap-6106	188	14	specific	specific	ADJ
ap-6106	188	15	internal	internal	ADJ
ap-6106	188	16	energy	energy	NOUN
ap-6106	188	17	is	be	AUX
ap-6106	188	18	constant	constant	ADJ
ap-6106	188	19	ε0	ε0	NOUN
ap-6106	188	20	=	=	SYM
ap-6106	188	21	e0	e0	PROPN
ap-6106	188	22	=	=	SYM
ap-6106	188	23	3/4	3/4	NUM
ap-6106	188	24	and	and	CCONJ
ap-6106	188	25	the	the	DET
ap-6106	188	26	gas	gas	NOUN
ap-6106	188	27	is	be	AUX
ap-6106	188	28	initially	initially	ADV
ap-6106	188	29	at	at	ADP
ap-6106	188	30	rest	rest	NOUN
ap-6106	188	31	.	.	PUNCT
ap-6106	189	1	the	the	DET
ap-6106	189	2	final	final	ADJ
ap-6106	189	3	time	time	NOUN
ap-6106	189	4	was	be	AUX
ap-6106	189	5	set	set	VERB
ap-6106	189	6	to	to	ADP
ap-6106	189	7	tfinal	tfinal	ADJ
ap-6106	189	8	=	=	NOUN
ap-6106	189	9	1	1	X
ap-6106	189	10	.	.	PUNCT
ap-6106	190	1	this	this	DET
ap-6106	190	2	polar	polar	ADJ
ap-6106	190	3	symmetric	symmetric	ADJ
ap-6106	190	4	problem	problem	NOUN
ap-6106	190	5	has	have	AUX
ap-6106	190	6	been	be	AUX
ap-6106	190	7	also	also	ADV
ap-6106	190	8	solved	solve	VERB
ap-6106	190	9	in	in	ADP
ap-6106	190	10	1d	1d	NUM
ap-6106	190	11	on	on	ADP
ap-6106	190	12	a	a	DET
ap-6106	190	13	high	high	ADJ
ap-6106	190	14	resolution	resolution	NOUN
ap-6106	190	15	mesh	mesh	NOUN
ap-6106	190	16	with	with	ADP
ap-6106	190	17	5,000	5,000	NUM
ap-6106	190	18	cells	cell	NOUN
ap-6106	190	19	.	.	PUNCT
ap-6106	191	1	the	the	DET
ap-6106	191	2	obtained	obtain	VERB
ap-6106	191	3	high	high	ADJ
ap-6106	191	4	resolution	resolution	NOUN
ap-6106	191	5	solution	solution	NOUN
ap-6106	191	6	is	be	AUX
ap-6106	191	7	used	use	VERB
ap-6106	191	8	as	as	ADP
ap-6106	191	9	a	a	DET
ap-6106	191	10	reference	reference	NOUN
ap-6106	191	11	solution	solution	NOUN
ap-6106	191	12	and	and	CCONJ
ap-6106	191	13	instead	instead	ADV
ap-6106	191	14	of	of	ADP
ap-6106	191	15	errors	error	NOUN
ap-6106	191	16	we	we	PRON
ap-6106	191	17	are	be	AUX
ap-6106	191	18	looking	look	VERB
ap-6106	191	19	at	at	ADP
ap-6106	191	20	the	the	DET
ap-6106	191	21	deviations	deviation	NOUN
ap-6106	191	22	of	of	ADP
ap-6106	191	23	the	the	DET
ap-6106	191	24	2d	2d	PROPN
ap-6106	191	25	numerical	numerical	ADJ
ap-6106	191	26	solutions	solution	NOUN
ap-6106	191	27	from	from	ADP
ap-6106	191	28	this	this	DET
ap-6106	191	29	reference	reference	NOUN
ap-6106	191	30	.	.	PUNCT
ap-6106	192	1	74	74	NUM
ap-6106	192	2	vol	vol	NOUN
ap-6106	192	3	.	.	PUNCT
ap-6106	193	1	61	61	NUM
ap-6106	193	2	special	special	ADJ
ap-6106	193	3	issue/2021	issue/2021	NOUN
ap-6106	193	4	lagrangian	lagrangian	ADJ
ap-6106	193	5	lax	lax	PROPN
ap-6106	193	6	-	-	PUNCT
ap-6106	193	7	wendroff	wendroff	NOUN
ap-6106	193	8	hll	hll	PROPN
ap-6106	193	9	scheme	scheme	PROPN
ap-6106	193	10	0.0	0.0	NUM
ap-6106	193	11	0.2	0.2	NUM
ap-6106	193	12	0.4	0.4	NUM
ap-6106	193	13	0.6	0.6	NUM
ap-6106	193	14	0.8	0.8	NUM
ap-6106	193	15	1.0	1.0	NUM
ap-6106	193	16	1.2	1.2	NUM
ap-6106	193	17	0.0	0.0	NUM
ap-6106	193	18	0.2	0.2	NUM
ap-6106	193	19	0.4	0.4	NUM
ap-6106	193	20	0.6	0.6	NUM
ap-6106	193	21	0.8	0.8	NUM
ap-6106	193	22	1.0	1.0	NUM
ap-6106	193	23	1.2	1.2	NUM
ap-6106	193	24	0	0	NUM
ap-6106	193	25	1	1	NUM
ap-6106	193	26	2	2	NUM
ap-6106	193	27	3	3	NUM
ap-6106	193	28	4	4	NUM
ap-6106	193	29	5	5	NUM
ap-6106	193	30	6	6	NUM
ap-6106	193	31	figure	figure	NOUN
ap-6106	193	32	14	14	NUM
ap-6106	193	33	.	.	PUNCT
ap-6106	194	1	density	density	NOUN
ap-6106	194	2	and	and	CCONJ
ap-6106	194	3	mesh	mesh	NOUN
ap-6106	194	4	for	for	ADP
ap-6106	194	5	sedov	sedov	PROPN
ap-6106	194	6	problem	problem	NOUN
ap-6106	194	7	on	on	ADP
ap-6106	194	8	regular	regular	ADJ
ap-6106	194	9	hexagonal	hexagonal	ADJ
ap-6106	194	10	mesh	mesh	NOUN
ap-6106	194	11	of	of	ADP
ap-6106	194	12	10083	10083	NUM
ap-6106	194	13	cells	cell	NOUN
ap-6106	194	14	with	with	ADP
ap-6106	194	15	τ	τ	PROPN
ap-6106	194	16	=	=	SYM
ap-6106	194	17	1.25	1.25	NUM
ap-6106	194	18	.	.	PUNCT
ap-6106	194	19	0	0	NUM
ap-6106	195	1	0.5	0.5	NUM
ap-6106	195	2	1	1	NUM
ap-6106	195	3	0	0	NUM
ap-6106	195	4	1	1	NUM
ap-6106	195	5	2	2	NUM
ap-6106	195	6	3	3	NUM
ap-6106	195	7	4	4	NUM
ap-6106	195	8	5	5	NUM
ap-6106	195	9	6	6	NUM
ap-6106	195	10	7	7	NUM
ap-6106	195	11	(	(	PUNCT
ap-6106	195	12	a	a	NOUN
ap-6106	195	13	)	)	PUNCT
ap-6106	195	14	.	.	PUNCT
ap-6106	196	1	(	(	PUNCT
ap-6106	196	2	b	b	X
ap-6106	196	3	)	)	PUNCT
ap-6106	196	4	.	.	PUNCT
ap-6106	197	1	figure	figure	NOUN
ap-6106	197	2	15	15	NUM
ap-6106	197	3	.	.	PUNCT
ap-6106	198	1	density	density	NOUN
ap-6106	198	2	scatter	scatter	NOUN
ap-6106	198	3	plot	plot	NOUN
ap-6106	198	4	for	for	ADP
ap-6106	198	5	sedov	sedov	PROPN
ap-6106	198	6	problem	problem	NOUN
ap-6106	198	7	on	on	ADP
ap-6106	198	8	regular	regular	ADJ
ap-6106	198	9	triangular	triangular	NOUN
ap-6106	198	10	meshes	mesh	VERB
ap-6106	198	11	with	with	ADP
ap-6106	198	12	τ	τ	PROPN
ap-6106	198	13	=	=	SYM
ap-6106	198	14	2	2	NUM
ap-6106	198	15	on	on	ADP
ap-6106	198	16	coarse	coarse	ADV
ap-6106	198	17	(	(	PUNCT
ap-6106	198	18	a	a	NOUN
ap-6106	198	19	)	)	PUNCT
ap-6106	198	20	and	and	CCONJ
ap-6106	198	21	fine	fine	ADJ
ap-6106	198	22	mesh	mesh	NOUN
ap-6106	198	23	(	(	PUNCT
ap-6106	198	24	b	b	NOUN
ap-6106	198	25	)	)	PUNCT
ap-6106	198	26	.	.	PUNCT
ap-6106	199	1	the	the	DET
ap-6106	199	2	2d	2d	NUM
ap-6106	199	3	solutions	solution	NOUN
ap-6106	199	4	were	be	AUX
ap-6106	199	5	calculated	calculate	VERB
ap-6106	199	6	on	on	ADP
ap-6106	199	7	honeycomb	honeycomb	NOUN
ap-6106	199	8	meshes	mesh	NOUN
ap-6106	199	9	,	,	PUNCT
ap-6106	199	10	which	which	PRON
ap-6106	199	11	were	be	AUX
ap-6106	199	12	constructed	construct	VERB
ap-6106	199	13	by	by	ADP
ap-6106	199	14	the	the	DET
ap-6106	199	15	voronoi	voronoi	PROPN
ap-6106	199	16	tessellation	tessellation	NOUN
ap-6106	199	17	of	of	ADP
ap-6106	199	18	the	the	DET
ap-6106	199	19	initial	initial	ADJ
ap-6106	199	20	circular	circular	ADJ
ap-6106	199	21	domain	domain	NOUN
ap-6106	199	22	.	.	PUNCT
ap-6106	200	1	since	since	SCONJ
ap-6106	200	2	the	the	DET
ap-6106	200	3	solution	solution	NOUN
ap-6106	200	4	is	be	AUX
ap-6106	200	5	smooth	smooth	ADJ
ap-6106	200	6	,	,	PUNCT
ap-6106	200	7	the	the	DET
ap-6106	200	8	calculations	calculation	NOUN
ap-6106	200	9	were	be	AUX
ap-6106	200	10	performed	perform	VERB
ap-6106	200	11	by	by	ADP
ap-6106	200	12	the	the	DET
ap-6106	200	13	pure	pure	ADJ
ap-6106	200	14	lw	lw	NOUN
ap-6106	200	15	method	method	NOUN
ap-6106	200	16	without	without	ADP
ap-6106	200	17	any	any	DET
ap-6106	200	18	artificial	artificial	ADJ
ap-6106	200	19	dissipation	dissipation	NOUN
ap-6106	200	20	.	.	PUNCT
ap-6106	201	1	at	at	ADP
ap-6106	201	2	the	the	DET
ap-6106	201	3	final	final	ADJ
ap-6106	201	4	time	time	NOUN
ap-6106	201	5	,	,	PUNCT
ap-6106	201	6	the	the	DET
ap-6106	201	7	deviations	deviation	NOUN
ap-6106	201	8	from	from	ADP
ap-6106	201	9	the	the	DET
ap-6106	201	10	linearly	linearly	ADV
ap-6106	201	11	interpolated	interpolate	VERB
ap-6106	201	12	1d	1d	NUM
ap-6106	201	13	reference	reference	NOUN
ap-6106	201	14	solution	solution	NOUN
ap-6106	201	15	were	be	AUX
ap-6106	201	16	compared	compare	VERB
ap-6106	201	17	at	at	ADP
ap-6106	201	18	the	the	DET
ap-6106	201	19	cell	cell	NOUN
ap-6106	201	20	centers	center	NOUN
ap-6106	201	21	;	;	PUNCT
ap-6106	201	22	i.e.	i.e.	X
ap-6106	201	23	,	,	PUNCT
ap-6106	201	24	for	for	ADP
ap-6106	201	25	each	each	DET
ap-6106	201	26	cell	cell	NOUN
ap-6106	201	27	we	we	PRON
ap-6106	201	28	evaluate	evaluate	VERB
ap-6106	201	29	the	the	DET
ap-6106	201	30	radius	radius	NOUN
ap-6106	201	31	of	of	ADP
ap-6106	201	32	its	its	PRON
ap-6106	201	33	center	center	NOUN
ap-6106	201	34	and	and	CCONJ
ap-6106	201	35	compare	compare	VERB
ap-6106	201	36	the	the	DET
ap-6106	201	37	2d	2d	NUM
ap-6106	201	38	value	value	NOUN
ap-6106	201	39	at	at	ADP
ap-6106	201	40	the	the	DET
ap-6106	201	41	center	center	NOUN
ap-6106	201	42	with	with	ADP
ap-6106	201	43	the	the	DET
ap-6106	201	44	value	value	NOUN
ap-6106	201	45	of	of	ADP
ap-6106	201	46	the	the	DET
ap-6106	201	47	1d	1d	NUM
ap-6106	201	48	reference	reference	NOUN
ap-6106	201	49	solution	solution	NOUN
ap-6106	201	50	linearly	linearly	ADV
ap-6106	201	51	interpolated	interpolate	VERB
ap-6106	201	52	to	to	ADP
ap-6106	201	53	this	this	DET
ap-6106	201	54	radius	radius	NOUN
ap-6106	201	55	.	.	PUNCT
ap-6106	202	1	table	table	NOUN
ap-6106	202	2	1	1	NUM
ap-6106	202	3	shows	show	VERB
ap-6106	202	4	the	the	DET
ap-6106	202	5	maximum	maximum	ADJ
ap-6106	202	6	deviations	deviation	NOUN
ap-6106	202	7	of	of	ADP
ap-6106	202	8	density	density	NOUN
ap-6106	202	9	for	for	ADP
ap-6106	202	10	consecutively	consecutively	ADV
ap-6106	202	11	refined	refine	VERB
ap-6106	202	12	meshes	mesh	NOUN
ap-6106	202	13	.	.	PUNCT
ap-6106	203	1	each	each	DET
ap-6106	203	2	finer	fine	ADJ
ap-6106	203	3	mesh	mesh	NOUN
ap-6106	203	4	has	have	VERB
ap-6106	203	5	about	about	ADV
ap-6106	203	6	four	four	NUM
ap-6106	203	7	times	time	NOUN
ap-6106	203	8	as	as	ADV
ap-6106	203	9	many	many	ADJ
ap-6106	203	10	cells	cell	NOUN
ap-6106	203	11	as	as	ADP
ap-6106	203	12	0	0	NUM
ap-6106	203	13	0.5	0.5	NUM
ap-6106	203	14	1	1	NUM
ap-6106	203	15	0	0	NUM
ap-6106	203	16	1	1	NUM
ap-6106	203	17	2	2	NUM
ap-6106	203	18	3	3	NUM
ap-6106	203	19	4	4	NUM
ap-6106	203	20	5	5	NUM
ap-6106	203	21	6	6	NUM
ap-6106	203	22	7	7	NUM
ap-6106	203	23	(	(	PUNCT
ap-6106	203	24	a	a	NOUN
ap-6106	203	25	)	)	PUNCT
ap-6106	203	26	.	.	PUNCT
ap-6106	204	1	0	0	NUM
ap-6106	205	1	0.5	0.5	NUM
ap-6106	205	2	1	1	NUM
ap-6106	205	3	0	0	NUM
ap-6106	205	4	1	1	NUM
ap-6106	205	5	2	2	NUM
ap-6106	205	6	3	3	NUM
ap-6106	205	7	4	4	NUM
ap-6106	205	8	5	5	NUM
ap-6106	205	9	6	6	NUM
ap-6106	205	10	7	7	NUM
ap-6106	205	11	(	(	PUNCT
ap-6106	205	12	b	b	NOUN
ap-6106	205	13	)	)	PUNCT
ap-6106	205	14	.	.	PUNCT
ap-6106	206	1	figure	figure	NOUN
ap-6106	206	2	16	16	NUM
ap-6106	206	3	.	.	PUNCT
ap-6106	207	1	density	density	NOUN
ap-6106	207	2	scatter	scatter	NOUN
ap-6106	207	3	plot	plot	NOUN
ap-6106	207	4	for	for	ADP
ap-6106	207	5	sedov	sedov	PROPN
ap-6106	207	6	problem	problem	NOUN
ap-6106	207	7	on	on	ADP
ap-6106	207	8	regular	regular	ADJ
ap-6106	207	9	hexagonal	hexagonal	ADJ
ap-6106	207	10	meshes	mesh	NOUN
ap-6106	207	11	with	with	ADP
ap-6106	207	12	τ	τ	PROPN
ap-6106	207	13	=	=	SYM
ap-6106	207	14	1.25	1.25	NUM
ap-6106	207	15	on	on	ADP
ap-6106	207	16	coarse	coarse	ADV
ap-6106	207	17	(	(	PUNCT
ap-6106	207	18	a	a	NOUN
ap-6106	207	19	)	)	PUNCT
ap-6106	207	20	and	and	CCONJ
ap-6106	207	21	fine	fine	ADJ
ap-6106	207	22	mesh	mesh	NOUN
ap-6106	207	23	(	(	PUNCT
ap-6106	207	24	b	b	NOUN
ap-6106	207	25	)	)	PUNCT
ap-6106	207	26	.	.	PUNCT
ap-6106	208	1	0.0	0.0	NUM
ap-6106	208	2	0.2	0.2	NUM
ap-6106	208	3	0.4	0.4	NUM
ap-6106	208	4	0.6	0.6	NUM
ap-6106	208	5	0.8	0.8	NUM
ap-6106	208	6	1.0	1.0	NUM
ap-6106	208	7	1.2	1.2	NUM
ap-6106	208	8	0.0	0.0	NUM
ap-6106	208	9	0.2	0.2	NUM
ap-6106	208	10	0.4	0.4	NUM
ap-6106	208	11	0.6	0.6	NUM
ap-6106	208	12	0.8	0.8	NUM
ap-6106	208	13	1.0	1.0	NUM
ap-6106	208	14	1.2	1.2	NUM
ap-6106	208	15	0	0	NUM
ap-6106	208	16	1	1	NUM
ap-6106	208	17	2	2	NUM
ap-6106	208	18	3	3	NUM
ap-6106	208	19	4	4	NUM
ap-6106	208	20	5	5	NUM
ap-6106	208	21	6	6	NUM
ap-6106	208	22	figure	figure	NOUN
ap-6106	208	23	17	17	NUM
ap-6106	208	24	.	.	PUNCT
ap-6106	209	1	density	density	NOUN
ap-6106	209	2	and	and	CCONJ
ap-6106	209	3	mesh	mesh	NOUN
ap-6106	209	4	for	for	ADP
ap-6106	209	5	sedov	sedov	PROPN
ap-6106	209	6	problem	problem	NOUN
ap-6106	209	7	on	on	ADP
ap-6106	209	8	irregular	irregular	ADJ
ap-6106	209	9	polygonal	polygonal	ADJ
ap-6106	209	10	mesh	mesh	NOUN
ap-6106	209	11	of	of	ADP
ap-6106	209	12	10083	10083	NUM
ap-6106	209	13	cells	cell	NOUN
ap-6106	209	14	with	with	ADP
ap-6106	209	15	τ	τ	PROPN
ap-6106	209	16	=	=	SYM
ap-6106	209	17	1.25	1.25	NUM
ap-6106	209	18	.	.	PUNCT
ap-6106	210	1	than	than	ADP
ap-6106	210	2	the	the	DET
ap-6106	210	3	previous	previous	ADJ
ap-6106	210	4	one	one	NUM
ap-6106	210	5	,	,	PUNCT
ap-6106	210	6	which	which	PRON
ap-6106	210	7	amounts	amount	VERB
ap-6106	210	8	to	to	ADP
ap-6106	210	9	doubling	double	VERB
ap-6106	210	10	the	the	DET
ap-6106	210	11	resolution	resolution	NOUN
ap-6106	210	12	in	in	ADP
ap-6106	210	13	each	each	DET
ap-6106	210	14	direction	direction	NOUN
ap-6106	210	15	.	.	PUNCT
ap-6106	211	1	the	the	DET
ap-6106	211	2	ratio	ratio	NOUN
ap-6106	211	3	of	of	ADP
ap-6106	211	4	the	the	DET
ap-6106	211	5	deviations	deviation	NOUN
ap-6106	211	6	is	be	AUX
ap-6106	211	7	about	about	ADV
ap-6106	211	8	4	4	NUM
ap-6106	211	9	,	,	PUNCT
ap-6106	211	10	which	which	PRON
ap-6106	211	11	confirms	confirm	VERB
ap-6106	211	12	that	that	SCONJ
ap-6106	211	13	the	the	DET
ap-6106	211	14	lw	lw	PROPN
ap-6106	211	15	method	method	NOUN
ap-6106	211	16	is	be	AUX
ap-6106	211	17	2nd	2nd	ADJ
ap-6106	211	18	order	order	NOUN
ap-6106	211	19	accurate	accurate	ADJ
ap-6106	211	20	.	.	PUNCT
ap-6106	212	1	6	6	X
ap-6106	212	2	.	.	PUNCT
ap-6106	212	3	conclusions	conclusion	NOUN
ap-6106	212	4	we	we	PRON
ap-6106	212	5	have	have	AUX
ap-6106	212	6	presented	present	VERB
ap-6106	212	7	the	the	DET
ap-6106	212	8	cell	cell	NOUN
ap-6106	212	9	-	-	PUNCT
ap-6106	212	10	centered	center	VERB
ap-6106	212	11	hybrid	hybrid	NOUN
ap-6106	212	12	laxwendroff	laxwendroff	NOUN
ap-6106	212	13	hll	hll	PROPN
ap-6106	212	14	lagrangian	lagrangian	ADJ
ap-6106	212	15	scheme	scheme	NOUN
ap-6106	212	16	for	for	ADP
ap-6106	212	17	compressible	compressible	ADJ
ap-6106	212	18	hydrodynamics	hydrodynamic	NOUN
ap-6106	212	19	on	on	ADP
ap-6106	212	20	unstructured	unstructured	ADJ
ap-6106	212	21	computational	computational	ADJ
ap-6106	212	22	meshes	mesh	NOUN
ap-6106	212	23	.	.	PUNCT
ap-6106	213	1	the	the	DET
ap-6106	213	2	results	result	NOUN
ap-6106	213	3	of	of	ADP
ap-6106	213	4	noh	noh	PROPN
ap-6106	213	5	and	and	CCONJ
ap-6106	213	6	sedov	sedov	PROPN
ap-6106	213	7	problems	problem	NOUN
ap-6106	213	8	on	on	ADP
ap-6106	213	9	uniform	uniform	ADJ
ap-6106	213	10	honeycomb	honeycomb	NOUN
ap-6106	213	11	hexagonal	hexagonal	ADJ
ap-6106	213	12	,	,	PUNCT
ap-6106	213	13	uniform	uniform	NOUN
ap-6106	213	14	triangular	triangular	NOUN
ap-6106	213	15	,	,	PUNCT
ap-6106	213	16	non75	non75	PROPN
ap-6106	213	17	d.	d.	PROPN
ap-6106	213	18	fridrich	fridrich	PROPN
ap-6106	213	19	,	,	PUNCT
ap-6106	213	20	r.	r.	PROPN
ap-6106	213	21	liska	liska	PROPN
ap-6106	213	22	,	,	PUNCT
ap-6106	213	23	i.	i.	PROPN
ap-6106	213	24	tarant	tarant	PROPN
ap-6106	213	25	et	et	PROPN
ap-6106	213	26	al	al	PROPN
ap-6106	213	27	.	.	PROPN
ap-6106	213	28	acta	acta	PROPN
ap-6106	213	29	polytechnica	polytechnica	PROPN
ap-6106	214	1	no	no	PROPN
ap-6106	214	2	.	.	PUNCT
ap-6106	214	3	of	of	ADP
ap-6106	214	4	cells	cells	PROPN
ap-6106	214	5	max	max	PROPN
ap-6106	214	6	.	.	PUNCT
ap-6106	215	1	ratio	ratio	PROPN
ap-6106	215	2	w.	w.	PROPN
ap-6106	215	3	r.	r.	PROPN
ap-6106	215	4	t.	t.	PROPN
ap-6106	215	5	in	in	ADP
ap-6106	215	6	the	the	DET
ap-6106	215	7	mesh	mesh	NOUN
ap-6106	215	8	deviation	deviation	NOUN
ap-6106	215	9	prev	prev	NOUN
ap-6106	215	10	.	.	PUNCT
ap-6106	216	1	resol	resol	NOUN
ap-6106	216	2	.	.	PUNCT
ap-6106	217	1	75	75	NUM
ap-6106	217	2	0.036	0.036	NUM
ap-6106	217	3	309	309	NUM
ap-6106	217	4	0.0088	0.0088	NUM
ap-6106	217	5	4.1	4.1	NUM
ap-6106	217	6	1	1	NUM
ap-6106	217	7	251	251	NUM
ap-6106	217	8	0.0021	0.0021	NUM
ap-6106	217	9	4.2	4.2	NUM
ap-6106	217	10	5	5	NUM
ap-6106	217	11	012	012	NUM
ap-6106	217	12	0.00051	0.00051	NUM
ap-6106	217	13	4.1	4.1	NUM
ap-6106	217	14	20	20	NUM
ap-6106	217	15	094	094	NUM
ap-6106	217	16	0.00013	0.00013	NUM
ap-6106	217	17	4.0	4.0	NUM
ap-6106	217	18	table	table	NOUN
ap-6106	217	19	1	1	NUM
ap-6106	217	20	.	.	PUNCT
ap-6106	218	1	maximum	maximum	ADJ
ap-6106	218	2	density	density	NOUN
ap-6106	218	3	deviations	deviation	NOUN
ap-6106	218	4	of	of	ADP
ap-6106	218	5	2d	2d	NUM
ap-6106	218	6	solutions	solution	NOUN
ap-6106	218	7	from	from	ADP
ap-6106	218	8	the	the	DET
ap-6106	218	9	interpolated	interpolate	VERB
ap-6106	218	10	1d	1d	NUM
ap-6106	218	11	reference	reference	NOUN
ap-6106	218	12	solution	solution	NOUN
ap-6106	218	13	and	and	CCONJ
ap-6106	218	14	the	the	DET
ap-6106	218	15	ratios	ratio	NOUN
ap-6106	218	16	of	of	ADP
ap-6106	218	17	the	the	DET
ap-6106	218	18	deviations	deviation	NOUN
ap-6106	218	19	.	.	PUNCT
ap-6106	219	1	uniform	uniform	ADJ
ap-6106	219	2	polygonal	polygonal	ADJ
ap-6106	219	3	and	and	CCONJ
ap-6106	219	4	non	non	ADJ
ap-6106	219	5	-	-	ADJ
ap-6106	219	6	uniform	uniform	ADJ
ap-6106	219	7	triangular	triangular	NOUN
ap-6106	219	8	meshes	mesh	NOUN
ap-6106	219	9	confirm	confirm	VERB
ap-6106	219	10	the	the	DET
ap-6106	219	11	quality	quality	NOUN
ap-6106	219	12	of	of	ADP
ap-6106	219	13	the	the	DET
ap-6106	219	14	approach	approach	NOUN
ap-6106	219	15	.	.	PUNCT
ap-6106	220	1	the	the	DET
ap-6106	220	2	method	method	NOUN
ap-6106	220	3	preserves	preserve	VERB
ap-6106	220	4	polar	polar	ADJ
ap-6106	220	5	symmetry	symmetry	NOUN
ap-6106	220	6	of	of	ADP
ap-6106	220	7	the	the	DET
ap-6106	220	8	solution	solution	NOUN
ap-6106	220	9	very	very	ADV
ap-6106	220	10	well	well	ADV
ap-6106	220	11	.	.	PUNCT
ap-6106	221	1	acknowledgements	acknowledgement	NOUN
ap-6106	221	2	the	the	DET
ap-6106	221	3	first	first	ADJ
ap-6106	221	4	four	four	NUM
ap-6106	221	5	authors	author	NOUN
ap-6106	221	6	have	have	AUX
ap-6106	221	7	been	be	AUX
ap-6106	221	8	supported	support	VERB
ap-6106	221	9	by	by	ADP
ap-6106	221	10	the	the	DET
ap-6106	221	11	czech	czech	PROPN
ap-6106	221	12	science	science	PROPN
ap-6106	221	13	foundation	foundation	PROPN
ap-6106	221	14	project	project	PROPN
ap-6106	221	15	18	18	NUM
ap-6106	221	16	-	-	PUNCT
ap-6106	221	17	20962s	20962s	NUM
ap-6106	221	18	,	,	PUNCT
ap-6106	221	19	by	by	ADP
ap-6106	221	20	the	the	DET
ap-6106	221	21	project	project	NOUN
ap-6106	221	22	cz.02.1.01/0.0/0.0/16_019/0000778	cz.02.1.01/0.0/0.0/16_019/0000778	NUM
ap-6106	221	23	from	from	ADP
ap-6106	221	24	european	european	PROPN
ap-6106	221	25	regional	regional	PROPN
ap-6106	221	26	development	development	PROPN
ap-6106	221	27	fund	fund	PROPN
ap-6106	221	28	,	,	PUNCT
ap-6106	221	29	by	by	ADP
ap-6106	221	30	the	the	DET
ap-6106	221	31	czech	czech	PROPN
ap-6106	221	32	technical	technical	PROPN
ap-6106	221	33	university	university	PROPN
ap-6106	221	34	in	in	ADP
ap-6106	221	35	prague	prague	PROPN
ap-6106	221	36	project	project	NOUN
ap-6106	221	37	sgs19/191	sgs19/191	PROPN
ap-6106	221	38	/	/	SYM
ap-6106	221	39	ohk4/3t/14	ohk4/3t/14	PROPN
ap-6106	221	40	and	and	CCONJ
ap-6106	221	41	by	by	ADP
ap-6106	221	42	the	the	DET
ap-6106	221	43	czech	czech	PROPN
ap-6106	221	44	ministry	ministry	PROPN
ap-6106	221	45	of	of	ADP
ap-6106	221	46	education	education	PROPN
ap-6106	221	47	project	project	NOUN
ap-6106	221	48	rvo	rvo	VERB
ap-6106	221	49	68407700	68407700	NUM
ap-6106	221	50	.	.	PUNCT
ap-6106	222	1	references	reference	NOUN
ap-6106	222	2	[	[	X
ap-6106	222	3	1	1	X
ap-6106	222	4	]	]	PUNCT
ap-6106	222	5	e.	e.	PROPN
ap-6106	222	6	j.	j.	PROPN
ap-6106	222	7	caramana	caramana	PROPN
ap-6106	222	8	,	,	PUNCT
ap-6106	222	9	d.	d.	PROPN
ap-6106	222	10	e.	e.	PROPN
ap-6106	222	11	burton	burton	PROPN
ap-6106	222	12	,	,	PUNCT
ap-6106	222	13	m.	m.	PROPN
ap-6106	222	14	j.	j.	PROPN
ap-6106	222	15	shashkov	shashkov	PROPN
ap-6106	222	16	,	,	PUNCT
ap-6106	222	17	p.	p.	NOUN
ap-6106	222	18	p.	p.	PROPN
ap-6106	222	19	whalen	whalen	PROPN
ap-6106	222	20	.	.	PUNCT
ap-6106	223	1	the	the	DET
ap-6106	223	2	construction	construction	NOUN
ap-6106	223	3	of	of	ADP
ap-6106	223	4	compatible	compatible	ADJ
ap-6106	223	5	hydrodynamics	hydrodynamic	NOUN
ap-6106	223	6	algorithms	algorithm	NOUN
ap-6106	223	7	utilizing	utilize	VERB
ap-6106	223	8	conservation	conservation	NOUN
ap-6106	223	9	of	of	ADP
ap-6106	223	10	total	total	ADJ
ap-6106	223	11	energy	energy	NOUN
ap-6106	223	12	.	.	PUNCT
ap-6106	224	1	journal	journal	NOUN
ap-6106	224	2	of	of	ADP
ap-6106	224	3	computational	computational	ADJ
ap-6106	224	4	physics	physic	NOUN
ap-6106	224	5	146(1):227–262	146(1):227–262	NUM
ap-6106	224	6	,	,	PUNCT
ap-6106	224	7	1998	1998	NUM
ap-6106	224	8	.	.	PUNCT
ap-6106	225	1	doi:10.1006	doi:10.1006	PROPN
ap-6106	225	2	/	/	SYM
ap-6106	225	3	jcph.1998.6029	jcph.1998.6029	NOUN
ap-6106	225	4	.	.	PUNCT
ap-6106	226	1	[	[	X
ap-6106	226	2	2	2	X
ap-6106	226	3	]	]	PUNCT
ap-6106	226	4	e.	e.	PROPN
ap-6106	226	5	j.	j.	PROPN
ap-6106	226	6	caramana	caramana	PROPN
ap-6106	226	7	,	,	PUNCT
ap-6106	226	8	m.	m.	PROPN
ap-6106	226	9	j.	j.	PROPN
ap-6106	226	10	shashkov	shashkov	PROPN
ap-6106	226	11	,	,	PUNCT
ap-6106	226	12	p.	p.	NOUN
ap-6106	226	13	p.	p.	PROPN
ap-6106	226	14	whalen	whalen	PROPN
ap-6106	226	15	.	.	PUNCT
ap-6106	227	1	formulations	formulation	NOUN
ap-6106	227	2	of	of	ADP
ap-6106	227	3	artificial	artificial	ADJ
ap-6106	227	4	viscosity	viscosity	NOUN
ap-6106	227	5	for	for	ADP
ap-6106	227	6	multi	multi	ADJ
ap-6106	227	7	-	-	ADJ
ap-6106	227	8	dimensional	dimensional	ADJ
ap-6106	227	9	shock	shock	NOUN
ap-6106	227	10	wave	wave	NOUN
ap-6106	227	11	computations	computation	NOUN
ap-6106	227	12	.	.	PUNCT
ap-6106	228	1	journal	journal	NOUN
ap-6106	228	2	of	of	ADP
ap-6106	228	3	computational	computational	ADJ
ap-6106	228	4	physics	physic	NOUN
ap-6106	228	5	144(1):70–97	144(1):70–97	NUM
ap-6106	228	6	,	,	PUNCT
ap-6106	228	7	1998	1998	NUM
ap-6106	228	8	.	.	PUNCT
ap-6106	229	1	doi:10.1006	doi:10.1006	PROPN
ap-6106	229	2	/	/	SYM
ap-6106	229	3	jcph.1998.5989	jcph.1998.5989	PROPN
ap-6106	229	4	.	.	PUNCT
ap-6106	230	1	[	[	X
ap-6106	230	2	3	3	X
ap-6106	230	3	]	]	X
ap-6106	230	4	e.	e.	PROPN
ap-6106	230	5	j.	j.	PROPN
ap-6106	230	6	caramana	caramana	PROPN
ap-6106	230	7	,	,	PUNCT
ap-6106	230	8	m.	m.	PROPN
ap-6106	230	9	j.	j.	PROPN
ap-6106	230	10	shashkov	shashkov	PROPN
ap-6106	230	11	.	.	PUNCT
ap-6106	231	1	elimination	elimination	NOUN
ap-6106	231	2	of	of	ADP
ap-6106	231	3	artificial	artificial	ADJ
ap-6106	231	4	grid	grid	NOUN
ap-6106	231	5	distortion	distortion	NOUN
ap-6106	231	6	and	and	CCONJ
ap-6106	231	7	hourglass	hourglass	NOUN
ap-6106	231	8	-	-	PUNCT
ap-6106	231	9	type	type	NOUN
ap-6106	231	10	motions	motion	NOUN
ap-6106	231	11	by	by	ADP
ap-6106	231	12	means	mean	NOUN
ap-6106	231	13	of	of	ADP
ap-6106	231	14	lagrangian	lagrangian	ADJ
ap-6106	231	15	subzonal	subzonal	ADJ
ap-6106	231	16	masses	masse	NOUN
ap-6106	231	17	and	and	CCONJ
ap-6106	231	18	pressures	pressure	NOUN
ap-6106	231	19	.	.	PUNCT
ap-6106	232	1	journal	journal	NOUN
ap-6106	232	2	of	of	ADP
ap-6106	232	3	computational	computational	ADJ
ap-6106	232	4	physics	physics	NOUN
ap-6106	232	5	142(2):521–561	142(2):521–561	NUM
ap-6106	232	6	,	,	PUNCT
ap-6106	232	7	1998	1998	NUM
ap-6106	232	8	.	.	PUNCT
ap-6106	233	1	doi:10.1006	doi:10.1006	PROPN
ap-6106	233	2	/	/	SYM
ap-6106	233	3	jcph.1998.5952	jcph.1998.5952	NOUN
ap-6106	233	4	.	.	PUNCT
ap-6106	234	1	[	[	X
ap-6106	234	2	4	4	X
ap-6106	234	3	]	]	PUNCT
ap-6106	234	4	j.	j.	PROPN
ap-6106	234	5	vonneumann	vonneumann	PROPN
ap-6106	234	6	,	,	PUNCT
ap-6106	234	7	r.	r.	PROPN
ap-6106	234	8	d.	d.	PROPN
ap-6106	234	9	richtmyer	richtmyer	PROPN
ap-6106	234	10	.	.	PUNCT
ap-6106	235	1	a	a	DET
ap-6106	235	2	method	method	NOUN
ap-6106	235	3	for	for	ADP
ap-6106	235	4	the	the	DET
ap-6106	235	5	numerical	numerical	ADJ
ap-6106	235	6	calculation	calculation	NOUN
ap-6106	235	7	of	of	ADP
ap-6106	235	8	hydrodynamic	hydrodynamic	ADJ
ap-6106	235	9	shocks	shock	NOUN
ap-6106	235	10	.	.	PUNCT
ap-6106	236	1	journal	journal	NOUN
ap-6106	236	2	of	of	ADP
ap-6106	236	3	applied	applied	ADJ
ap-6106	236	4	physics	physics	NOUN
ap-6106	236	5	21(3):232–237	21(3):232–237	PROPN
ap-6106	236	6	,	,	PUNCT
ap-6106	236	7	1950	1950	NUM
ap-6106	236	8	.	.	PUNCT
ap-6106	237	1	doi:10.1063/1.1699639	doi:10.1063/1.1699639	NOUN
ap-6106	237	2	.	.	PUNCT
ap-6106	238	1	[	[	X
ap-6106	238	2	5	5	X
ap-6106	238	3	]	]	PUNCT
ap-6106	238	4	v.	v.	ADP
ap-6106	238	5	a.	a.	PROPN
ap-6106	238	6	dobrev	dobrev	PROPN
ap-6106	238	7	,	,	PUNCT
ap-6106	238	8	tz	tz	PROPN
ap-6106	238	9	.	.	PUNCT
ap-6106	239	1	v.	v.	ADP
ap-6106	239	2	kolev	kolev	NOUN
ap-6106	239	3	,	,	PUNCT
ap-6106	239	4	r.	r.	PROPN
ap-6106	239	5	n.	n.	PROPN
ap-6106	239	6	rieben	rieben	PROPN
ap-6106	239	7	.	.	PUNCT
ap-6106	240	1	high	high	ADJ
ap-6106	240	2	-	-	PUNCT
ap-6106	240	3	order	order	NOUN
ap-6106	240	4	curvilinear	curvilinear	PROPN
ap-6106	240	5	finite	finite	PROPN
ap-6106	240	6	element	element	NOUN
ap-6106	240	7	methods	method	NOUN
ap-6106	240	8	for	for	ADP
ap-6106	240	9	lagrangian	lagrangian	ADJ
ap-6106	240	10	hydrodynamics	hydrodynamic	NOUN
ap-6106	240	11	.	.	PUNCT
ap-6106	241	1	siam	siam	PROPN
ap-6106	241	2	journal	journal	PROPN
ap-6106	241	3	on	on	ADP
ap-6106	241	4	scientific	scientific	ADJ
ap-6106	241	5	computing	computing	NOUN
ap-6106	241	6	34(5):b606	34(5):b606	NUM
ap-6106	241	7	–	–	PUNCT
ap-6106	241	8	b641	b641	PROPN
ap-6106	241	9	,	,	PUNCT
ap-6106	241	10	2012	2012	NUM
ap-6106	241	11	.	.	PUNCT
ap-6106	242	1	doi:10.1137/120864672	doi:10.1137/120864672	NOUN
ap-6106	242	2	.	.	PUNCT
ap-6106	243	1	[	[	X
ap-6106	243	2	6	6	NUM
ap-6106	243	3	]	]	PUNCT
ap-6106	243	4	b.	b.	PROPN
ap-6106	243	5	després	després	PROPN
ap-6106	243	6	,	,	PUNCT
ap-6106	243	7	c.	c.	PROPN
ap-6106	243	8	mazeran	mazeran	PROPN
ap-6106	243	9	.	.	PUNCT
ap-6106	244	1	lagrangian	lagrangian	ADJ
ap-6106	244	2	gas	gas	NOUN
ap-6106	244	3	dynamics	dynamic	NOUN
ap-6106	244	4	in	in	ADP
ap-6106	244	5	two	two	NUM
ap-6106	244	6	dimensions	dimension	NOUN
ap-6106	244	7	and	and	CCONJ
ap-6106	244	8	lagrangian	lagrangian	ADJ
ap-6106	244	9	systems	system	NOUN
ap-6106	244	10	.	.	PUNCT
ap-6106	245	1	archive	archive	NOUN
ap-6106	245	2	for	for	ADP
ap-6106	245	3	rational	rational	ADJ
ap-6106	245	4	mechanics	mechanic	NOUN
ap-6106	245	5	and	and	CCONJ
ap-6106	245	6	analysis	analysis	NOUN
ap-6106	245	7	178(3):327–372	178(3):327–372	NUM
ap-6106	245	8	,	,	PUNCT
ap-6106	245	9	2005	2005	NUM
ap-6106	245	10	.	.	PUNCT
ap-6106	246	1	doi:10.1007	doi:10.1007	NOUN
ap-6106	246	2	/	/	SYM
ap-6106	246	3	s00205	s00205	NOUN
ap-6106	246	4	-	-	PUNCT
ap-6106	246	5	005	005	NUM
ap-6106	246	6	-	-	PUNCT
ap-6106	246	7	0375	0375	NUM
ap-6106	246	8	-	-	SYM
ap-6106	246	9	4	4	NUM
ap-6106	246	10	.	.	PUNCT
ap-6106	247	1	[	[	X
ap-6106	247	2	7	7	NUM
ap-6106	247	3	]	]	X
ap-6106	247	4	p.-h	p.-h	NOUN
ap-6106	247	5	.	.	PUNCT
ap-6106	248	1	maire	maire	PROPN
ap-6106	248	2	,	,	PUNCT
ap-6106	248	3	r.	r.	PROPN
ap-6106	248	4	abgrall	abgrall	PROPN
ap-6106	248	5	,	,	PUNCT
ap-6106	248	6	j.	j.	PROPN
ap-6106	248	7	breil	breil	PROPN
ap-6106	248	8	,	,	PUNCT
ap-6106	248	9	j.	j.	PROPN
ap-6106	248	10	ovadia	ovadia	PROPN
ap-6106	248	11	.	.	PUNCT
ap-6106	249	1	a	a	DET
ap-6106	249	2	cell	cell	NOUN
ap-6106	249	3	-	-	PUNCT
ap-6106	249	4	centered	center	VERB
ap-6106	249	5	lagrangian	lagrangian	ADJ
ap-6106	249	6	scheme	scheme	NOUN
ap-6106	249	7	for	for	ADP
ap-6106	249	8	two	two	NUM
ap-6106	249	9	-	-	PUNCT
ap-6106	249	10	dimensional	dimensional	ADJ
ap-6106	249	11	compressible	compressible	ADJ
ap-6106	249	12	flow	flow	NOUN
ap-6106	249	13	problems	problem	NOUN
ap-6106	249	14	.	.	PUNCT
ap-6106	250	1	siam	siam	PROPN
ap-6106	250	2	journal	journal	PROPN
ap-6106	250	3	on	on	ADP
ap-6106	250	4	scientific	scientific	ADJ
ap-6106	250	5	computing	computing	NOUN
ap-6106	250	6	29(4):1781–1824	29(4):1781–1824	NUM
ap-6106	250	7	,	,	PUNCT
ap-6106	250	8	2007	2007	NUM
ap-6106	250	9	.	.	PUNCT
ap-6106	251	1	doi:10.1137/050633019	doi:10.1137/050633019	ADJ
ap-6106	251	2	.	.	PUNCT
ap-6106	252	1	[	[	X
ap-6106	252	2	8	8	NUM
ap-6106	252	3	]	]	X
ap-6106	252	4	p.-h	p.-h	NOUN
ap-6106	252	5	.	.	PUNCT
ap-6106	253	1	maire	maire	PROPN
ap-6106	253	2	.	.	PUNCT
ap-6106	254	1	a	a	DET
ap-6106	254	2	high	high	ADJ
ap-6106	254	3	-	-	PUNCT
ap-6106	254	4	order	order	NOUN
ap-6106	254	5	cell	cell	NOUN
ap-6106	254	6	-	-	PUNCT
ap-6106	254	7	centered	center	VERB
ap-6106	254	8	lagrangian	lagrangian	ADJ
ap-6106	254	9	scheme	scheme	NOUN
ap-6106	254	10	for	for	ADP
ap-6106	254	11	two	two	NUM
ap-6106	254	12	-	-	PUNCT
ap-6106	254	13	dimensional	dimensional	ADJ
ap-6106	254	14	compressible	compressible	ADJ
ap-6106	254	15	fluid	fluid	NOUN
ap-6106	254	16	flows	flow	NOUN
ap-6106	254	17	on	on	ADP
ap-6106	254	18	unstructured	unstructured	ADJ
ap-6106	254	19	meshes	mesh	NOUN
ap-6106	254	20	.	.	PUNCT
ap-6106	255	1	journal	journal	PROPN
ap-6106	255	2	of	of	ADP
ap-6106	255	3	computational	computational	ADJ
ap-6106	255	4	physics	physics	NOUN
ap-6106	255	5	228(7):2391–2425	228(7):2391–2425	NUM
ap-6106	255	6	,	,	PUNCT
ap-6106	255	7	2009	2009	NUM
ap-6106	255	8	.	.	PUNCT
ap-6106	256	1	doi:10.1016	doi:10.1016	PROPN
ap-6106	256	2	/	/	SYM
ap-6106	256	3	j.jcp.2008.12.007	j.jcp.2008.12.007	ADJ
ap-6106	256	4	.	.	PUNCT
ap-6106	257	1	[	[	X
ap-6106	257	2	9	9	NUM
ap-6106	257	3	]	]	PUNCT
ap-6106	257	4	p.-h	p.-h	NOUN
ap-6106	257	5	.	.	PUNCT
ap-6106	258	1	maire	maire	PROPN
ap-6106	258	2	,	,	PUNCT
ap-6106	258	3	b.	b.	PROPN
ap-6106	258	4	nkonga	nkonga	PROPN
ap-6106	258	5	.	.	PUNCT
ap-6106	259	1	multi	multi	ADJ
ap-6106	259	2	-	-	ADJ
ap-6106	259	3	scale	scale	ADJ
ap-6106	259	4	godunov	godunov	NOUN
ap-6106	259	5	-	-	PUNCT
ap-6106	259	6	type	type	NOUN
ap-6106	259	7	method	method	NOUN
ap-6106	259	8	for	for	ADP
ap-6106	259	9	cell	cell	NOUN
ap-6106	259	10	-	-	PUNCT
ap-6106	259	11	centered	center	VERB
ap-6106	259	12	discrete	discrete	ADJ
ap-6106	259	13	lagrangian	lagrangian	ADJ
ap-6106	259	14	hydrodynamics	hydrodynamic	NOUN
ap-6106	259	15	.	.	PUNCT
ap-6106	260	1	journal	journal	PROPN
ap-6106	260	2	of	of	ADP
ap-6106	260	3	computational	computational	ADJ
ap-6106	260	4	physics	physic	NOUN
ap-6106	260	5	228(3):799–821	228(3):799–821	NUM
ap-6106	260	6	,	,	PUNCT
ap-6106	260	7	2009	2009	NUM
ap-6106	260	8	.	.	PUNCT
ap-6106	261	1	doi:10.1016	doi:10.1016	PROPN
ap-6106	261	2	/	/	SYM
ap-6106	261	3	j.jcp.2008.10.012	j.jcp.2008.10.012	PROPN
ap-6106	261	4	.	.	PUNCT
ap-6106	262	1	[	[	X
ap-6106	262	2	10	10	NUM
ap-6106	262	3	]	]	X
ap-6106	262	4	d.	d.	PROPN
ap-6106	262	5	e.	e.	PROPN
ap-6106	262	6	burton	burton	PROPN
ap-6106	262	7	,	,	PUNCT
ap-6106	262	8	n.	n.	PROPN
ap-6106	262	9	r.	r.	PROPN
ap-6106	262	10	morgan	morgan	PROPN
ap-6106	262	11	,	,	PUNCT
ap-6106	262	12	t.	t.	PROPN
ap-6106	262	13	c.	c.	PROPN
ap-6106	262	14	carney	carney	PROPN
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ap-6106	262	16	m.	m.	NOUN
ap-6106	262	17	a.	a.	NOUN
ap-6106	262	18	kenamond	kenamond	PROPN
ap-6106	262	19	.	.	PUNCT
ap-6106	263	1	reduction	reduction	NOUN
ap-6106	263	2	of	of	ADP
ap-6106	263	3	dissipation	dissipation	NOUN
ap-6106	263	4	in	in	ADP
ap-6106	263	5	lagrange	lagrange	PROPN
ap-6106	263	6	cellcentered	cellcentere	VERB
ap-6106	263	7	hydrodynamics	hydrodynamic	NOUN
ap-6106	263	8	(	(	PUNCT
ap-6106	263	9	cch	cch	NOUN
ap-6106	263	10	)	)	PUNCT
ap-6106	263	11	through	through	ADP
ap-6106	263	12	corner	corner	NOUN
ap-6106	263	13	gradient	gradient	NOUN
ap-6106	263	14	reconstruction	reconstruction	NOUN
ap-6106	263	15	(	(	PUNCT
ap-6106	263	16	cgr	cgr	PROPN
ap-6106	263	17	)	)	PUNCT
ap-6106	263	18	.	.	PUNCT
ap-6106	264	1	journal	journal	PROPN
ap-6106	264	2	of	of	ADP
ap-6106	264	3	computational	computational	ADJ
ap-6106	264	4	physics	physic	NOUN
ap-6106	264	5	299:229–280	299:229–280	NUM
ap-6106	264	6	,	,	PUNCT
ap-6106	264	7	2015	2015	NUM
ap-6106	264	8	.	.	PUNCT
ap-6106	265	1	doi:10.1016	doi:10.1016	PROPN
ap-6106	265	2	/	/	SYM
ap-6106	265	3	j.jcp.2015.06.041	j.jcp.2015.06.041	PROPN
ap-6106	265	4	.	.	PUNCT
ap-6106	266	1	[	[	X
ap-6106	266	2	11	11	NUM
ap-6106	266	3	]	]	PUNCT
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ap-6106	266	5	cheng	cheng	PROPN
ap-6106	266	6	,	,	PUNCT
ap-6106	266	7	c.-w	c.-w	PROPN
ap-6106	266	8	.	.	PUNCT
ap-6106	267	1	shu	shu	PROPN
ap-6106	267	2	.	.	PUNCT
ap-6106	268	1	positivity	positivity	NOUN
ap-6106	268	2	-	-	PUNCT
ap-6106	268	3	preserving	preserve	VERB
ap-6106	268	4	lagrangian	lagrangian	ADJ
ap-6106	268	5	scheme	scheme	NOUN
ap-6106	268	6	for	for	ADP
ap-6106	268	7	multi	multi	ADJ
ap-6106	268	8	-	-	ADJ
ap-6106	268	9	material	material	ADJ
ap-6106	268	10	compressible	compressible	ADJ
ap-6106	268	11	flow	flow	NOUN
ap-6106	268	12	.	.	PUNCT
ap-6106	269	1	journal	journal	NOUN
ap-6106	269	2	of	of	ADP
ap-6106	269	3	computational	computational	ADJ
ap-6106	269	4	physics	physics	NOUN
ap-6106	269	5	257(a):143–168	257(a):143–168	PROPN
ap-6106	269	6	,	,	PUNCT
ap-6106	269	7	2014	2014	NUM
ap-6106	269	8	.	.	PUNCT
ap-6106	270	1	doi:10.1016	doi:10.1016	PROPN
ap-6106	270	2	/	/	SYM
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ap-6106	270	4	.	.	PUNCT
ap-6106	271	1	[	[	X
ap-6106	271	2	12	12	NUM
ap-6106	271	3	]	]	X
ap-6106	271	4	w.	w.	PROPN
ap-6106	271	5	boscheri	boscheri	PROPN
ap-6106	271	6	,	,	PUNCT
ap-6106	271	7	m.	m.	NOUN
ap-6106	271	8	dumbser	dumbser	PROPN
ap-6106	271	9	,	,	PUNCT
ap-6106	271	10	r.	r.	PROPN
ap-6106	271	11	loubere	loubere	PROPN
ap-6106	271	12	,	,	PUNCT
ap-6106	271	13	p.-h	p.-h	PROPN
ap-6106	271	14	.	.	PUNCT
ap-6106	272	1	maire	maire	PROPN
ap-6106	272	2	.	.	PUNCT
ap-6106	273	1	a	a	DET
ap-6106	273	2	second	second	ADJ
ap-6106	273	3	-	-	PUNCT
ap-6106	273	4	order	order	NOUN
ap-6106	273	5	cell	cell	NOUN
ap-6106	273	6	-	-	PUNCT
ap-6106	273	7	centered	center	VERB
ap-6106	273	8	lagrangian	lagrangian	ADJ
ap-6106	273	9	ader	ader	NOUN
ap-6106	273	10	-	-	PUNCT
ap-6106	273	11	mood	mood	NOUN
ap-6106	273	12	finite	finite	ADJ
ap-6106	273	13	volume	volume	NOUN
ap-6106	273	14	scheme	scheme	NOUN
ap-6106	273	15	on	on	ADP
ap-6106	273	16	multidimensional	multidimensional	ADJ
ap-6106	273	17	unstructured	unstructured	ADJ
ap-6106	273	18	meshes	mesh	NOUN
ap-6106	273	19	for	for	ADP
ap-6106	273	20	hydrodynamics	hydrodynamic	NOUN
ap-6106	273	21	.	.	PUNCT
ap-6106	274	1	journal	journal	PROPN
ap-6106	274	2	of	of	ADP
ap-6106	274	3	computational	computational	ADJ
ap-6106	274	4	physics	physic	NOUN
ap-6106	274	5	358:103–129	358:103–129	NUM
ap-6106	274	6	,	,	PUNCT
ap-6106	274	7	2018	2018	NUM
ap-6106	274	8	.	.	PUNCT
ap-6106	275	1	doi:10.1016	doi:10.1016	PROPN
ap-6106	275	2	/	/	SYM
ap-6106	275	3	j.jcp.2017.12.040	j.jcp.2017.12.040	PROPN
ap-6106	275	4	.	.	PUNCT
ap-6106	276	1	[	[	X
ap-6106	276	2	13	13	NUM
ap-6106	276	3	]	]	X
ap-6106	276	4	d.	d.	PROPN
ap-6106	276	5	fridrich	fridrich	PROPN
ap-6106	276	6	,	,	PUNCT
ap-6106	276	7	r.	r.	PROPN
ap-6106	276	8	liska	liska	PROPN
ap-6106	276	9	,	,	PUNCT
ap-6106	276	10	b.	b.	PROPN
ap-6106	276	11	wendroff	wendroff	PROPN
ap-6106	276	12	.	.	PUNCT
ap-6106	277	1	some	some	DET
ap-6106	277	2	cell	cell	NOUN
ap-6106	277	3	-	-	PUNCT
ap-6106	277	4	centered	center	VERB
ap-6106	277	5	lagrangian	lagrangian	ADJ
ap-6106	277	6	lax	lax	NOUN
ap-6106	277	7	-	-	PUNCT
ap-6106	277	8	wendroff	wendroff	NOUN
ap-6106	277	9	hll	hll	PROPN
ap-6106	277	10	hybrid	hybrid	ADJ
ap-6106	277	11	schemes	scheme	NOUN
ap-6106	277	12	.	.	PUNCT
ap-6106	278	1	journal	journal	NOUN
ap-6106	278	2	of	of	ADP
ap-6106	278	3	computational	computational	ADJ
ap-6106	278	4	physics	physic	NOUN
ap-6106	278	5	326:878–892	326:878–892	NUM
ap-6106	278	6	,	,	PUNCT
ap-6106	278	7	2016	2016	NUM
ap-6106	278	8	.	.	PUNCT
ap-6106	279	1	doi:10.1016	doi:10.1016	PROPN
ap-6106	279	2	/	/	SYM
ap-6106	279	3	j.jcp.2016.09.022	j.jcp.2016.09.022	PROPN
ap-6106	279	4	.	.	PUNCT
ap-6106	280	1	[	[	X
ap-6106	280	2	14	14	NUM
ap-6106	280	3	]	]	PUNCT
ap-6106	280	4	a.	a.	NOUN
ap-6106	280	5	harten	harten	PROPN
ap-6106	280	6	,	,	PUNCT
ap-6106	280	7	p.	p.	PROPN
ap-6106	280	8	d.	d.	PROPN
ap-6106	280	9	lax	lax	PROPN
ap-6106	280	10	,	,	PUNCT
ap-6106	280	11	b.	b.	PROPN
ap-6106	280	12	van	van	PROPN
ap-6106	280	13	leer	leer	PROPN
ap-6106	280	14	.	.	PUNCT
ap-6106	281	1	on	on	ADP
ap-6106	281	2	upstream	upstream	ADJ
ap-6106	281	3	differencing	differencing	NOUN
ap-6106	281	4	and	and	CCONJ
ap-6106	281	5	godunov	godunov	NOUN
ap-6106	281	6	-	-	PUNCT
ap-6106	281	7	type	type	NOUN
ap-6106	281	8	schemes	scheme	NOUN
ap-6106	281	9	for	for	ADP
ap-6106	281	10	hyperbolic	hyperbolic	ADJ
ap-6106	281	11	conservation	conservation	NOUN
ap-6106	281	12	laws	law	NOUN
ap-6106	281	13	.	.	PUNCT
ap-6106	282	1	siam	siam	PROPN
ap-6106	282	2	review	review	NOUN
ap-6106	282	3	25(1):35–61	25(1):35–61	NUM
ap-6106	282	4	,	,	PUNCT
ap-6106	282	5	1983	1983	NUM
ap-6106	282	6	.	.	PUNCT
ap-6106	283	1	doi:10.1137/1025002	doi:10.1137/1025002	NOUN
ap-6106	283	2	.	.	PUNCT
ap-6106	284	1	[	[	X
ap-6106	284	2	15	15	NUM
ap-6106	284	3	]	]	X
ap-6106	284	4	r.	r.	NOUN
ap-6106	284	5	loubère	loubère	PROPN
ap-6106	284	6	,	,	PUNCT
ap-6106	284	7	m.	m.	NOUN
ap-6106	284	8	shashkov	shashkov	PROPN
ap-6106	284	9	.	.	PUNCT
ap-6106	285	1	a	a	DET
ap-6106	285	2	subcell	subcell	NOUN
ap-6106	285	3	remapping	remapping	NOUN
ap-6106	285	4	method	method	NOUN
ap-6106	285	5	on	on	ADP
ap-6106	285	6	staggered	staggered	ADJ
ap-6106	285	7	polygonal	polygonal	ADJ
ap-6106	285	8	grids	grid	NOUN
ap-6106	285	9	for	for	ADP
ap-6106	285	10	arbitrary	arbitrary	ADJ
ap-6106	285	11	-	-	PUNCT
ap-6106	285	12	lagrangian	lagrangian	ADJ
ap-6106	285	13	-	-	PUNCT
ap-6106	285	14	eulerian	eulerian	ADJ
ap-6106	285	15	methods	method	NOUN
ap-6106	285	16	.	.	PUNCT
ap-6106	286	1	journal	journal	NOUN
ap-6106	286	2	of	of	ADP
ap-6106	286	3	computational	computational	ADJ
ap-6106	286	4	physics	physics	NOUN
ap-6106	286	5	209(1):105–138	209(1):105–138	PROPN
ap-6106	286	6	,	,	PUNCT
ap-6106	286	7	2005	2005	NUM
ap-6106	286	8	.	.	PUNCT
ap-6106	287	1	doi:10.1016	doi:10.1016	PROPN
ap-6106	287	2	/	/	SYM
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ap-6106	287	4	.	.	PUNCT
ap-6106	288	1	[	[	X
ap-6106	288	2	16	16	NUM
ap-6106	288	3	]	]	PUNCT
ap-6106	288	4	r.	r.	PROPN
ap-6106	288	5	d.	d.	PROPN
ap-6106	288	6	richtmyer	richtmyer	PROPN
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ap-6106	289	1	a	a	DET
ap-6106	289	2	survey	survey	NOUN
ap-6106	289	3	of	of	ADP
ap-6106	289	4	difference	difference	NOUN
ap-6106	289	5	methods	method	NOUN
ap-6106	289	6	for	for	ADP
ap-6106	289	7	non	non	ADJ
ap-6106	289	8	-	-	ADJ
ap-6106	289	9	steady	steady	ADJ
ap-6106	289	10	fluid	fluid	ADJ
ap-6106	289	11	dynamics	dynamic	NOUN
ap-6106	289	12	.	.	PUNCT
ap-6106	290	1	ncar	ncar	NOUN
ap-6106	290	2	technical	technical	ADJ
ap-6106	290	3	notes	note	NOUN
ap-6106	290	4	63	63	NUM
ap-6106	290	5	-	-	SYM
ap-6106	290	6	2	2	NUM
ap-6106	290	7	,	,	PUNCT
ap-6106	290	8	national	national	ADJ
ap-6106	290	9	center	center	NOUN
ap-6106	290	10	for	for	ADP
ap-6106	290	11	atmospheric	atmospheric	ADJ
ap-6106	290	12	research	research	NOUN
ap-6106	290	13	,	,	PUNCT
ap-6106	290	14	boulder	boulder	NOUN
ap-6106	290	15	,	,	PUNCT
ap-6106	290	16	colorado	colorado	PROPN
ap-6106	290	17	,	,	PUNCT
ap-6106	290	18	1962	1962	NUM
ap-6106	290	19	.	.	PUNCT
ap-6106	291	1	doi:10.5065	doi:10.5065	PROPN
ap-6106	291	2	/	/	SYM
ap-6106	291	3	d67p8wcq	d67p8wcq	NOUN
ap-6106	291	4	.	.	PUNCT
ap-6106	292	1	[	[	X
ap-6106	292	2	17	17	NUM
ap-6106	292	3	]	]	X
ap-6106	292	4	b.	b.	PROPN
ap-6106	292	5	wendroff	wendroff	PROPN
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ap-6106	292	7	a.	a.	PROPN
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ap-6106	292	10	.	.	PUNCT
ap-6106	293	1	a	a	DET
ap-6106	293	2	supraconvergent	supraconvergent	ADJ
ap-6106	293	3	scheme	scheme	NOUN
ap-6106	293	4	for	for	ADP
ap-6106	293	5	nonlinear	nonlinear	ADJ
ap-6106	293	6	hyperbolic	hyperbolic	ADJ
ap-6106	293	7	systems	system	NOUN
ap-6106	293	8	.	.	PUNCT
ap-6106	294	1	computers	computer	NOUN
ap-6106	294	2	&	&	CCONJ
ap-6106	294	3	mathematics	mathematics	PROPN
ap-6106	294	4	with	with	ADP
ap-6106	294	5	applications	application	NOUN
ap-6106	294	6	18(8):761–767	18(8):761–767	NOUN
ap-6106	294	7	,	,	PUNCT
ap-6106	294	8	1989	1989	NUM
ap-6106	294	9	.	.	PUNCT
ap-6106	295	1	doi:10.1016/0898	doi:10.1016/0898	PROPN
ap-6106	295	2	-	-	PUNCT
ap-6106	295	3	1221(89)90232	1221(89)90232	PROPN
ap-6106	295	4	-	-	PUNCT
ap-6106	295	5	0	0	NUM
ap-6106	295	6	.	.	PUNCT
ap-6106	296	1	[	[	X
ap-6106	296	2	18	18	NUM
ap-6106	296	3	]	]	X
ap-6106	296	4	j.	j.	PROPN
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ap-6106	296	13	m.	m.	NOUN
ap-6106	296	14	shashkov	shashkov	PROPN
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ap-6106	297	1	shapo	shapo	PROPN
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ap-6106	297	3	advances	advance	NOUN
ap-6106	297	4	on	on	ADP
ap-6106	297	5	the	the	DET
ap-6106	297	6	voronoi	voronoi	ADJ
ap-6106	297	7	mesh	mesh	NOUN
ap-6106	297	8	generation	generation	NOUN
ap-6106	297	9	toolkit	toolkit	NOUN
ap-6106	297	10	.	.	PUNCT
ap-6106	297	11	presented	present	VERB
ap-6106	297	12	at	at	ADP
ap-6106	297	13	the	the	DET
ap-6106	297	14	9	9	NUM
ap-6106	297	15	-	-	PUNCT
ap-6106	297	16	th	th	X
ap-6106	297	17	international	international	ADJ
ap-6106	297	18	conference	conference	NOUN
ap-6106	297	19	on	on	ADP
ap-6106	297	20	numerical	numerical	ADJ
ap-6106	297	21	methods	method	NOUN
ap-6106	297	22	for	for	ADP
ap-6106	297	23	multi	multi	ADJ
ap-6106	297	24	-	-	ADJ
ap-6106	297	25	material	material	ADJ
ap-6106	297	26	fluid	fluid	NOUN
ap-6106	297	27	flow	flow	NOUN
ap-6106	297	28	(	(	PUNCT
ap-6106	297	29	multimat	multimat	NOUN
ap-6106	297	30	2019	2019	NUM
ap-6106	297	31	)	)	PUNCT
ap-6106	297	32	,	,	PUNCT
ap-6106	297	33	trento	trento	PROPN
ap-6106	297	34	,	,	PUNCT
ap-6106	297	35	italy	italy	PROPN
ap-6106	297	36	,	,	PUNCT
ap-6106	297	37	september	september	PROPN
ap-6106	297	38	9	9	NUM
ap-6106	297	39	-	-	SYM
ap-6106	297	40	13	13	NUM
ap-6106	297	41	,	,	PUNCT
ap-6106	297	42	2019	2019	NUM
ap-6106	297	43	.	.	PUNCT
ap-6106	298	1	[	[	X
ap-6106	298	2	19	19	NUM
ap-6106	298	3	]	]	X
ap-6106	298	4	w.	w.	PROPN
ap-6106	298	5	f.	f.	PROPN
ap-6106	298	6	noh	noh	PROPN
ap-6106	298	7	.	.	PUNCT
ap-6106	299	1	errors	error	NOUN
ap-6106	299	2	for	for	ADP
ap-6106	299	3	calculations	calculation	NOUN
ap-6106	299	4	of	of	ADP
ap-6106	299	5	strong	strong	ADJ
ap-6106	299	6	shocks	shock	NOUN
ap-6106	299	7	using	use	VERB
ap-6106	299	8	an	an	DET
ap-6106	299	9	artificial	artificial	ADJ
ap-6106	299	10	viscosity	viscosity	NOUN
ap-6106	299	11	and	and	CCONJ
ap-6106	299	12	artificial	artificial	ADJ
ap-6106	299	13	heat	heat	NOUN
ap-6106	299	14	flux	flux	NOUN
ap-6106	299	15	.	.	PUNCT
ap-6106	300	1	journal	journal	PROPN
ap-6106	300	2	of	of	ADP
ap-6106	300	3	computational	computational	ADJ
ap-6106	300	4	physics	physic	NOUN
ap-6106	300	5	72(1):78–120	72(1):78–120	NUM
ap-6106	300	6	,	,	PUNCT
ap-6106	300	7	1987	1987	NUM
ap-6106	300	8	.	.	PUNCT
ap-6106	301	1	doi:10.1016/0021	doi:10.1016/0021	PROPN
ap-6106	301	2	-	-	PUNCT
ap-6106	301	3	9991(87)90074	9991(87)90074	NOUN
ap-6106	301	4	-	-	NOUN
ap-6106	301	5	x.	x.	NOUN
ap-6106	302	1	[	[	X
ap-6106	302	2	20	20	NUM
ap-6106	302	3	]	]	PUNCT
ap-6106	302	4	l.	l.	PROPN
ap-6106	302	5	i.	i.	PROPN
ap-6106	302	6	sedov	sedov	PROPN
ap-6106	302	7	.	.	PUNCT
ap-6106	303	1	similarity	similarity	NOUN
ap-6106	303	2	and	and	CCONJ
ap-6106	303	3	dimensional	dimensional	ADJ
ap-6106	303	4	methods	method	NOUN
ap-6106	303	5	in	in	ADP
ap-6106	303	6	mechanics	mechanic	NOUN
ap-6106	303	7	.	.	PUNCT
ap-6106	304	1	academic	academic	ADJ
ap-6106	304	2	press	press	NOUN
ap-6106	304	3	,	,	PUNCT
ap-6106	304	4	new	new	PROPN
ap-6106	304	5	york	york	PROPN
ap-6106	304	6	,	,	PUNCT
ap-6106	304	7	1959	1959	NUM
ap-6106	304	8	.	.	PUNCT
ap-6106	305	1	[	[	X
ap-6106	305	2	21	21	NUM
ap-6106	305	3	]	]	X
ap-6106	305	4	j.	j.	PROPN
ap-6106	305	5	r.	r.	PROPN
ap-6106	305	6	kamm	kamm	PROPN
ap-6106	305	7	,	,	PUNCT
ap-6106	305	8	f.	f.	PROPN
ap-6106	305	9	x.	x.	PROPN
ap-6106	305	10	timmes	timmes	PROPN
ap-6106	305	11	.	.	PUNCT
ap-6106	305	12	cococubed	cococube	VERB
ap-6106	305	13	.	.	PUNCT
ap-6106	306	1	sedov	sedov	PROPN
ap-6106	306	2	verification	verification	PROPN
ap-6106	306	3	code	code	PROPN
ap-6106	306	4	.	.	PUNCT
ap-6106	307	1	la	la	ADJ
ap-6106	307	2	-	-	PUNCT
ap-6106	307	3	cc-07	cc-07	NUM
ap-6106	307	4	-	-	PUNCT
ap-6106	307	5	020	020	NUM
ap-6106	307	6	,	,	PUNCT
ap-6106	307	7	2007	2007	NUM
ap-6106	307	8	.	.	PUNCT
ap-6106	308	1	http	http	ADJ
ap-6106	308	2	:	:	PUNCT
ap-6106	308	3	//cococubed.asu.edu	//cococubed.asu.edu	PUNCT
ap-6106	308	4	/	/	SYM
ap-6106	308	5	research_pages	research_page	NOUN
ap-6106	308	6	/	/	SYM
ap-6106	308	7	sedov.shtml	sedov.shtml	PROPN
ap-6106	308	8	.	.	PUNCT
ap-6106	309	1	76	76	NUM
ap-6106	309	2	http://dx.doi.org/10.1006/jcph.1998.6029	http://dx.doi.org/10.1006/jcph.1998.6029	NOUN
ap-6106	309	3	http://dx.doi.org/10.1006/jcph.1998.5989	http://dx.doi.org/10.1006/jcph.1998.5989	ADJ
ap-6106	309	4	http://dx.doi.org/10.1006/jcph.1998.5952	http://dx.doi.org/10.1006/jcph.1998.5952	NOUN
ap-6106	309	5	http://dx.doi.org/10.1063/1.1699639	http://dx.doi.org/10.1063/1.1699639	PROPN
ap-6106	309	6	http://dx.doi.org/10.1137/120864672	http://dx.doi.org/10.1137/120864672	VERB
ap-6106	309	7	http://dx.doi.org/10.1007/s00205-005-0375-4	http://dx.doi.org/10.1007/s00205-005-0375-4	X
ap-6106	309	8	http://dx.doi.org/10.1137/050633019	http://dx.doi.org/10.1137/050633019	X
ap-6106	309	9	http://dx.doi.org/10.1016/j.jcp.2008.12.007	http://dx.doi.org/10.1016/j.jcp.2008.12.007	VERB
ap-6106	309	10	http://dx.doi.org/10.1016/j.jcp.2008.10.012	http://dx.doi.org/10.1016/j.jcp.2008.10.012	NOUN
ap-6106	309	11	http://dx.doi.org/10.1016/j.jcp.2015.06.041	http://dx.doi.org/10.1016/j.jcp.2015.06.041	VERB
ap-6106	309	12	http://dx.doi.org/10.1016/j.jcp.2013.09.047	http://dx.doi.org/10.1016/j.jcp.2013.09.047	NOUN
ap-6106	309	13	http://dx.doi.org/{10.1016/j.jcp.2017.12.040	http://dx.doi.org/{10.1016/j.jcp.2017.12.040	NOUN
ap-6106	309	14	}	}	PUNCT
ap-6106	309	15	http://dx.doi.org/10.1016/j.jcp.2016.09.022	http://dx.doi.org/10.1016/j.jcp.2016.09.022	NOUN
ap-6106	309	16	http://dx.doi.org/10.1137/1025002	http://dx.doi.org/10.1137/1025002	ADJ
ap-6106	309	17	http://dx.doi.org/10.1016/j.jcp.2005.03.019	http://dx.doi.org/10.1016/j.jcp.2005.03.019	PROPN
ap-6106	309	18	http://dx.doi.org/10.5065/d67p8wcq	http://dx.doi.org/10.5065/d67p8wcq	PROPN
ap-6106	309	19	http://dx.doi.org/10.1016/0898-1221(89)90232-0	http://dx.doi.org/10.1016/0898-1221(89)90232-0	PRON
ap-6106	309	20	http://dx.doi.org/10.1016/0021-9991(87)90074-x	http://dx.doi.org/10.1016/0021-9991(87)90074-x	ADV
ap-6106	309	21	http://cococubed.asu.edu/research_pages/sedov.shtml	http://cococubed.asu.edu/research_pages/sedov.shtml	X
ap-6106	309	22	http://cococubed.asu.edu/research_pages/sedov.shtml	http://cococubed.asu.edu/research_pages/sedov.shtml	PROPN
ap-6106	309	23	acta	acta	PROPN
ap-6106	309	24	polytechnica	polytechnica	PROPN
ap-6106	309	25	61(si):68–76	61(si):68–76	NUM
ap-6106	309	26	,	,	PUNCT
ap-6106	309	27	2021	2021	NUM
ap-6106	309	28	1	1	NUM
ap-6106	309	29	introduction	introduction	NOUN
ap-6106	309	30	2	2	NUM
ap-6106	309	31	lagrangian	lagrangian	ADJ
ap-6106	309	32	finite	finite	ADJ
ap-6106	309	33	volume	volume	NOUN
ap-6106	309	34	3	3	NUM
ap-6106	309	35	meshes	mesh	VERB
ap-6106	309	36	4	4	NUM
ap-6106	309	37	schemes	scheme	NOUN
ap-6106	309	38	4.1	4.1	NUM
ap-6106	309	39	predictor	predictor	NOUN
ap-6106	309	40	4.2	4.2	NUM
ap-6106	309	41	corrector	corrector	NOUN
ap-6106	309	42	4.3	4.3	NUM
ap-6106	309	43	mesh	mesh	NOUN
ap-6106	309	44	positions	position	NOUN
ap-6106	309	45	update	update	VERB
ap-6106	309	46	4.4	4.4	NUM
ap-6106	309	47	artificial	artificial	ADJ
ap-6106	309	48	dissipation	dissipation	NOUN
ap-6106	309	49	5	5	NUM
ap-6106	309	50	numerical	numerical	ADJ
ap-6106	309	51	results	result	NOUN
ap-6106	309	52	5.1	5.1	NUM
ap-6106	309	53	time	time	NOUN
ap-6106	309	54	step	step	NOUN
ap-6106	309	55	control	control	NOUN
ap-6106	309	56	5.2	5.2	NUM
ap-6106	309	57	noh	noh	PROPN
ap-6106	309	58	problem	problem	NOUN
ap-6106	309	59	5.3	5.3	NUM
ap-6106	309	60	sedov	sedov	PROPN
ap-6106	309	61	problem	problem	VERB
ap-6106	309	62	5.4	5.4	NUM
ap-6106	309	63	smooth	smooth	ADJ
ap-6106	309	64	expansion	expansion	NOUN
ap-6106	309	65	problem	problem	NOUN
ap-6106	309	66	6	6	NUM
ap-6106	309	67	conclusions	conclusion	NOUN
ap-6106	309	68	acknowledgements	acknowledgement	NOUN
ap-6106	309	69	references	reference	NOUN