id	sid	tid	token	lemma	pos
ap-3989	1	1	acta	acta	PROPN
ap-3989	1	2	polytechnica	polytechnica	PROPN
ap-3989	1	3	doi:10.14311	doi:10.14311	PROPN
ap-3989	1	4	/	/	SYM
ap-3989	1	5	ap.2017.57.0245	ap.2017.57.0245	PROPN
ap-3989	1	6	acta	acta	PROPN
ap-3989	1	7	polytechnica	polytechnica	PROPN
ap-3989	1	8	57(4):245–251	57(4):245–251	PROPN
ap-3989	1	9	,	,	PUNCT
ap-3989	1	10	2017	2017	NUM
ap-3989	1	11	©	©	PROPN
ap-3989	1	12	czech	czech	PROPN
ap-3989	1	13	technical	technical	PROPN
ap-3989	1	14	university	university	PROPN
ap-3989	1	15	in	in	ADP
ap-3989	1	16	prague	prague	PROPN
ap-3989	1	17	,	,	PUNCT
ap-3989	1	18	2017	2017	NUM
ap-3989	1	19	available	available	ADJ
ap-3989	1	20	online	online	ADV
ap-3989	1	21	at	at	ADP
ap-3989	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3989	1	23	fictitious	fictitious	ADJ
ap-3989	1	24	domain	domain	NOUN
ap-3989	1	25	method	method	NOUN
ap-3989	1	26	for	for	ADP
ap-3989	1	27	numerical	numerical	ADJ
ap-3989	1	28	simulation	simulation	NOUN
ap-3989	1	29	of	of	ADP
ap-3989	1	30	incompressible	incompressible	ADJ
ap-3989	1	31	viscous	viscous	ADJ
ap-3989	1	32	flow	flow	NOUN
ap-3989	1	33	around	around	ADP
ap-3989	1	34	rigid	rigid	ADJ
ap-3989	1	35	bodies	body	NOUN
ap-3989	1	36	matej	matej	PROPN
ap-3989	1	37	beňo∗	beňo∗	PROPN
ap-3989	1	38	,	,	PUNCT
ap-3989	1	39	bořek	bořek	NOUN
ap-3989	1	40	patzák	patzák	VERB
ap-3989	1	41	czech	czech	PROPN
ap-3989	1	42	technical	technical	PROPN
ap-3989	1	43	university	university	PROPN
ap-3989	1	44	in	in	ADP
ap-3989	1	45	prague	prague	PROPN
ap-3989	1	46	,	,	PUNCT
ap-3989	1	47	faculty	faculty	NOUN
ap-3989	1	48	of	of	ADP
ap-3989	1	49	civil	civil	ADJ
ap-3989	1	50	engineering	engineering	NOUN
ap-3989	1	51	,	,	PUNCT
ap-3989	1	52	department	department	NOUN
ap-3989	1	53	of	of	ADP
ap-3989	1	54	mechanics	mechanic	NOUN
ap-3989	1	55	,	,	PUNCT
ap-3989	1	56	thákurova	thákurova	X
ap-3989	1	57	7	7	NUM
ap-3989	1	58	,	,	PUNCT
ap-3989	1	59	166	166	NUM
ap-3989	1	60	29	29	NUM
ap-3989	1	61	prague	prague	NOUN
ap-3989	1	62	,	,	PUNCT
ap-3989	1	63	czech	czech	PROPN
ap-3989	1	64	republic	republic	NOUN
ap-3989	1	65	∗	∗	NOUN
ap-3989	1	66	corresponding	correspond	VERB
ap-3989	1	67	author	author	NOUN
ap-3989	1	68	:	:	PUNCT
ap-3989	1	69	matej.beno@fsv.cvut.cz	matej.beno@fsv.cvut.cz	NOUN
ap-3989	1	70	abstract	abstract	NOUN
ap-3989	1	71	.	.	PUNCT
ap-3989	2	1	this	this	DET
ap-3989	2	2	article	article	NOUN
ap-3989	2	3	describes	describe	VERB
ap-3989	2	4	the	the	DET
ap-3989	2	5	method	method	NOUN
ap-3989	2	6	of	of	ADP
ap-3989	2	7	efficient	efficient	ADJ
ap-3989	2	8	simulation	simulation	NOUN
ap-3989	2	9	of	of	ADP
ap-3989	2	10	the	the	DET
ap-3989	2	11	flow	flow	NOUN
ap-3989	2	12	around	around	ADP
ap-3989	2	13	potentially	potentially	ADV
ap-3989	2	14	many	many	ADJ
ap-3989	2	15	rigid	rigid	ADJ
ap-3989	2	16	obstacles	obstacle	NOUN
ap-3989	2	17	.	.	PUNCT
ap-3989	3	1	the	the	DET
ap-3989	3	2	finite	finite	PROPN
ap-3989	3	3	element	element	NOUN
ap-3989	3	4	implementation	implementation	NOUN
ap-3989	3	5	is	be	AUX
ap-3989	3	6	based	base	VERB
ap-3989	3	7	on	on	ADP
ap-3989	3	8	the	the	DET
ap-3989	3	9	incompressible	incompressible	ADJ
ap-3989	3	10	navier	navier	NOUN
ap-3989	3	11	-	-	PUNCT
ap-3989	3	12	stokes	stoke	NOUN
ap-3989	3	13	equations	equation	NOUN
ap-3989	3	14	using	use	VERB
ap-3989	3	15	structured	structure	VERB
ap-3989	3	16	,	,	PUNCT
ap-3989	3	17	regular	regular	ADJ
ap-3989	3	18	,	,	PUNCT
ap-3989	3	19	two	two	NUM
ap-3989	3	20	dimensional	dimensional	ADJ
ap-3989	3	21	triangular	triangular	NOUN
ap-3989	3	22	mesh	mesh	NOUN
ap-3989	3	23	.	.	PUNCT
ap-3989	4	1	the	the	DET
ap-3989	4	2	fictitious	fictitious	ADJ
ap-3989	4	3	domain	domain	NOUN
ap-3989	4	4	method	method	NOUN
ap-3989	4	5	is	be	AUX
ap-3989	4	6	introduced	introduce	VERB
ap-3989	4	7	to	to	PART
ap-3989	4	8	account	account	VERB
ap-3989	4	9	for	for	ADP
ap-3989	4	10	the	the	DET
ap-3989	4	11	presence	presence	NOUN
ap-3989	4	12	of	of	ADP
ap-3989	4	13	rigid	rigid	ADJ
ap-3989	4	14	particles	particle	NOUN
ap-3989	4	15	,	,	PUNCT
ap-3989	4	16	representing	represent	VERB
ap-3989	4	17	obstacles	obstacle	NOUN
ap-3989	4	18	to	to	ADP
ap-3989	4	19	the	the	DET
ap-3989	4	20	flow	flow	NOUN
ap-3989	4	21	.	.	PUNCT
ap-3989	5	1	to	to	PART
ap-3989	5	2	enforce	enforce	VERB
ap-3989	5	3	rigid	rigid	ADJ
ap-3989	5	4	body	body	NOUN
ap-3989	5	5	constraints	constraint	NOUN
ap-3989	5	6	in	in	ADP
ap-3989	5	7	parts	part	NOUN
ap-3989	5	8	corresponding	correspond	VERB
ap-3989	5	9	to	to	ADP
ap-3989	5	10	rigid	rigid	ADJ
ap-3989	5	11	obstacles	obstacle	NOUN
ap-3989	5	12	,	,	PUNCT
ap-3989	5	13	lagrange	lagrange	NOUN
ap-3989	5	14	multipliers	multiplier	NOUN
ap-3989	5	15	are	be	AUX
ap-3989	5	16	used	use	VERB
ap-3989	5	17	.	.	PUNCT
ap-3989	6	1	for	for	ADP
ap-3989	6	2	time	time	NOUN
ap-3989	6	3	discretization	discretization	NOUN
ap-3989	6	4	,	,	PUNCT
ap-3989	6	5	an	an	DET
ap-3989	6	6	operator	operator	NOUN
ap-3989	6	7	splitting	splitting	NOUN
ap-3989	6	8	technique	technique	NOUN
ap-3989	6	9	is	be	AUX
ap-3989	6	10	used	use	VERB
ap-3989	6	11	.	.	PUNCT
ap-3989	7	1	the	the	DET
ap-3989	7	2	model	model	NOUN
ap-3989	7	3	is	be	AUX
ap-3989	7	4	validated	validate	VERB
ap-3989	7	5	using	use	VERB
ap-3989	7	6	2d	2d	NUM
ap-3989	7	7	channel	channel	NOUN
ap-3989	7	8	flow	flow	NOUN
ap-3989	7	9	simulations	simulation	NOUN
ap-3989	7	10	with	with	ADP
ap-3989	7	11	circular	circular	ADJ
ap-3989	7	12	obstacles	obstacle	NOUN
ap-3989	7	13	.	.	PUNCT
ap-3989	8	1	different	different	ADJ
ap-3989	8	2	possibilities	possibility	NOUN
ap-3989	8	3	of	of	ADP
ap-3989	8	4	enforcing	enforce	VERB
ap-3989	8	5	rigid	rigid	ADJ
ap-3989	8	6	body	body	NOUN
ap-3989	8	7	constraints	constraint	NOUN
ap-3989	8	8	are	be	AUX
ap-3989	8	9	compared	compare	VERB
ap-3989	8	10	to	to	ADP
ap-3989	8	11	the	the	DET
ap-3989	8	12	fully	fully	ADV
ap-3989	8	13	resolved	resolve	VERB
ap-3989	8	14	simulations	simulation	NOUN
ap-3989	8	15	and	and	CCONJ
ap-3989	8	16	optimal	optimal	ADJ
ap-3989	8	17	strategy	strategy	NOUN
ap-3989	8	18	is	be	AUX
ap-3989	8	19	recommended	recommend	VERB
ap-3989	8	20	.	.	PUNCT
ap-3989	9	1	keywords	keyword	NOUN
ap-3989	9	2	:	:	PUNCT
ap-3989	9	3	finite	finite	PROPN
ap-3989	9	4	element	element	NOUN
ap-3989	9	5	method	method	NOUN
ap-3989	9	6	;	;	PUNCT
ap-3989	9	7	computational	computational	ADJ
ap-3989	9	8	fluid	fluid	NOUN
ap-3989	9	9	dynamics	dynamic	NOUN
ap-3989	9	10	;	;	PUNCT
ap-3989	9	11	fictitious	fictitious	ADJ
ap-3989	9	12	domain	domain	NOUN
ap-3989	9	13	method	method	NOUN
ap-3989	9	14	;	;	PUNCT
ap-3989	9	15	lagrange	lagrange	NOUN
ap-3989	9	16	multipliers	multiplier	NOUN
ap-3989	9	17	;	;	PUNCT
ap-3989	9	18	flow	flow	VERB
ap-3989	9	19	around	around	ADP
ap-3989	9	20	obstacles	obstacle	NOUN
ap-3989	9	21	.	.	PUNCT
ap-3989	10	1	1	1	X
ap-3989	10	2	.	.	X
ap-3989	10	3	introduction	introduction	NOUN
ap-3989	10	4	the	the	DET
ap-3989	10	5	motivation	motivation	NOUN
ap-3989	10	6	of	of	ADP
ap-3989	10	7	the	the	DET
ap-3989	10	8	paper	paper	NOUN
ap-3989	10	9	comes	come	VERB
ap-3989	10	10	from	from	ADP
ap-3989	10	11	the	the	DET
ap-3989	10	12	modeling	modeling	NOUN
ap-3989	10	13	of	of	ADP
ap-3989	10	14	the	the	DET
ap-3989	10	15	fresh	fresh	ADJ
ap-3989	10	16	concrete	concrete	ADJ
ap-3989	10	17	casting	casting	NOUN
ap-3989	10	18	.	.	PUNCT
ap-3989	11	1	the	the	DET
ap-3989	11	2	simulation	simulation	NOUN
ap-3989	11	3	models	model	NOUN
ap-3989	11	4	of	of	ADP
ap-3989	11	5	fresh	fresh	ADJ
ap-3989	11	6	concrete	concrete	NOUN
ap-3989	11	7	aiming	aiming	NOUN
ap-3989	11	8	at	at	ADP
ap-3989	11	9	structural	structural	ADJ
ap-3989	11	10	-	-	PUNCT
ap-3989	11	11	scale	scale	NOUN
ap-3989	11	12	applications	application	NOUN
ap-3989	11	13	typically	typically	ADV
ap-3989	11	14	consider	consider	VERB
ap-3989	11	15	concrete	concrete	ADJ
ap-3989	11	16	suspension	suspension	NOUN
ap-3989	11	17	as	as	ADP
ap-3989	11	18	a	a	DET
ap-3989	11	19	homogeneous	homogeneous	ADJ
ap-3989	11	20	,	,	PUNCT
ap-3989	11	21	non	non	ADJ
ap-3989	11	22	-	-	ADJ
ap-3989	11	23	newtonian	newtonian	ADJ
ap-3989	11	24	fluid	fluid	NOUN
ap-3989	11	25	,	,	PUNCT
ap-3989	11	26	whose	whose	DET
ap-3989	11	27	rheological	rheological	ADJ
ap-3989	11	28	properties	property	NOUN
ap-3989	11	29	can	can	AUX
ap-3989	11	30	be	be	AUX
ap-3989	11	31	derived	derive	VERB
ap-3989	11	32	from	from	ADP
ap-3989	11	33	the	the	DET
ap-3989	11	34	mix	mix	NOUN
ap-3989	11	35	composition	composition	NOUN
ap-3989	11	36	[	[	X
ap-3989	11	37	1	1	NUM
ap-3989	11	38	]	]	PUNCT
ap-3989	11	39	.	.	PUNCT
ap-3989	12	1	the	the	DET
ap-3989	12	2	flow	flow	NOUN
ap-3989	12	3	can	can	AUX
ap-3989	12	4	be	be	AUX
ap-3989	12	5	then	then	ADV
ap-3989	12	6	efficiently	efficiently	ADV
ap-3989	12	7	described	describe	VERB
ap-3989	12	8	by	by	ADP
ap-3989	12	9	navierstokes	navierstoke	NOUN
ap-3989	12	10	equations	equation	NOUN
ap-3989	12	11	considering	consider	VERB
ap-3989	12	12	non	non	ADJ
ap-3989	12	13	-	-	ADJ
ap-3989	12	14	newtonian	newtonian	ADJ
ap-3989	12	15	fluid	fluid	NOUN
ap-3989	12	16	and	and	CCONJ
ap-3989	12	17	solved	solve	VERB
ap-3989	12	18	using	use	VERB
ap-3989	12	19	the	the	DET
ap-3989	12	20	finite	finite	ADJ
ap-3989	12	21	element	element	NOUN
ap-3989	12	22	method	method	NOUN
ap-3989	12	23	(	(	PUNCT
ap-3989	12	24	fem	fem	NOUN
ap-3989	12	25	)	)	PUNCT
ap-3989	12	26	,	,	PUNCT
ap-3989	12	27	for	for	ADP
ap-3989	12	28	example	example	NOUN
ap-3989	12	29	.	.	PUNCT
ap-3989	13	1	of	of	ADP
ap-3989	13	2	course	course	NOUN
ap-3989	13	3	,	,	PUNCT
ap-3989	13	4	the	the	DET
ap-3989	13	5	efficiency	efficiency	NOUN
ap-3989	13	6	of	of	ADP
ap-3989	13	7	the	the	DET
ap-3989	13	8	homogeneous	homogeneous	ADJ
ap-3989	13	9	approach	approach	NOUN
ap-3989	13	10	comes	come	VERB
ap-3989	13	11	at	at	ADP
ap-3989	13	12	the	the	DET
ap-3989	13	13	expense	expense	NOUN
ap-3989	13	14	of	of	ADP
ap-3989	13	15	the	the	DET
ap-3989	13	16	coarser	coarse	ADJ
ap-3989	13	17	description	description	NOUN
ap-3989	13	18	of	of	ADP
ap-3989	13	19	the	the	DET
ap-3989	13	20	flow	flow	NOUN
ap-3989	13	21	,	,	PUNCT
ap-3989	13	22	where	where	SCONJ
ap-3989	13	23	sub	sub	ADJ
ap-3989	13	24	-	-	ADJ
ap-3989	13	25	scale	scale	ADJ
ap-3989	13	26	phenomena	phenomenon	NOUN
ap-3989	13	27	can	can	AUX
ap-3989	13	28	only	only	ADV
ap-3989	13	29	be	be	AUX
ap-3989	13	30	approximately	approximately	ADV
ap-3989	13	31	accounted	account	VERB
ap-3989	13	32	for	for	ADP
ap-3989	13	33	by	by	ADP
ap-3989	13	34	post	post	ADJ
ap-3989	13	35	-	-	ADJ
ap-3989	13	36	processing	processing	ADJ
ap-3989	13	37	simulation	simulation	NOUN
ap-3989	13	38	results	result	NOUN
ap-3989	13	39	,	,	PUNCT
ap-3989	13	40	e.g.	e.g.	ADV
ap-3989	13	41	to	to	PART
ap-3989	13	42	determine	determine	VERB
ap-3989	13	43	the	the	DET
ap-3989	13	44	distribution	distribution	NOUN
ap-3989	13	45	and	and	CCONJ
ap-3989	13	46	orientation	orientation	NOUN
ap-3989	13	47	of	of	ADP
ap-3989	13	48	reinforcing	reinforce	VERB
ap-3989	13	49	fibers	fiber	NOUN
ap-3989	13	50	[	[	X
ap-3989	13	51	2	2	NUM
ap-3989	13	52	]	]	PUNCT
ap-3989	13	53	,	,	PUNCT
ap-3989	13	54	or	or	CCONJ
ap-3989	13	55	by	by	ADP
ap-3989	13	56	heuristic	heuristic	ADJ
ap-3989	13	57	modification	modification	NOUN
ap-3989	13	58	of	of	ADP
ap-3989	13	59	constitutive	constitutive	ADJ
ap-3989	13	60	parameters	parameter	NOUN
ap-3989	13	61	,	,	PUNCT
ap-3989	13	62	e.g.	e.g.	ADV
ap-3989	13	63	to	to	PART
ap-3989	13	64	account	account	VERB
ap-3989	13	65	for	for	ADP
ap-3989	13	66	the	the	DET
ap-3989	13	67	effect	effect	NOUN
ap-3989	13	68	of	of	ADP
ap-3989	13	69	traditional	traditional	ADJ
ap-3989	13	70	reinforcement	reinforcement	NOUN
ap-3989	13	71	[	[	X
ap-3989	13	72	3	3	NUM
ap-3989	13	73	]	]	PUNCT
ap-3989	13	74	.	.	PUNCT
ap-3989	14	1	especially	especially	ADV
ap-3989	14	2	the	the	DET
ap-3989	14	3	latter	latter	ADJ
ap-3989	14	4	aspect	aspect	NOUN
ap-3989	14	5	is	be	AUX
ap-3989	14	6	critical	critical	ADJ
ap-3989	14	7	in	in	ADP
ap-3989	14	8	the	the	DET
ap-3989	14	9	modeling	modeling	NOUN
ap-3989	14	10	of	of	ADP
ap-3989	14	11	casting	cast	VERB
ap-3989	14	12	processes	process	NOUN
ap-3989	14	13	in	in	ADP
ap-3989	14	14	highly	highly	ADV
ap-3989	14	15	-	-	PUNCT
ap-3989	14	16	reinforced	reinforce	VERB
ap-3989	14	17	structures	structure	NOUN
ap-3989	14	18	that	that	PRON
ap-3989	14	19	represent	represent	VERB
ap-3989	14	20	the	the	DET
ap-3989	14	21	major	major	ADJ
ap-3989	14	22	field	field	NOUN
ap-3989	14	23	of	of	ADP
ap-3989	14	24	application	application	NOUN
ap-3989	14	25	for	for	ADP
ap-3989	14	26	selfcompacting	selfcompacte	VERB
ap-3989	14	27	concrete	concrete	NOUN
ap-3989	14	28	.	.	PUNCT
ap-3989	15	1	the	the	DET
ap-3989	15	2	explicit	explicit	ADJ
ap-3989	15	3	representation	representation	NOUN
ap-3989	15	4	of	of	ADP
ap-3989	15	5	individual	individual	ADJ
ap-3989	15	6	reinforcing	reinforce	VERB
ap-3989	15	7	bars	bar	NOUN
ap-3989	15	8	in	in	ADP
ap-3989	15	9	the	the	DET
ap-3989	15	10	fe	fe	NOUN
ap-3989	15	11	model	model	NOUN
ap-3989	15	12	would	would	AUX
ap-3989	15	13	lead	lead	VERB
ap-3989	15	14	to	to	ADP
ap-3989	15	15	extremely	extremely	ADV
ap-3989	15	16	fine	fine	ADJ
ap-3989	15	17	computational	computational	ADJ
ap-3989	15	18	meshes	mesh	NOUN
ap-3989	15	19	and	and	CCONJ
ap-3989	15	20	will	will	AUX
ap-3989	15	21	result	result	VERB
ap-3989	15	22	in	in	ADP
ap-3989	15	23	extremely	extremely	ADV
ap-3989	15	24	high	high	ADJ
ap-3989	15	25	computational	computational	ADJ
ap-3989	15	26	demands	demand	NOUN
ap-3989	15	27	in	in	ADP
ap-3989	15	28	terms	term	NOUN
ap-3989	15	29	of	of	ADP
ap-3989	15	30	resources	resource	NOUN
ap-3989	15	31	and	and	CCONJ
ap-3989	15	32	time	time	NOUN
ap-3989	15	33	.	.	PUNCT
ap-3989	16	1	this	this	DET
ap-3989	16	2	article	article	NOUN
ap-3989	16	3	aims	aim	VERB
ap-3989	16	4	at	at	ADP
ap-3989	16	5	reducing	reduce	VERB
ap-3989	16	6	these	these	DET
ap-3989	16	7	computational	computational	ADJ
ap-3989	16	8	costs	cost	NOUN
ap-3989	16	9	by	by	ADP
ap-3989	16	10	avoiding	avoid	VERB
ap-3989	16	11	the	the	DET
ap-3989	16	12	need	need	NOUN
ap-3989	16	13	of	of	ADP
ap-3989	16	14	explicit	explicit	ADJ
ap-3989	16	15	representation	representation	NOUN
ap-3989	16	16	of	of	ADP
ap-3989	16	17	individual	individual	ADJ
ap-3989	16	18	reinforcing	reinforce	VERB
ap-3989	16	19	bars	bar	NOUN
ap-3989	16	20	by	by	ADP
ap-3989	16	21	adopting	adopt	VERB
ap-3989	16	22	an	an	DET
ap-3989	16	23	approach	approach	NOUN
ap-3989	16	24	based	base	VERB
ap-3989	16	25	on	on	ADP
ap-3989	16	26	fictitious	fictitious	ADJ
ap-3989	16	27	domain	domain	NOUN
ap-3989	16	28	method	method	NOUN
ap-3989	16	29	to	to	PART
ap-3989	16	30	solve	solve	VERB
ap-3989	16	31	the	the	DET
ap-3989	16	32	problem	problem	NOUN
ap-3989	16	33	of	of	ADP
ap-3989	16	34	newtonian	newtonian	ADJ
ap-3989	16	35	incompressible	incompressible	ADJ
ap-3989	16	36	flow	flow	NOUN
ap-3989	16	37	with	with	ADP
ap-3989	16	38	rigid	rigid	ADJ
ap-3989	16	39	body	body	NOUN
ap-3989	16	40	obstacles	obstacle	NOUN
ap-3989	16	41	on	on	ADP
ap-3989	16	42	regular	regular	ADJ
ap-3989	16	43	,	,	PUNCT
ap-3989	16	44	structured	structured	ADJ
ap-3989	16	45	computational	computational	ADJ
ap-3989	16	46	grid	grid	NOUN
ap-3989	16	47	,	,	PUNCT
ap-3989	16	48	where	where	SCONJ
ap-3989	16	49	the	the	DET
ap-3989	16	50	individual	individual	ADJ
ap-3989	16	51	reinforcing	reinforce	VERB
ap-3989	16	52	bars	bar	NOUN
ap-3989	16	53	can	can	AUX
ap-3989	16	54	be	be	AUX
ap-3989	16	55	inserted	insert	VERB
ap-3989	16	56	arbitrarily	arbitrarily	ADV
ap-3989	16	57	and	and	CCONJ
ap-3989	16	58	independently	independently	ADV
ap-3989	16	59	of	of	ADP
ap-3989	16	60	the	the	DET
ap-3989	16	61	underlying	underlying	ADJ
ap-3989	16	62	mesh	mesh	NOUN
ap-3989	16	63	.	.	PUNCT
ap-3989	17	1	the	the	DET
ap-3989	17	2	individual	individual	ADJ
ap-3989	17	3	bars	bar	NOUN
ap-3989	17	4	are	be	AUX
ap-3989	17	5	accounted	account	VERB
ap-3989	17	6	for	for	ADP
ap-3989	17	7	by	by	ADP
ap-3989	17	8	enforcing	enforce	VERB
ap-3989	17	9	no	no	DET
ap-3989	17	10	-	-	PUNCT
ap-3989	17	11	flow	flow	NOUN
ap-3989	17	12	constraints	constraint	NOUN
ap-3989	17	13	in	in	ADP
ap-3989	17	14	a	a	DET
ap-3989	17	15	volume	volume	NOUN
ap-3989	17	16	occupied	occupy	VERB
ap-3989	17	17	by	by	ADP
ap-3989	17	18	the	the	DET
ap-3989	17	19	bar	bar	NOUN
ap-3989	17	20	using	use	VERB
ap-3989	17	21	lagrange	lagrange	NOUN
ap-3989	17	22	multipliers	multiplier	NOUN
ap-3989	17	23	.	.	PUNCT
ap-3989	18	1	to	to	PART
ap-3989	18	2	solve	solve	VERB
ap-3989	18	3	the	the	DET
ap-3989	18	4	incompressible	incompressible	ADJ
ap-3989	18	5	navier	navier	NOUN
ap-3989	18	6	-	-	PUNCT
ap-3989	18	7	stokes	stoke	NOUN
ap-3989	18	8	problem	problem	NOUN
ap-3989	18	9	,	,	PUNCT
ap-3989	18	10	a	a	DET
ap-3989	18	11	2d	2d	NUM
ap-3989	18	12	eulerian	eulerian	ADJ
ap-3989	18	13	formulation	formulation	NOUN
ap-3989	18	14	of	of	ADP
ap-3989	18	15	finite	finite	PROPN
ap-3989	18	16	element	element	NOUN
ap-3989	18	17	method	method	NOUN
ap-3989	18	18	is	be	AUX
ap-3989	18	19	developed	develop	VERB
ap-3989	18	20	,	,	PUNCT
ap-3989	18	21	using	use	VERB
ap-3989	18	22	the	the	DET
ap-3989	18	23	“	"	PUNCT
ap-3989	18	24	taylor	taylor	PROPN
ap-3989	18	25	-	-	PUNCT
ap-3989	18	26	hood	hood	NOUN
ap-3989	18	27	”	"	PUNCT
ap-3989	18	28	p2	p2	PROPN
ap-3989	18	29	/	/	SYM
ap-3989	18	30	p1	p1	NOUN
ap-3989	18	31	elements	element	NOUN
ap-3989	18	32	,	,	PUNCT
ap-3989	18	33	which	which	PRON
ap-3989	18	34	are	be	AUX
ap-3989	18	35	quadratic	quadratic	ADJ
ap-3989	18	36	in	in	ADP
ap-3989	18	37	velocity	velocity	NOUN
ap-3989	18	38	and	and	CCONJ
ap-3989	18	39	linear	linear	NOUN
ap-3989	18	40	in	in	ADP
ap-3989	18	41	pressure	pressure	NOUN
ap-3989	18	42	,	,	PUNCT
ap-3989	18	43	satisfying	satisfy	VERB
ap-3989	18	44	the	the	DET
ap-3989	18	45	lbb	lbb	PROPN
ap-3989	18	46	condition	condition	NOUN
ap-3989	18	47	[	[	X
ap-3989	18	48	4	4	NUM
ap-3989	18	49	]	]	PUNCT
ap-3989	18	50	.	.	PUNCT
ap-3989	19	1	the	the	DET
ap-3989	19	2	time	time	NOUN
ap-3989	19	3	discretization	discretization	NOUN
ap-3989	19	4	is	be	AUX
ap-3989	19	5	based	base	VERB
ap-3989	19	6	on	on	ADP
ap-3989	19	7	operator	operator	NOUN
ap-3989	19	8	splitting	splitting	NOUN
ap-3989	19	9	approach	approach	NOUN
ap-3989	19	10	,	,	PUNCT
ap-3989	19	11	in	in	ADP
ap-3989	19	12	particular	particular	ADJ
ap-3989	19	13	,	,	PUNCT
ap-3989	19	14	the	the	DET
ap-3989	19	15	fractional	fractional	ADJ
ap-3989	19	16	-	-	PUNCT
ap-3989	19	17	time	time	NOUN
ap-3989	19	18	-	-	PUNCT
ap-3989	19	19	step	step	NOUN
ap-3989	19	20	scheme	scheme	NOUN
ap-3989	19	21	described	describe	VERB
ap-3989	19	22	by	by	ADP
ap-3989	19	23	marchuk	marchuk	PROPN
ap-3989	19	24	has	have	AUX
ap-3989	19	25	been	be	AUX
ap-3989	19	26	employed	employ	VERB
ap-3989	19	27	[	[	X
ap-3989	19	28	5	5	NUM
ap-3989	19	29	]	]	PUNCT
ap-3989	19	30	.	.	PUNCT
ap-3989	20	1	the	the	DET
ap-3989	20	2	fundamental	fundamental	ADJ
ap-3989	20	3	idea	idea	NOUN
ap-3989	20	4	of	of	ADP
ap-3989	20	5	fictitious	fictitious	ADJ
ap-3989	20	6	domain	domain	NOUN
ap-3989	20	7	method	method	NOUN
ap-3989	20	8	consists	consist	VERB
ap-3989	20	9	in	in	ADP
ap-3989	20	10	extending	extend	VERB
ap-3989	20	11	the	the	DET
ap-3989	20	12	problem	problem	NOUN
ap-3989	20	13	to	to	ADP
ap-3989	20	14	one	one	NUM
ap-3989	20	15	geometrically	geometrically	ADV
ap-3989	20	16	simpler	simple	ADJ
ap-3989	20	17	domain	domain	NOUN
ap-3989	20	18	covering	cover	VERB
ap-3989	20	19	both	both	CCONJ
ap-3989	20	20	fluid	fluid	NOUN
ap-3989	20	21	and	and	CCONJ
ap-3989	20	22	obstacles	obstacle	NOUN
ap-3989	20	23	–	–	PUNCT
ap-3989	20	24	the	the	DET
ap-3989	20	25	so	so	ADV
ap-3989	20	26	-	-	PUNCT
ap-3989	20	27	called	call	VERB
ap-3989	20	28	fictitious	fictitious	ADJ
ap-3989	20	29	domain	domain	NOUN
ap-3989	20	30	.	.	PUNCT
ap-3989	21	1	the	the	DET
ap-3989	21	2	no	no	DET
ap-3989	21	3	-	-	PUNCT
ap-3989	21	4	flow	flow	NOUN
ap-3989	21	5	constraints	constraint	NOUN
ap-3989	21	6	in	in	ADP
ap-3989	21	7	subdomains	subdomain	NOUN
ap-3989	21	8	corresponding	correspond	VERB
ap-3989	21	9	to	to	ADP
ap-3989	21	10	individual	individual	ADJ
ap-3989	21	11	bars	bar	NOUN
ap-3989	21	12	are	be	AUX
ap-3989	21	13	enforced	enforce	VERB
ap-3989	21	14	using	use	VERB
ap-3989	21	15	distributed	distribute	VERB
ap-3989	21	16	lagrange	lagrange	NOUN
ap-3989	21	17	multipliers	multiplier	NOUN
ap-3989	21	18	,	,	PUNCT
ap-3989	21	19	which	which	PRON
ap-3989	21	20	represent	represent	VERB
ap-3989	21	21	the	the	DET
ap-3989	21	22	additional	additional	ADJ
ap-3989	21	23	body	body	NOUN
ap-3989	21	24	forces	force	NOUN
ap-3989	21	25	needed	need	VERB
ap-3989	21	26	to	to	PART
ap-3989	21	27	enforce	enforce	VERB
ap-3989	21	28	zero	zero	NUM
ap-3989	21	29	flow	flow	NOUN
ap-3989	21	30	inside	inside	ADP
ap-3989	21	31	the	the	DET
ap-3989	21	32	regions	region	NOUN
ap-3989	21	33	representing	represent	VERB
ap-3989	21	34	obstacles	obstacle	NOUN
ap-3989	21	35	.	.	PUNCT
ap-3989	22	1	the	the	DET
ap-3989	22	2	pressure	pressure	NOUN
ap-3989	22	3	is	be	AUX
ap-3989	22	4	constrained	constrain	VERB
ap-3989	22	5	by	by	ADP
ap-3989	22	6	incompressibility	incompressibility	NOUN
ap-3989	22	7	of	of	ADP
ap-3989	22	8	the	the	DET
ap-3989	22	9	fluid	fluid	NOUN
ap-3989	22	10	in	in	ADP
ap-3989	22	11	the	the	DET
ap-3989	22	12	fictitious	fictitious	ADJ
ap-3989	22	13	domain	domain	NOUN
ap-3989	22	14	.	.	PUNCT
ap-3989	23	1	this	this	DET
ap-3989	23	2	so	so	ADV
ap-3989	23	3	called	call	VERB
ap-3989	23	4	distributed	distribute	VERB
ap-3989	23	5	lagrange	lagrange	NOUN
ap-3989	23	6	multiplier	multipli	ADJ
ap-3989	23	7	fictitious	fictitious	ADJ
ap-3989	23	8	domain	domain	NOUN
ap-3989	23	9	method	method	NOUN
ap-3989	23	10	has	have	AUX
ap-3989	23	11	been	be	AUX
ap-3989	23	12	introduced	introduce	VERB
ap-3989	23	13	by	by	ADP
ap-3989	23	14	glowinski	glowinski	PROPN
ap-3989	23	15	et	et	PROPN
ap-3989	23	16	al	al	PROPN
ap-3989	23	17	.	.	PUNCT
ap-3989	24	1	[	[	X
ap-3989	24	2	6	6	NUM
ap-3989	24	3	]	]	PUNCT
ap-3989	24	4	.	.	PUNCT
ap-3989	25	1	the	the	DET
ap-3989	25	2	method	method	NOUN
ap-3989	25	3	has	have	AUX
ap-3989	25	4	then	then	ADV
ap-3989	25	5	been	be	AUX
ap-3989	25	6	used	use	VERB
ap-3989	25	7	by	by	ADP
ap-3989	25	8	bertrand	bertrand	PROPN
ap-3989	25	9	et	et	PROPN
ap-3989	25	10	al	al	PROPN
ap-3989	25	11	.	.	PUNCT
ap-3989	26	1	[	[	X
ap-3989	26	2	7	7	X
ap-3989	26	3	]	]	PUNCT
ap-3989	26	4	and	and	CCONJ
ap-3989	26	5	tanguy	tanguy	NOUN
ap-3989	26	6	et	et	PROPN
ap-3989	26	7	al	al	PROPN
ap-3989	26	8	.	.	PUNCT
ap-3989	27	1	[	[	X
ap-3989	27	2	8	8	NUM
ap-3989	27	3	]	]	PUNCT
ap-3989	27	4	to	to	PART
ap-3989	27	5	calculate	calculate	VERB
ap-3989	27	6	threedimensional	threedimensional	ADJ
ap-3989	27	7	flows	flow	NOUN
ap-3989	27	8	.	.	PUNCT
ap-3989	28	1	recently	recently	ADV
ap-3989	28	2	,	,	PUNCT
ap-3989	28	3	the	the	DET
ap-3989	28	4	method	method	NOUN
ap-3989	28	5	has	have	AUX
ap-3989	28	6	been	be	AUX
ap-3989	28	7	extended	extend	VERB
ap-3989	28	8	by	by	ADP
ap-3989	28	9	baaijens	baaijen	NOUN
ap-3989	28	10	[	[	X
ap-3989	28	11	9	9	NUM
ap-3989	28	12	]	]	PUNCT
ap-3989	28	13	and	and	CCONJ
ap-3989	28	14	yu	yu	PRON
ap-3989	29	1	[	[	X
ap-3989	29	2	10	10	NUM
ap-3989	29	3	]	]	PUNCT
ap-3989	29	4	to	to	PART
ap-3989	29	5	handle	handle	VERB
ap-3989	29	6	fluidstructure	fluidstructure	NOUN
ap-3989	29	7	interactions	interaction	NOUN
ap-3989	29	8	.	.	PUNCT
ap-3989	30	1	the	the	DET
ap-3989	30	2	main	main	ADJ
ap-3989	30	3	advantage	advantage	NOUN
ap-3989	30	4	of	of	ADP
ap-3989	30	5	this	this	DET
ap-3989	30	6	method	method	NOUN
ap-3989	30	7	is	be	AUX
ap-3989	30	8	a	a	DET
ap-3989	30	9	much	much	ADV
ap-3989	30	10	simpler	simple	ADJ
ap-3989	30	11	generation	generation	NOUN
ap-3989	30	12	of	of	ADP
ap-3989	30	13	the	the	DET
ap-3989	30	14	computational	computational	ADJ
ap-3989	30	15	grid	grid	NOUN
ap-3989	30	16	,	,	PUNCT
ap-3989	30	17	because	because	SCONJ
ap-3989	30	18	the	the	DET
ap-3989	30	19	mesh	mesh	NOUN
ap-3989	30	20	does	do	AUX
ap-3989	30	21	not	not	PART
ap-3989	30	22	need	need	VERB
ap-3989	30	23	to	to	PART
ap-3989	30	24	conform	conform	VERB
ap-3989	30	25	to	to	ADP
ap-3989	30	26	the	the	DET
ap-3989	30	27	geometry	geometry	NOUN
ap-3989	30	28	of	of	ADP
ap-3989	30	29	the	the	DET
ap-3989	30	30	reinforcement	reinforcement	NOUN
ap-3989	30	31	.	.	PUNCT
ap-3989	31	1	it	it	PRON
ap-3989	31	2	can	can	AUX
ap-3989	31	3	be	be	AUX
ap-3989	31	4	fully	fully	ADV
ap-3989	31	5	structured	structure	VERB
ap-3989	31	6	and	and	CCONJ
ap-3989	31	7	regular	regular	ADJ
ap-3989	31	8	,	,	PUNCT
ap-3989	31	9	allowing	allow	VERB
ap-3989	31	10	to	to	PART
ap-3989	31	11	take	take	VERB
ap-3989	31	12	advantage	advantage	NOUN
ap-3989	31	13	of	of	ADP
ap-3989	31	14	specialized	specialized	ADJ
ap-3989	31	15	,	,	PUNCT
ap-3989	31	16	fast	fast	ADJ
ap-3989	31	17	numerical	numerical	ADJ
ap-3989	31	18	solvers	solver	NOUN
ap-3989	31	19	.	.	PUNCT
ap-3989	32	1	this	this	DET
ap-3989	32	2	feature	feature	NOUN
ap-3989	32	3	can	can	AUX
ap-3989	32	4	significantly	significantly	ADV
ap-3989	32	5	reduce	reduce	VERB
ap-3989	32	6	computational	computational	ADJ
ap-3989	32	7	requirements	requirement	NOUN
ap-3989	32	8	of	of	ADP
ap-3989	32	9	the	the	DET
ap-3989	32	10	problem	problem	NOUN
ap-3989	32	11	.	.	PUNCT
ap-3989	33	1	to	to	ADP
ap-3989	33	2	the	the	DET
ap-3989	33	3	authors	author	NOUN
ap-3989	33	4	knowledge	knowledge	NOUN
ap-3989	33	5	,	,	PUNCT
ap-3989	33	6	there	there	PRON
ap-3989	33	7	has	have	AUX
ap-3989	33	8	been	be	AUX
ap-3989	33	9	no	no	DET
ap-3989	33	10	study	study	NOUN
ap-3989	33	11	published	publish	VERB
ap-3989	33	12	investigating	investigate	VERB
ap-3989	33	13	the	the	DET
ap-3989	33	14	influence	influence	NOUN
ap-3989	33	15	of	of	ADP
ap-3989	33	16	the	the	DET
ap-3989	33	17	sampling	sampling	NOUN
ap-3989	33	18	point	point	NOUN
ap-3989	33	19	selection	selection	NOUN
ap-3989	33	20	on	on	ADP
ap-3989	33	21	the	the	DET
ap-3989	33	22	quality	quality	NOUN
ap-3989	33	23	of	of	ADP
ap-3989	33	24	the	the	DET
ap-3989	33	25	solution	solution	NOUN
ap-3989	33	26	.	.	PUNCT
ap-3989	34	1	the	the	DET
ap-3989	34	2	245	245	NUM
ap-3989	34	3	http://dx.doi.org/10.14311/ap.2017.57.0245	http://dx.doi.org/10.14311/ap.2017.57.0245	NOUN
ap-3989	34	4	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3989	34	5	matej	matej	PROPN
ap-3989	34	6	beňo	beňo	PROPN
ap-3989	34	7	,	,	PUNCT
ap-3989	34	8	bořek	bořek	PROPN
ap-3989	34	9	patzák	patzák	VERB
ap-3989	34	10	acta	acta	PROPN
ap-3989	34	11	polytechnica	polytechnica	PROPN
ap-3989	34	12	figure	figure	NOUN
ap-3989	34	13	1	1	NUM
ap-3989	34	14	.	.	PUNCT
ap-3989	35	1	original	original	ADJ
ap-3989	35	2	and	and	CCONJ
ap-3989	35	3	fictitious	fictitious	ADJ
ap-3989	35	4	domain	domain	NOUN
ap-3989	35	5	problems	problem	NOUN
ap-3989	35	6	.	.	PUNCT
ap-3989	36	1	goal	goal	NOUN
ap-3989	36	2	of	of	ADP
ap-3989	36	3	this	this	DET
ap-3989	36	4	paper	paper	NOUN
ap-3989	36	5	is	be	AUX
ap-3989	36	6	to	to	PART
ap-3989	36	7	propose	propose	VERB
ap-3989	36	8	and	and	CCONJ
ap-3989	36	9	evaluate	evaluate	VERB
ap-3989	36	10	different	different	ADJ
ap-3989	36	11	strategies	strategy	NOUN
ap-3989	36	12	for	for	ADP
ap-3989	36	13	enforcing	enforce	VERB
ap-3989	36	14	no	no	DET
ap-3989	36	15	-	-	PUNCT
ap-3989	36	16	flow	flow	NOUN
ap-3989	36	17	constraints	constraint	NOUN
ap-3989	36	18	using	use	VERB
ap-3989	36	19	different	different	ADJ
ap-3989	36	20	sets	set	NOUN
ap-3989	36	21	of	of	ADP
ap-3989	36	22	sampling	sample	VERB
ap-3989	36	23	points	point	NOUN
ap-3989	36	24	and	and	CCONJ
ap-3989	36	25	compare	compare	VERB
ap-3989	36	26	their	their	PRON
ap-3989	36	27	performance	performance	NOUN
ap-3989	36	28	to	to	ADP
ap-3989	36	29	the	the	DET
ap-3989	36	30	fully	fully	ADV
ap-3989	36	31	resolved	resolve	VERB
ap-3989	36	32	simulations	simulation	NOUN
ap-3989	36	33	.	.	PUNCT
ap-3989	37	1	1.1	1.1	NUM
ap-3989	37	2	.	.	PUNCT
ap-3989	37	3	fictitious	fictitious	ADJ
ap-3989	37	4	domain	domain	NOUN
ap-3989	37	5	method	method	NOUN
ap-3989	37	6	the	the	DET
ap-3989	37	7	basic	basic	ADJ
ap-3989	37	8	idea	idea	NOUN
ap-3989	37	9	of	of	ADP
ap-3989	37	10	the	the	DET
ap-3989	37	11	method	method	NOUN
ap-3989	37	12	is	be	AUX
ap-3989	37	13	based	base	VERB
ap-3989	37	14	on	on	ADP
ap-3989	37	15	a	a	DET
ap-3989	37	16	cancellation	cancellation	NOUN
ap-3989	37	17	of	of	ADP
ap-3989	37	18	the	the	DET
ap-3989	37	19	forces	force	NOUN
ap-3989	37	20	and	and	CCONJ
ap-3989	37	21	moments	moment	NOUN
ap-3989	37	22	between	between	ADP
ap-3989	37	23	obstacles	obstacle	NOUN
ap-3989	37	24	and	and	CCONJ
ap-3989	37	25	fluid	fluid	NOUN
ap-3989	37	26	in	in	ADP
ap-3989	37	27	the	the	DET
ap-3989	37	28	combined	combine	VERB
ap-3989	37	29	weak	weak	ADJ
ap-3989	37	30	formulation	formulation	NOUN
ap-3989	37	31	for	for	ADP
ap-3989	37	32	particle	particle	NOUN
ap-3989	37	33	-	-	PUNCT
ap-3989	37	34	fluid	fluid	NOUN
ap-3989	37	35	motion	motion	NOUN
ap-3989	37	36	solved	solve	VERB
ap-3989	37	37	everywhere	everywhere	ADV
ap-3989	37	38	in	in	ADP
ap-3989	37	39	the	the	DET
ap-3989	37	40	fictitious	fictitious	ADJ
ap-3989	37	41	domain	domain	NOUN
ap-3989	37	42	.	.	PUNCT
ap-3989	38	1	to	to	PART
ap-3989	38	2	enforce	enforce	VERB
ap-3989	38	3	the	the	DET
ap-3989	38	4	no	no	DET
ap-3989	38	5	-	-	PUNCT
ap-3989	38	6	flow	flow	NOUN
ap-3989	38	7	constraints	constraint	NOUN
ap-3989	38	8	(	(	PUNCT
ap-3989	38	9	sometimes	sometimes	ADV
ap-3989	38	10	referred	refer	VERB
ap-3989	38	11	as	as	ADP
ap-3989	38	12	rigid	rigid	ADJ
ap-3989	38	13	-	-	PUNCT
ap-3989	38	14	body	body	NOUN
ap-3989	38	15	constraints	constraint	NOUN
ap-3989	38	16	when	when	SCONJ
ap-3989	38	17	moving	move	VERB
ap-3989	38	18	rigid	rigid	ADJ
ap-3989	38	19	particles	particle	NOUN
ap-3989	38	20	are	be	AUX
ap-3989	38	21	considered	consider	VERB
ap-3989	38	22	)	)	PUNCT
ap-3989	38	23	to	to	PART
ap-3989	38	24	account	account	VERB
ap-3989	38	25	for	for	ADP
ap-3989	38	26	rigid	rigid	ADJ
ap-3989	38	27	particles	particle	NOUN
ap-3989	38	28	,	,	PUNCT
ap-3989	38	29	lagrange	lagrange	NOUN
ap-3989	38	30	multipliers	multiplier	NOUN
ap-3989	38	31	are	be	AUX
ap-3989	38	32	introduced	introduce	VERB
ap-3989	38	33	.	.	PUNCT
ap-3989	39	1	these	these	DET
ap-3989	39	2	multipliers	multiplier	NOUN
ap-3989	39	3	represent	represent	VERB
ap-3989	39	4	the	the	DET
ap-3989	39	5	additional	additional	ADJ
ap-3989	39	6	body	body	NOUN
ap-3989	39	7	forces	force	NOUN
ap-3989	39	8	needed	need	VERB
ap-3989	39	9	to	to	PART
ap-3989	39	10	maintain	maintain	VERB
ap-3989	39	11	the	the	DET
ap-3989	39	12	rigid	rigid	ADJ
ap-3989	39	13	body	body	NOUN
ap-3989	39	14	motion	motion	NOUN
ap-3989	39	15	inside	inside	ADP
ap-3989	39	16	the	the	DET
ap-3989	39	17	moving	move	VERB
ap-3989	39	18	particles	particle	NOUN
ap-3989	39	19	or	or	CCONJ
ap-3989	39	20	the	the	DET
ap-3989	39	21	no	no	DET
ap-3989	39	22	flow	flow	NOUN
ap-3989	39	23	constraint	constraint	NOUN
ap-3989	39	24	inside	inside	ADP
ap-3989	39	25	the	the	DET
ap-3989	39	26	regions	region	NOUN
ap-3989	39	27	representing	represent	VERB
ap-3989	39	28	fixed	fix	VERB
ap-3989	39	29	particles	particle	NOUN
ap-3989	39	30	.	.	PUNCT
ap-3989	40	1	as	as	SCONJ
ap-3989	40	2	already	already	ADV
ap-3989	40	3	mentioned	mention	VERB
ap-3989	40	4	,	,	PUNCT
ap-3989	40	5	the	the	DET
ap-3989	40	6	advantage	advantage	NOUN
ap-3989	40	7	of	of	ADP
ap-3989	40	8	this	this	DET
ap-3989	40	9	approach	approach	NOUN
ap-3989	40	10	consist	consist	VERB
ap-3989	40	11	in	in	ADP
ap-3989	40	12	ability	ability	NOUN
ap-3989	40	13	to	to	PART
ap-3989	40	14	use	use	VERB
ap-3989	40	15	geometrically	geometrically	ADV
ap-3989	40	16	simpler	simple	ADJ
ap-3989	40	17	,	,	PUNCT
ap-3989	40	18	regular	regular	ADJ
ap-3989	40	19	meshes	mesh	NOUN
ap-3989	40	20	.	.	PUNCT
ap-3989	41	1	2	2	X
ap-3989	41	2	.	.	X
ap-3989	41	3	problem	problem	NOUN
ap-3989	41	4	formulation	formulation	NOUN
ap-3989	41	5	2.1	2.1	NUM
ap-3989	41	6	.	.	PUNCT
ap-3989	42	1	the	the	DET
ap-3989	42	2	governing	govern	VERB
ap-3989	42	3	equation	equation	NOUN
ap-3989	42	4	of	of	ADP
ap-3989	42	5	the	the	DET
ap-3989	42	6	flow	flow	NOUN
ap-3989	42	7	assume	assume	VERB
ap-3989	42	8	an	an	DET
ap-3989	42	9	incompressible	incompressible	ADJ
ap-3989	42	10	,	,	PUNCT
ap-3989	42	11	viscous	viscous	ADJ
ap-3989	42	12	,	,	PUNCT
ap-3989	42	13	newtonian	newtonian	ADJ
ap-3989	42	14	fluid	fluid	NOUN
ap-3989	42	15	occupying	occupying	NOUN
ap-3989	42	16	at	at	ADP
ap-3989	42	17	the	the	DET
ap-3989	42	18	given	give	VERB
ap-3989	42	19	time	time	NOUN
ap-3989	42	20	t	t	PROPN
ap-3989	42	21	∈	∈	PROPN
ap-3989	42	22	(	(	PUNCT
ap-3989	42	23	0	0	NUM
ap-3989	42	24	,	,	PUNCT
ap-3989	42	25	t	t	NOUN
ap-3989	42	26	)	)	PUNCT
ap-3989	42	27	the	the	DET
ap-3989	42	28	delimited	delimit	VERB
ap-3989	42	29	domain	domain	NOUN
ap-3989	42	30	ω	ω	NUM
ap-3989	42	31	⊂	⊂	PROPN
ap-3989	42	32	r2	r2	PROPN
ap-3989	42	33	with	with	ADP
ap-3989	42	34	boundary	boundary	ADJ
ap-3989	42	35	γ	γ	PROPN
ap-3989	42	36	.	.	PROPN
ap-3989	42	37	let	let	AUX
ap-3989	42	38	denote	denote	VERB
ap-3989	42	39	by	by	ADP
ap-3989	42	40	x	x	X
ap-3989	42	41	=	=	PRON
ap-3989	42	42	{	{	PUNCT
ap-3989	42	43	xi}2i=1	xi}2i=1	PROPN
ap-3989	42	44	a	a	DET
ap-3989	42	45	generic	generic	ADJ
ap-3989	42	46	point	point	NOUN
ap-3989	42	47	in	in	ADP
ap-3989	42	48	ω	ω	PROPN
ap-3989	42	49	.	.	PUNCT
ap-3989	43	1	let	let	AUX
ap-3989	43	2	further	far	ADV
ap-3989	43	3	denote	denote	VERB
ap-3989	43	4	by	by	ADP
ap-3989	43	5	u(x	u(x	NOUN
ap-3989	43	6	,	,	PUNCT
ap-3989	43	7	t	t	NOUN
ap-3989	43	8	)	)	PUNCT
ap-3989	43	9	velocity	velocity	NOUN
ap-3989	43	10	and	and	CCONJ
ap-3989	43	11	by	by	ADP
ap-3989	43	12	p(x	p(x	PROPN
ap-3989	43	13	,	,	PUNCT
ap-3989	43	14	t	t	NOUN
ap-3989	43	15	)	)	PUNCT
ap-3989	43	16	pressure	pressure	NOUN
ap-3989	43	17	,	,	PUNCT
ap-3989	43	18	both	both	PRON
ap-3989	43	19	governed	govern	VERB
ap-3989	43	20	by	by	ADP
ap-3989	43	21	navier	navier	NOUN
ap-3989	43	22	-	-	PUNCT
ap-3989	43	23	stokes	stokes	PROPN
ap-3989	43	24	equations	equation	NOUN
ap-3989	43	25	%	%	INTJ
ap-3989	43	26	du	du	NOUN
ap-3989	43	27	dt	dt	PROPN
ap-3989	44	1	=	=	NOUN
ap-3989	44	2	%	%	INTJ
ap-3989	44	3	g	g	PROPN
ap-3989	44	4	+	+	NOUN
ap-3989	44	5	∇	∇	X
ap-3989	44	6	·	·	PUNCT
ap-3989	44	7	σ	σ	NOUN
ap-3989	44	8	on	on	ADP
ap-3989	44	9	ω	ω	PROPN
ap-3989	44	10	\	\	PROPN
ap-3989	44	11	p	p	X
ap-3989	44	12	,	,	PUNCT
ap-3989	44	13	(	(	PUNCT
ap-3989	44	14	1	1	X
ap-3989	44	15	)	)	PUNCT
ap-3989	44	16	∇	∇	X
ap-3989	44	17	·	·	PUNCT
ap-3989	44	18	u	u	NOUN
ap-3989	44	19	=	=	NOUN
ap-3989	44	20	0	0	NUM
ap-3989	44	21	on	on	ADP
ap-3989	44	22	ω	ω	PROPN
ap-3989	44	23	\	\	PROPN
ap-3989	44	24	p	p	X
ap-3989	44	25	,	,	PUNCT
ap-3989	44	26	(	(	PUNCT
ap-3989	44	27	2	2	X
ap-3989	44	28	)	)	PUNCT
ap-3989	44	29	where	where	SCONJ
ap-3989	44	30	%	%	NOUN
ap-3989	44	31	is	be	AUX
ap-3989	44	32	density	density	NOUN
ap-3989	44	33	of	of	ADP
ap-3989	44	34	the	the	DET
ap-3989	44	35	fluid	fluid	NOUN
ap-3989	44	36	,	,	PUNCT
ap-3989	44	37	u	u	NOUN
ap-3989	44	38	is	be	AUX
ap-3989	44	39	velocity	velocity	NOUN
ap-3989	44	40	of	of	ADP
ap-3989	44	41	the	the	DET
ap-3989	44	42	fluid	fluid	NOUN
ap-3989	44	43	,	,	PUNCT
ap-3989	44	44	and	and	CCONJ
ap-3989	44	45	σ	σ	PROPN
ap-3989	44	46	is	be	AUX
ap-3989	44	47	stress	stress	ADJ
ap-3989	44	48	tensor	tensor	NOUN
ap-3989	44	49	.	.	PUNCT
ap-3989	45	1	for	for	ADP
ap-3989	45	2	an	an	DET
ap-3989	45	3	incompressible	incompressible	ADJ
ap-3989	45	4	,	,	PUNCT
ap-3989	45	5	newtonian	newtonian	ADJ
ap-3989	45	6	viscous	viscous	ADJ
ap-3989	45	7	fluid	fluid	NOUN
ap-3989	45	8	,	,	PUNCT
ap-3989	45	9	the	the	DET
ap-3989	45	10	stress	stress	NOUN
ap-3989	45	11	can	can	AUX
ap-3989	45	12	be	be	AUX
ap-3989	45	13	decomposed	decompose	VERB
ap-3989	45	14	into	into	ADP
ap-3989	45	15	hydrostatic	hydrostatic	ADJ
ap-3989	45	16	and	and	CCONJ
ap-3989	45	17	deviatoric	deviatoric	ADJ
ap-3989	45	18	components	component	NOUN
ap-3989	45	19	σ	σ	NOUN
ap-3989	45	20	=	=	PUNCT
ap-3989	45	21	−pi	−pi	PROPN
ap-3989	45	22	+	+	NOUN
ap-3989	45	23	2ηd[u	2ηd[u	NUM
ap-3989	45	24	]	]	X
ap-3989	45	25	,	,	PUNCT
ap-3989	45	26	(	(	PUNCT
ap-3989	45	27	3	3	X
ap-3989	45	28	)	)	PUNCT
ap-3989	45	29	where	where	SCONJ
ap-3989	45	30	p	p	NOUN
ap-3989	45	31	is	be	AUX
ap-3989	45	32	hydrostatic	hydrostatic	ADJ
ap-3989	45	33	pressure	pressure	NOUN
ap-3989	45	34	in	in	ADP
ap-3989	45	35	the	the	DET
ap-3989	45	36	fluid	fluid	NOUN
ap-3989	45	37	,	,	PUNCT
ap-3989	45	38	η	η	PROPN
ap-3989	45	39	is	be	AUX
ap-3989	45	40	the	the	DET
ap-3989	45	41	viscosity	viscosity	NOUN
ap-3989	45	42	(	(	PUNCT
ap-3989	45	43	assumed	assume	VERB
ap-3989	45	44	constant	constant	ADJ
ap-3989	45	45	)	)	PUNCT
ap-3989	45	46	,	,	PUNCT
ap-3989	45	47	and	and	CCONJ
ap-3989	45	48	2ηd[u	2ηd[u	NUM
ap-3989	45	49	]	]	PUNCT
ap-3989	45	50	is	be	AUX
ap-3989	45	51	deviatoric	deviatoric	ADJ
ap-3989	45	52	stress	stress	NOUN
ap-3989	45	53	tensor	tensor	NOUN
ap-3989	45	54	.	.	PUNCT
ap-3989	46	1	relations	relation	NOUN
ap-3989	46	2	(	(	PUNCT
ap-3989	46	3	1)–(3	1)–(3	NUM
ap-3989	46	4	)	)	PUNCT
ap-3989	46	5	are	be	AUX
ap-3989	46	6	to	to	PART
ap-3989	46	7	be	be	AUX
ap-3989	46	8	complemented	complement	VERB
ap-3989	46	9	by	by	ADP
ap-3989	46	10	the	the	DET
ap-3989	46	11	appropriate	appropriate	ADJ
ap-3989	46	12	initial	initial	ADJ
ap-3989	46	13	and	and	CCONJ
ap-3989	46	14	boundary	boundary	ADJ
ap-3989	46	15	conditions	condition	NOUN
ap-3989	46	16	u(x	u(x	NOUN
ap-3989	46	17	,	,	PUNCT
ap-3989	46	18	0	0	NUM
ap-3989	46	19	)	)	PUNCT
ap-3989	47	1	=	=	PRON
ap-3989	47	2	u0	u0	ADJ
ap-3989	47	3	on	on	ADP
ap-3989	47	4	ω	ω	PROPN
ap-3989	47	5	\	\	PROPN
ap-3989	47	6	p	p	X
ap-3989	47	7	,	,	PUNCT
ap-3989	47	8	(	(	PUNCT
ap-3989	47	9	4	4	X
ap-3989	47	10	)	)	PUNCT
ap-3989	47	11	∇	∇	X
ap-3989	47	12	·	·	PUNCT
ap-3989	47	13	u0	u0	ADJ
ap-3989	47	14	=	=	NOUN
ap-3989	47	15	0	0	PROPN
ap-3989	47	16	,	,	PUNCT
ap-3989	47	17	(	(	PUNCT
ap-3989	47	18	5	5	X
ap-3989	47	19	)	)	PUNCT
ap-3989	47	20	u(x	u(x	NOUN
ap-3989	47	21	,	,	PUNCT
ap-3989	47	22	t	t	NOUN
ap-3989	47	23	)	)	PUNCT
ap-3989	47	24	=	=	PUNCT
ap-3989	47	25	uγ(t	uγ(t	NOUN
ap-3989	47	26	)	)	PUNCT
ap-3989	47	27	on	on	ADP
ap-3989	47	28	γ	γ	X
ap-3989	47	29	,	,	PUNCT
ap-3989	47	30	(	(	PUNCT
ap-3989	47	31	6)∫	6)∫	NUM
ap-3989	47	32	γ	γ	X
ap-3989	47	33	uγ(t)n̂dx	uγ(t)n̂dx	PROPN
ap-3989	47	34	=	=	SYM
ap-3989	47	35	0	0	NUM
ap-3989	47	36	,	,	PUNCT
ap-3989	47	37	(	(	PUNCT
ap-3989	47	38	7	7	X
ap-3989	47	39	)	)	PUNCT
ap-3989	47	40	where	where	SCONJ
ap-3989	47	41	n̂	n̂	PUNCT
ap-3989	47	42	is	be	AUX
ap-3989	47	43	unit	unit	NOUN
ap-3989	47	44	normal	normal	ADJ
ap-3989	47	45	vector	vector	NOUN
ap-3989	47	46	pointing	pointing	NOUN
ap-3989	47	47	out	out	ADP
ap-3989	47	48	of	of	ADP
ap-3989	47	49	γ	γ	PROPN
ap-3989	47	50	.	.	PROPN
ap-3989	47	51	2.2	2.2	NUM
ap-3989	47	52	.	.	PUNCT
ap-3989	48	1	governing	govern	VERB
ap-3989	48	2	equations	equation	NOUN
ap-3989	48	3	for	for	ADP
ap-3989	48	4	obstacles	obstacle	NOUN
ap-3989	48	5	hydrodynamic	hydrodynamic	ADJ
ap-3989	48	6	force	force	NOUN
ap-3989	48	7	fi	fi	NOUN
ap-3989	48	8	and	and	CCONJ
ap-3989	48	9	torque	torque	NOUN
ap-3989	48	10	ti	ti	NOUN
ap-3989	48	11	acting	act	VERB
ap-3989	48	12	on	on	ADP
ap-3989	48	13	the	the	DET
ap-3989	48	14	i	i	PROPN
ap-3989	48	15	-	-	PUNCT
ap-3989	48	16	th	th	VERB
ap-3989	48	17	particle	particle	NOUN
ap-3989	48	18	can	can	AUX
ap-3989	48	19	be	be	AUX
ap-3989	48	20	evaluated	evaluate	VERB
ap-3989	48	21	by	by	ADP
ap-3989	48	22	summing	sum	VERB
ap-3989	48	23	up	up	ADP
ap-3989	48	24	corresponding	correspond	VERB
ap-3989	48	25	fluid	fluid	ADJ
ap-3989	48	26	induced	induce	VERB
ap-3989	48	27	forces	force	NOUN
ap-3989	48	28	acting	act	VERB
ap-3989	48	29	on	on	ADP
ap-3989	48	30	the	the	DET
ap-3989	48	31	particle	particle	NOUN
ap-3989	48	32	boundary	boundary	NOUN
ap-3989	48	33	:	:	PUNCT
ap-3989	48	34	fi	fi	NOUN
ap-3989	48	35	=	=	PROPN
ap-3989	48	36	∫	∫	PROPN
ap-3989	48	37	∂pi	∂pi	PROPN
ap-3989	48	38	σn̂ds	σn̂ds	PROPN
ap-3989	48	39	,	,	PUNCT
ap-3989	48	40	ti	ti	PROPN
ap-3989	48	41	=	=	SYM
ap-3989	48	42	∫	∫	PROPN
ap-3989	48	43	∂pi	∂pi	PROPN
ap-3989	48	44	rixσn̂	rixσn̂	NOUN
ap-3989	48	45	ds	ds	PROPN
ap-3989	48	46	,	,	PUNCT
ap-3989	48	47	(	(	PUNCT
ap-3989	48	48	8)	8)	NUM
ap-3989	48	49	where	where	SCONJ
ap-3989	48	50	pi	pi	NOUN
ap-3989	48	51	is	be	AUX
ap-3989	48	52	the	the	DET
ap-3989	48	53	region	region	NOUN
ap-3989	48	54	occupied	occupy	VERB
ap-3989	48	55	by	by	ADP
ap-3989	48	56	the	the	DET
ap-3989	48	57	particle	particle	NOUN
ap-3989	48	58	and	and	CCONJ
ap-3989	48	59	ri	ri	NOUN
ap-3989	49	1	=	=	PUNCT
ap-3989	49	2	x	x	SYM
ap-3989	49	3	−	−	NOUN
ap-3989	49	4	xi	xi	X
ap-3989	49	5	is	be	AUX
ap-3989	49	6	relative	relative	ADJ
ap-3989	49	7	position	position	NOUN
ap-3989	49	8	vector	vector	NOUN
ap-3989	49	9	to	to	ADP
ap-3989	49	10	particle	particle	NOUN
ap-3989	49	11	center	center	NOUN
ap-3989	49	12	xi	xi	PROPN
ap-3989	49	13	.	.	PROPN
ap-3989	50	1	3	3	X
ap-3989	50	2	.	.	X
ap-3989	50	3	weak	weak	ADJ
ap-3989	50	4	form	form	NOUN
ap-3989	50	5	let	let	VERB
ap-3989	50	6	us	we	PRON
ap-3989	50	7	introduce	introduce	VERB
ap-3989	50	8	the	the	DET
ap-3989	50	9	approximation	approximation	NOUN
ap-3989	50	10	of	of	ADP
ap-3989	50	11	spaces	space	NOUN
ap-3989	50	12	for	for	ADP
ap-3989	50	13	test	test	NOUN
ap-3989	50	14	and	and	CCONJ
ap-3989	50	15	trial	trial	NOUN
ap-3989	50	16	functions	function	NOUN
ap-3989	50	17	for	for	ADP
ap-3989	50	18	velocities	velocity	NOUN
ap-3989	50	19	and	and	CCONJ
ap-3989	50	20	pressure	pressure	NOUN
ap-3989	50	21	in	in	ADP
ap-3989	50	22	the	the	DET
ap-3989	50	23	fluid	fluid	ADJ
ap-3989	50	24	part	part	NOUN
ap-3989	50	25	of	of	ADP
ap-3989	50	26	domain	domain	NOUN
ap-3989	50	27	ω	ω	PROPN
ap-3989	50	28	\	\	PROPN
ap-3989	50	29	p	p	NOUN
ap-3989	50	30	without	without	ADP
ap-3989	50	31	obstacles	obstacle	NOUN
ap-3989	50	32	:	:	PUNCT
ap-3989	50	33	w	w	X
ap-3989	50	34	=	=	SYM
ap-3989	50	35	{	{	PUNCT
ap-3989	50	36	u	u	NOUN
ap-3989	50	37	∈	∈	PROPN
ap-3989	50	38	h1(ω	h1(ω	PROPN
ap-3989	50	39	\	\	PROPN
ap-3989	50	40	p	p	NOUN
ap-3989	50	41	)	)	PUNCT
ap-3989	50	42	:	:	PUNCT
ap-3989	50	43	u	u	NOUN
ap-3989	50	44	=	=	PUNCT
ap-3989	50	45	uγ(t	uγ(t	X
ap-3989	50	46	)	)	PUNCT
ap-3989	50	47	on	on	ADP
ap-3989	50	48	γ	γ	X
ap-3989	50	49	}	}	PUNCT
ap-3989	50	50	,	,	PUNCT
ap-3989	50	51	v	v	X
ap-3989	50	52	=	=	SYM
ap-3989	50	53	{	{	PUNCT
ap-3989	50	54	v	v	NOUN
ap-3989	50	55	∈	∈	PROPN
ap-3989	50	56	h1(ω	h1(ω	PUNCT
ap-3989	50	57	\	\	PROPN
ap-3989	50	58	p	p	NOUN
ap-3989	50	59	)	)	PUNCT
ap-3989	50	60	:	:	PUNCT
ap-3989	50	61	v	v	X
ap-3989	50	62	=	=	SYM
ap-3989	50	63	0	0	NUM
ap-3989	50	64	on	on	ADP
ap-3989	50	65	γ	γ	X
ap-3989	50	66	}	}	PUNCT
ap-3989	50	67	,	,	PUNCT
ap-3989	50	68	l	l	NOUN
ap-3989	50	69	=	=	PUNCT
ap-3989	50	70	{	{	PUNCT
ap-3989	50	71	p	p	X
ap-3989	50	72	∈	∈	PROPN
ap-3989	50	73	l2(ω	l2(ω	NOUN
ap-3989	50	74	\	\	PROPN
ap-3989	50	75	p	p	NOUN
ap-3989	50	76	)	)	PUNCT
ap-3989	50	77	}	}	PUNCT
ap-3989	50	78	,	,	PUNCT
ap-3989	50	79	k	k	PROPN
ap-3989	50	80	=	=	PRON
ap-3989	50	81	{	{	PUNCT
ap-3989	50	82	q	q	NOUN
ap-3989	50	83	∈	∈	PROPN
ap-3989	50	84	l2(ω	l2(ω	NOUN
ap-3989	50	85	\	\	PROPN
ap-3989	50	86	p	p	NOUN
ap-3989	50	87	)	)	PUNCT
ap-3989	50	88	}	}	PUNCT
ap-3989	50	89	.	.	PUNCT
ap-3989	51	1	by	by	ADP
ap-3989	51	2	using	use	VERB
ap-3989	51	3	the	the	DET
ap-3989	51	4	method	method	NOUN
ap-3989	51	5	of	of	ADP
ap-3989	51	6	weighted	weight	VERB
ap-3989	51	7	residuals	residual	NOUN
ap-3989	51	8	applied	apply	VERB
ap-3989	51	9	to	to	ADP
ap-3989	51	10	(	(	PUNCT
ap-3989	51	11	1	1	NUM
ap-3989	51	12	)	)	PUNCT
ap-3989	51	13	,	,	PUNCT
ap-3989	51	14	(	(	PUNCT
ap-3989	51	15	2	2	X
ap-3989	51	16	)	)	PUNCT
ap-3989	51	17	and	and	CCONJ
ap-3989	51	18	using	use	VERB
ap-3989	51	19	finite	finite	ADJ
ap-3989	51	20	dimensional	dimensional	ADJ
ap-3989	51	21	spaces	space	NOUN
ap-3989	51	22	w0.h	w0.h	ADJ
ap-3989	51	23	,	,	PUNCT
ap-3989	51	24	v0.h	v0.h	ADJ
ap-3989	51	25	,	,	PUNCT
ap-3989	51	26	l0.h	l0.h	ADJ
ap-3989	51	27	,	,	PUNCT
ap-3989	51	28	k0.h	k0.h	PROPN
ap-3989	51	29	,	,	PUNCT
ap-3989	51	30	approximating	approximate	VERB
ap-3989	51	31	w	w	PROPN
ap-3989	51	32	,	,	PUNCT
ap-3989	51	33	v	v	NOUN
ap-3989	51	34	,	,	PUNCT
ap-3989	51	35	l	l	NOUN
ap-3989	51	36	,	,	PUNCT
ap-3989	51	37	k	k	PROPN
ap-3989	51	38	defined	define	VERB
ap-3989	51	39	above	above	ADP
ap-3989	51	40	we	we	PRON
ap-3989	51	41	arrive	arrive	VERB
ap-3989	51	42	at	at	ADP
ap-3989	51	43	the	the	DET
ap-3989	51	44	following	follow	VERB
ap-3989	51	45	finite	finite	ADJ
ap-3989	51	46	-	-	ADJ
ap-3989	51	47	element	element	ADJ
ap-3989	51	48	approximation	approximation	NOUN
ap-3989	51	49	of	of	ADP
ap-3989	51	50	the	the	DET
ap-3989	51	51	navier	navier	NOUN
ap-3989	51	52	-	-	PUNCT
ap-3989	51	53	stokes	stoke	NOUN
ap-3989	51	54	equations	equation	NOUN
ap-3989	51	55	:	:	PUNCT
ap-3989	51	56	find	find	VERB
ap-3989	51	57	uh	uh	INTJ
ap-3989	51	58	∈w0.h	∈w0.h	PROPN
ap-3989	51	59	,	,	PUNCT
ap-3989	51	60	p	p	PROPN
ap-3989	51	61	∈	∈	PROPN
ap-3989	51	62	l0.h	l0.h	VERB
ap-3989	51	63	satisfying∫	satisfying∫	NOUN
ap-3989	51	64	ω\p	ω\p	NUM
ap-3989	51	65	(	(	PUNCT
ap-3989	51	66	%	%	INTJ
ap-3989	51	67	∂uh	∂uh	PROPN
ap-3989	51	68	∂t	∂t	PROPN
ap-3989	52	1	+	+	CCONJ
ap-3989	52	2	(	(	PUNCT
ap-3989	52	3	uh	uh	INTJ
ap-3989	52	4	·	·	PUNCT
ap-3989	52	5	∇)uh	∇)uh	X
ap-3989	52	6	)	)	PUNCT
ap-3989	52	7	·	·	PUNCT
ap-3989	53	1	vh	vh	PROPN
ap-3989	53	2	dx	dx	PROPN
ap-3989	53	3	−	−	PROPN
ap-3989	53	4	∫	∫	PROPN
ap-3989	53	5	ω\p	ω\p	X
ap-3989	53	6	ph∇	ph∇	NOUN
ap-3989	53	7	·	·	PUNCT
ap-3989	53	8	vh	vh	PROPN
ap-3989	53	9	dx+	dx+	PROPN
ap-3989	53	10	∫	∫	PROPN
ap-3989	53	11	ω\p	ω\p	X
ap-3989	53	12	2ηd[uh	2ηd[uh	NUM
ap-3989	53	13	]	]	PUNCT
ap-3989	53	14	:	:	PUNCT
ap-3989	53	15	d[vh	d[vh	PROPN
ap-3989	53	16	]	]	PUNCT
ap-3989	53	17	dx	dx	PROPN
ap-3989	54	1	=	=	SYM
ap-3989	54	2	0	0	PROPN
ap-3989	54	3	for	for	ADP
ap-3989	54	4	all	all	DET
ap-3989	54	5	vh	vh	PROPN
ap-3989	54	6	∈w0.h	∈w0.h	PROPN
ap-3989	54	7	,	,	PUNCT
ap-3989	54	8	(	(	PUNCT
ap-3989	54	9	9)∫	9)∫	PROPN
ap-3989	54	10	ω\p	ω\p	X
ap-3989	54	11	qh∇	qh∇	PRON
ap-3989	54	12	·	·	PUNCT
ap-3989	54	13	uh	uh	INTJ
ap-3989	54	14	dx	dx	PROPN
ap-3989	54	15	=	=	SYM
ap-3989	54	16	0	0	PROPN
ap-3989	54	17	for	for	ADP
ap-3989	54	18	all	all	DET
ap-3989	54	19	qh	qh	NOUN
ap-3989	54	20	∈	∈	PROPN
ap-3989	54	21	l0.h	l0.h	PROPN
ap-3989	54	22	,	,	PUNCT
ap-3989	54	23	(	(	PUNCT
ap-3989	54	24	10	10	NUM
ap-3989	54	25	)	)	PUNCT
ap-3989	54	26	uh(0	uh(0	NOUN
ap-3989	54	27	)	)	PUNCT
ap-3989	54	28	=	=	SYM
ap-3989	54	29	u0,h	u0,h	PROPN
ap-3989	54	30	on	on	ADP
ap-3989	54	31	ω	ω	NUM
ap-3989	54	32	,	,	PUNCT
ap-3989	54	33	(	(	PUNCT
ap-3989	54	34	11	11	NUM
ap-3989	54	35	)	)	PUNCT
ap-3989	54	36	where	where	SCONJ
ap-3989	54	37	u0,h	u0,h	PROPN
ap-3989	54	38	is	be	AUX
ap-3989	54	39	a	a	DET
ap-3989	54	40	divergence	divergence	NOUN
ap-3989	54	41	-	-	PUNCT
ap-3989	54	42	free	free	ADJ
ap-3989	54	43	initial	initial	ADJ
ap-3989	54	44	velocity	velocity	NOUN
ap-3989	54	45	.	.	PUNCT
ap-3989	55	1	since	since	SCONJ
ap-3989	55	2	in	in	ADP
ap-3989	55	3	(	(	PUNCT
ap-3989	55	4	9	9	NUM
ap-3989	55	5	)	)	PUNCT
ap-3989	55	6	u	u	NOUN
ap-3989	55	7	is	be	AUX
ap-3989	55	8	divergence	divergence	NOUN
ap-3989	55	9	-	-	PUNCT
ap-3989	55	10	free	free	ADJ
ap-3989	55	11	and	and	CCONJ
ap-3989	55	12	satisfies	satisfy	VERB
ap-3989	55	13	the	the	DET
ap-3989	55	14	dirichlet	dirichlet	PROPN
ap-3989	55	15	boundary	boundary	ADJ
ap-3989	55	16	condition	condition	NOUN
ap-3989	55	17	(	(	PUNCT
ap-3989	55	18	4	4	NUM
ap-3989	55	19	)	)	PUNCT
ap-3989	55	20	on	on	ADP
ap-3989	55	21	γ	γ	PROPN
ap-3989	55	22	,	,	PUNCT
ap-3989	55	23	we	we	PRON
ap-3989	55	24	can	can	AUX
ap-3989	55	25	write∫	write∫	VERB
ap-3989	55	26	ω\p	ω\p	VERB
ap-3989	55	27	2ηd[uh	2ηd[uh	NUM
ap-3989	55	28	]	]	PUNCT
ap-3989	55	29	:	:	PUNCT
ap-3989	55	30	d[vh	d[vh	PROPN
ap-3989	55	31	]	]	PUNCT
ap-3989	55	32	dx	dx	PROPN
ap-3989	56	1	=	=	SYM
ap-3989	56	2	∫	∫	PROPN
ap-3989	56	3	ω\p	ω\p	NUM
ap-3989	56	4	η∇uh	η∇uh	NOUN
ap-3989	56	5	:	:	PUNCT
ap-3989	56	6	∇vh	∇vh	VERB
ap-3989	56	7	dx	dx	VERB
ap-3989	56	8	for	for	ADP
ap-3989	56	9	all	all	DET
ap-3989	56	10	vh	vh	PROPN
ap-3989	56	11	∈w0.h	∈w0.h	PROPN
ap-3989	56	12	.	.	PUNCT
ap-3989	57	1	246	246	NUM
ap-3989	57	2	vol	vol	NOUN
ap-3989	57	3	.	.	PUNCT
ap-3989	57	4	57	57	NUM
ap-3989	57	5	no	no	NOUN
ap-3989	57	6	.	.	PUNCT
ap-3989	58	1	4/2017	4/2017	NUM
ap-3989	58	2	fictitious	fictitious	ADJ
ap-3989	58	3	domain	domain	NOUN
ap-3989	58	4	method	method	NOUN
ap-3989	58	5	for	for	ADP
ap-3989	58	6	a	a	DET
ap-3989	58	7	numerical	numerical	ADJ
ap-3989	58	8	simulation	simulation	NOUN
ap-3989	58	9	3.1	3.1	NUM
ap-3989	58	10	.	.	PUNCT
ap-3989	59	1	a	a	DET
ap-3989	59	2	fictitious	fictitious	ADJ
ap-3989	59	3	domain	domain	NOUN
ap-3989	59	4	formulation	formulation	NOUN
ap-3989	59	5	to	to	PART
ap-3989	59	6	extend	extend	VERB
ap-3989	59	7	from	from	ADP
ap-3989	59	8	the	the	DET
ap-3989	59	9	domain	domain	NOUN
ap-3989	59	10	ω	ω	PROPN
ap-3989	59	11	\	\	PROPN
ap-3989	60	1	p	p	NOUN
ap-3989	60	2	to	to	ADP
ap-3989	60	3	the	the	DET
ap-3989	60	4	fictitious	fictitious	ADJ
ap-3989	60	5	domain	domain	NOUN
ap-3989	60	6	ω	ω	NOUN
ap-3989	60	7	,	,	PUNCT
ap-3989	60	8	it	it	PRON
ap-3989	60	9	is	be	AUX
ap-3989	60	10	necessary	necessary	ADJ
ap-3989	60	11	to	to	PART
ap-3989	60	12	enforce	enforce	VERB
ap-3989	60	13	no	no	DET
ap-3989	60	14	-	-	PUNCT
ap-3989	60	15	flow	flow	NOUN
ap-3989	60	16	constraints	constraint	NOUN
ap-3989	60	17	inside	inside	ADP
ap-3989	60	18	each	each	DET
ap-3989	60	19	pi	pi	NOUN
ap-3989	60	20	.	.	PUNCT
ap-3989	61	1	let	let	VERB
ap-3989	61	2	us	we	PRON
ap-3989	61	3	introduce	introduce	VERB
ap-3989	61	4	an	an	DET
ap-3989	61	5	approximation	approximation	NOUN
ap-3989	61	6	of	of	ADP
ap-3989	61	7	spaces	space	NOUN
ap-3989	61	8	for	for	ADP
ap-3989	61	9	test	test	NOUN
ap-3989	61	10	and	and	CCONJ
ap-3989	61	11	trial	trial	NOUN
ap-3989	61	12	functions	function	NOUN
ap-3989	61	13	velocities	velocity	NOUN
ap-3989	61	14	and	and	CCONJ
ap-3989	61	15	pressure	pressure	NOUN
ap-3989	61	16	for	for	ADP
ap-3989	61	17	the	the	DET
ap-3989	61	18	fictitious	fictitious	ADJ
ap-3989	61	19	domain	domain	NOUN
ap-3989	61	20	ω	ω	NOUN
ap-3989	61	21	:	:	PUNCT
ap-3989	61	22	w	w	NOUN
ap-3989	61	23	=	=	PUNCT
ap-3989	61	24	{	{	PUNCT
ap-3989	61	25	u	u	NOUN
ap-3989	61	26	∈	∈	PROPN
ap-3989	61	27	h1(ω	h1(ω	PROPN
ap-3989	61	28	)	)	PUNCT
ap-3989	61	29	:	:	PUNCT
ap-3989	61	30	u	u	NOUN
ap-3989	61	31	=	=	PUNCT
ap-3989	61	32	uγ(t	uγ(t	X
ap-3989	61	33	)	)	PUNCT
ap-3989	61	34	on	on	ADP
ap-3989	61	35	γ	γ	X
ap-3989	61	36	}	}	PUNCT
ap-3989	61	37	,	,	PUNCT
ap-3989	61	38	v	v	X
ap-3989	61	39	=	=	SYM
ap-3989	61	40	{	{	PUNCT
ap-3989	61	41	v	v	NOUN
ap-3989	61	42	∈	∈	PROPN
ap-3989	61	43	h1(ω	h1(ω	PROPN
ap-3989	61	44	)	)	PUNCT
ap-3989	61	45	:	:	PUNCT
ap-3989	61	46	v	v	X
ap-3989	61	47	=	=	SYM
ap-3989	61	48	0	0	NUM
ap-3989	61	49	on	on	ADP
ap-3989	61	50	γ	γ	X
ap-3989	61	51	}	}	PUNCT
ap-3989	61	52	,	,	PUNCT
ap-3989	61	53	l	l	NOUN
ap-3989	61	54	=	=	PUNCT
ap-3989	61	55	{	{	PUNCT
ap-3989	61	56	p	p	X
ap-3989	61	57	∈	∈	PROPN
ap-3989	61	58	l2(ω	l2(ω	NOUN
ap-3989	61	59	)	)	PUNCT
ap-3989	61	60	}	}	PUNCT
ap-3989	61	61	,	,	PUNCT
ap-3989	61	62	k	k	PROPN
ap-3989	61	63	=	=	PRON
ap-3989	61	64	{	{	PUNCT
ap-3989	61	65	q	q	NOUN
ap-3989	61	66	∈	∈	PROPN
ap-3989	61	67	l2(ω	l2(ω	NOUN
ap-3989	61	68	)	)	PUNCT
ap-3989	61	69	}	}	PUNCT
ap-3989	61	70	.	.	PUNCT
ap-3989	62	1	by	by	ADP
ap-3989	62	2	extending	extend	VERB
ap-3989	62	3	the	the	DET
ap-3989	62	4	incompressibility	incompressibility	NOUN
ap-3989	62	5	condition	condition	NOUN
ap-3989	62	6	to	to	ADP
ap-3989	62	7	the	the	DET
ap-3989	62	8	whole	whole	ADJ
ap-3989	62	9	ω	ω	NOUN
ap-3989	62	10	,	,	PUNCT
ap-3989	62	11	we	we	PRON
ap-3989	62	12	get∫	get∫	VERB
ap-3989	62	13	ω	ω	NUM
ap-3989	62	14	q∇	q∇	ADJ
ap-3989	62	15	·	·	PUNCT
ap-3989	62	16	udx	udx	NOUN
ap-3989	62	17	=	=	PUNCT
ap-3989	62	18	0	0	NUM
ap-3989	62	19	for	for	ADP
ap-3989	62	20	all	all	DET
ap-3989	62	21	q	q	PROPN
ap-3989	62	22	∈	∈	PROPN
ap-3989	62	23	l2	l2	NOUN
ap-3989	62	24	h(ω	h(ω	PROPN
ap-3989	62	25	)	)	PUNCT
ap-3989	62	26	.	.	PUNCT
ap-3989	63	1	the	the	DET
ap-3989	63	2	condition	condition	NOUN
ap-3989	63	3	to	to	PART
ap-3989	63	4	enforce	enforce	VERB
ap-3989	63	5	rigid	rigid	ADJ
ap-3989	63	6	body	body	NOUN
ap-3989	63	7	(	(	PUNCT
ap-3989	63	8	or	or	CCONJ
ap-3989	63	9	no	no	DET
ap-3989	63	10	-	-	PUNCT
ap-3989	63	11	flow	flow	NOUN
ap-3989	63	12	)	)	PUNCT
ap-3989	63	13	constrains	constrain	VERB
ap-3989	63	14	for	for	ADP
ap-3989	63	15	each	each	DET
ap-3989	63	16	obstacle	obstacle	NOUN
ap-3989	63	17	can	can	AUX
ap-3989	63	18	be	be	AUX
ap-3989	63	19	expressed	express	VERB
ap-3989	63	20	as	as	ADP
ap-3989	63	21	u(x	u(x	NOUN
ap-3989	63	22	,	,	PUNCT
ap-3989	63	23	t)−	t)−	PROPN
ap-3989	63	24	u(xi	u(xi	PROPN
ap-3989	63	25	,	,	PUNCT
ap-3989	63	26	t	t	PROPN
ap-3989	63	27	)	)	PUNCT
ap-3989	63	28	=	=	SYM
ap-3989	63	29	0	0	NUM
ap-3989	63	30	for	for	ADP
ap-3989	63	31	all	all	PRON
ap-3989	63	32	x	x	SYM
ap-3989	63	33	∈	∈	PROPN
ap-3989	63	34	p	p	NOUN
ap-3989	63	35	.	.	PUNCT
ap-3989	64	1	(	(	PUNCT
ap-3989	64	2	12	12	NUM
ap-3989	64	3	)	)	PUNCT
ap-3989	64	4	to	to	PART
ap-3989	64	5	relax	relax	VERB
ap-3989	64	6	the	the	DET
ap-3989	64	7	no	no	DET
ap-3989	64	8	-	-	PUNCT
ap-3989	64	9	flow	flow	NOUN
ap-3989	64	10	constraint	constraint	NOUN
ap-3989	64	11	defined	define	VERB
ap-3989	64	12	above	above	ADV
ap-3989	64	13	,	,	PUNCT
ap-3989	64	14	the	the	DET
ap-3989	64	15	family	family	NOUN
ap-3989	64	16	of	of	ADP
ap-3989	64	17	lagrange	lagrange	PROPN
ap-3989	64	18	multipliers	multiplier	NOUN
ap-3989	64	19	λj	λj	PROPN
ap-3989	64	20	is	be	AUX
ap-3989	64	21	introduced	introduce	VERB
ap-3989	64	22	representing	represent	VERB
ap-3989	64	23	a	a	DET
ap-3989	64	24	discrete	discrete	ADJ
ap-3989	64	25	set	set	NOUN
ap-3989	64	26	of	of	ADP
ap-3989	64	27	points	point	NOUN
ap-3989	64	28	covering	cover	VERB
ap-3989	64	29	pj	pj	PROPN
ap-3989	64	30	,	,	PUNCT
ap-3989	64	31	such	such	ADJ
ap-3989	64	32	that	that	SCONJ
ap-3989	64	33	λh	λh	VERB
ap-3989	64	34	=	=	PRON
ap-3989	64	35	{	{	PUNCT
ap-3989	64	36	µh	µh	INTJ
ap-3989	64	37	:	:	PUNCT
ap-3989	64	38	µh	µh	NOUN
ap-3989	64	39	=	=	PUNCT
ap-3989	64	40	m∑	m∑	PROPN
ap-3989	64	41	i=1	i=1	PROPN
ap-3989	64	42	µiδ(x−xi	µiδ(x−xi	PROPN
ap-3989	64	43	)	)	PUNCT
ap-3989	64	44	,	,	PUNCT
ap-3989	64	45	µ1	µ1	PROPN
ap-3989	64	46	,	,	PUNCT
ap-3989	64	47	.	.	PUNCT
ap-3989	64	48	.	.	PUNCT
ap-3989	65	1	.	.	PUNCT
ap-3989	66	1	,	,	PUNCT
ap-3989	66	2	µm	µm	ADP
ap-3989	66	3	∈r2	∈r2	PROPN
ap-3989	66	4	}	}	PUNCT
ap-3989	66	5	,	,	PUNCT
ap-3989	66	6	where	where	SCONJ
ap-3989	66	7	δ	δ	PROPN
ap-3989	66	8	is	be	AUX
ap-3989	66	9	the	the	DET
ap-3989	66	10	dirac	dirac	PROPN
ap-3989	66	11	delta	delta	NOUN
ap-3989	66	12	function	function	NOUN
ap-3989	66	13	at	at	ADP
ap-3989	66	14	x	x	X
ap-3989	66	15	=	=	NOUN
ap-3989	66	16	0	0	NUM
ap-3989	66	17	.	.	PUNCT
ap-3989	66	18	using	use	VERB
ap-3989	66	19	the	the	DET
ap-3989	66	20	space	space	NOUN
ap-3989	66	21	λh	λh	VERB
ap-3989	66	22	defined	define	VERB
ap-3989	66	23	above	above	ADV
ap-3989	66	24	,	,	PUNCT
ap-3989	66	25	the	the	DET
ap-3989	66	26	condition	condition	NOUN
ap-3989	66	27	(	(	PUNCT
ap-3989	66	28	12	12	NUM
ap-3989	66	29	)	)	PUNCT
ap-3989	66	30	is	be	AUX
ap-3989	66	31	relaxed	relax	VERB
ap-3989	66	32	to	to	ADP
ap-3989	66	33	〈	〈	PROPN
ap-3989	66	34	µh	µh	PROPN
ap-3989	66	35	,	,	PUNCT
ap-3989	66	36	u(x	u(x	PROPN
ap-3989	66	37	,	,	PUNCT
ap-3989	66	38	t)−	t)−	PROPN
ap-3989	66	39	u(xi	u(xi	PROPN
ap-3989	66	40	,	,	PUNCT
ap-3989	66	41	t	t	NOUN
ap-3989	66	42	)	)	PUNCT
ap-3989	66	43	〉	〉	NOUN
ap-3989	66	44	=	=	SYM
ap-3989	66	45	0	0	NUM
ap-3989	66	46	for	for	ADP
ap-3989	66	47	all	all	DET
ap-3989	66	48	µh	µh	PROPN
ap-3989	66	49	∈	∈	NOUN
ap-3989	66	50	λh	λh	ADP
ap-3989	66	51	,	,	PUNCT
ap-3989	66	52	(	(	PUNCT
ap-3989	66	53	13	13	NUM
ap-3989	66	54	)	)	PUNCT
ap-3989	66	55	where	where	SCONJ
ap-3989	66	56	the	the	DET
ap-3989	66	57	inner	inner	ADJ
ap-3989	66	58	product	product	NOUN
ap-3989	66	59	on	on	ADP
ap-3989	66	60	the	the	DET
ap-3989	66	61	obstacle	obstacle	NOUN
ap-3989	66	62	is	be	AUX
ap-3989	66	63	defined	define	VERB
ap-3989	66	64	as	as	ADP
ap-3989	66	65	〈	〈	PROPN
ap-3989	66	66	µh	µh	PROPN
ap-3989	66	67	,	,	PUNCT
ap-3989	66	68	vh〉p	vh〉p	PROPN
ap-3989	66	69	=	=	PUNCT
ap-3989	67	1	m∑	m∑	INTJ
ap-3989	67	2	i=1	i=1	PROPN
ap-3989	68	1	µh	µh	NOUN
ap-3989	68	2	,	,	PUNCT
ap-3989	68	3	i	i	PRON
ap-3989	68	4	·	·	PUNCT
ap-3989	68	5	vh(xi	vh(xi	NUM
ap-3989	68	6	)	)	PUNCT
ap-3989	68	7	.	.	PUNCT
ap-3989	69	1	in	in	ADP
ap-3989	69	2	case	case	NOUN
ap-3989	69	3	of	of	ADP
ap-3989	69	4	a	a	DET
ap-3989	69	5	fixed	fix	VERB
ap-3989	69	6	particle	particle	NOUN
ap-3989	69	7	,	,	PUNCT
ap-3989	69	8	it	it	PRON
ap-3989	69	9	is	be	AUX
ap-3989	69	10	necessary	necessary	ADJ
ap-3989	69	11	to	to	PART
ap-3989	69	12	prescribe	prescribe	VERB
ap-3989	69	13	zero	zero	NUM
ap-3989	69	14	velocity	velocity	NOUN
ap-3989	69	15	at	at	ADP
ap-3989	69	16	the	the	DET
ap-3989	69	17	particle	particle	NOUN
ap-3989	69	18	center	center	NOUN
ap-3989	69	19	.	.	PUNCT
ap-3989	70	1	in	in	ADP
ap-3989	70	2	case	case	NOUN
ap-3989	70	3	of	of	ADP
ap-3989	70	4	moving	move	VERB
ap-3989	70	5	particle	particle	NOUN
ap-3989	70	6	,	,	PUNCT
ap-3989	70	7	the	the	DET
ap-3989	70	8	equations	equation	NOUN
ap-3989	70	9	of	of	ADP
ap-3989	70	10	motions	motion	NOUN
ap-3989	70	11	for	for	ADP
ap-3989	70	12	a	a	DET
ap-3989	70	13	particle	particle	NOUN
ap-3989	70	14	have	have	VERB
ap-3989	70	15	to	to	PART
ap-3989	70	16	be	be	AUX
ap-3989	70	17	solved	solve	VERB
ap-3989	70	18	as	as	ADV
ap-3989	70	19	well	well	ADV
ap-3989	70	20	.	.	PUNCT
ap-3989	71	1	the	the	DET
ap-3989	71	2	combined	combine	VERB
ap-3989	71	3	weak	weak	ADJ
ap-3989	71	4	solution	solution	NOUN
ap-3989	71	5	is	be	AUX
ap-3989	71	6	then	then	ADV
ap-3989	71	7	to	to	PART
ap-3989	71	8	find	find	VERB
ap-3989	71	9	uh	uh	INTJ
ap-3989	71	10	∈	∈	ADJ
ap-3989	71	11	w0.h	w0.h	ADJ
ap-3989	71	12	,	,	PUNCT
ap-3989	71	13	ph	ph	PROPN
ap-3989	71	14	∈	∈	PROPN
ap-3989	71	15	l0.h	l0.h	PROPN
ap-3989	71	16	,	,	PUNCT
ap-3989	71	17	where	where	SCONJ
ap-3989	71	18	finite	finite	ADJ
ap-3989	71	19	dimensional	dimensional	ADJ
ap-3989	71	20	spacesw0.h	spacesw0.h	ADJ
ap-3989	71	21	,	,	PUNCT
ap-3989	71	22	l0.h	l0.h	VERB
ap-3989	71	23	are	be	AUX
ap-3989	71	24	approximating	approximate	VERB
ap-3989	71	25	w	w	PRON
ap-3989	71	26	,	,	PUNCT
ap-3989	71	27	l	l	NOUN
ap-3989	71	28	spaces	space	NOUN
ap-3989	71	29	defined	define	VERB
ap-3989	71	30	above	above	ADP
ap-3989	71	31	and	and	CCONJ
ap-3989	71	32	λh	λh	ADP
ap-3989	71	33	∈	∈	PROPN
ap-3989	71	34	λh	λh	SCONJ
ap-3989	71	35	is	be	AUX
ap-3989	71	36	such	such	ADJ
ap-3989	71	37	that∫	that∫	NOUN
ap-3989	71	38	ω	ω	NUM
ap-3989	71	39	%	%	NOUN
ap-3989	71	40	(	(	PUNCT
ap-3989	71	41	∂u	∂u	PROPN
ap-3989	71	42	∂t	∂t	PROPN
ap-3989	71	43	+	+	CCONJ
ap-3989	71	44	(	(	PUNCT
ap-3989	71	45	uh	uh	INTJ
ap-3989	71	46	·	·	PUNCT
ap-3989	71	47	∇)uh	∇)uh	ADJ
ap-3989	71	48	)	)	PUNCT
ap-3989	71	49	vh	vh	PROPN
ap-3989	71	50	dx−	dx−	NUM
ap-3989	71	51	∫	∫	PROPN
ap-3989	72	1	ω	ω	PROPN
ap-3989	72	2	ph∇	ph∇	X
ap-3989	73	1	·	·	PUNCT
ap-3989	73	2	vh	vh	PROPN
ap-3989	73	3	dx	dx	PROPN
ap-3989	73	4	+	+	CCONJ
ap-3989	73	5	∫	∫	PROPN
ap-3989	73	6	ω	ω	NUM
ap-3989	73	7	2ηd[uh	2ηd[uh	NUM
ap-3989	73	8	]	]	PUNCT
ap-3989	73	9	:	:	PUNCT
ap-3989	73	10	d[vh	d[vh	PROPN
ap-3989	73	11	]	]	PUNCT
ap-3989	73	12	dx	dx	PROPN
ap-3989	73	13	=	=	SYM
ap-3989	73	14	〈	〈	PROPN
ap-3989	73	15	λh	λh	PROPN
ap-3989	73	16	,	,	PUNCT
ap-3989	73	17	vh〉p	vh〉p	NOUN
ap-3989	73	18	for	for	ADP
ap-3989	73	19	all	all	DET
ap-3989	73	20	vh	vh	PROPN
ap-3989	73	21	∈	∈	PROPN
ap-3989	73	22	vh,∫	vh,∫	X
ap-3989	73	23	ω	ω	NUM
ap-3989	73	24	qh∇	qh∇	NUM
ap-3989	73	25	·	·	PUNCT
ap-3989	73	26	uh	uh	INTJ
ap-3989	73	27	dx	dx	PROPN
ap-3989	73	28	=	=	SYM
ap-3989	73	29	0	0	PROPN
ap-3989	73	30	for	for	ADP
ap-3989	73	31	all	all	DET
ap-3989	73	32	qh	qh	NOUN
ap-3989	73	33	∈	∈	PROPN
ap-3989	73	34	l2	l2	NOUN
ap-3989	73	35	h	h	NOUN
ap-3989	73	36	,	,	PUNCT
ap-3989	73	37	〈	〈	PROPN
ap-3989	73	38	µh	µh	PRON
ap-3989	73	39	,	,	PUNCT
ap-3989	73	40	uh〉p	uh〉p	ADJ
ap-3989	73	41	=	=	NOUN
ap-3989	73	42	0	0	NUM
ap-3989	73	43	for	for	ADP
ap-3989	73	44	all	all	DET
ap-3989	73	45	µh	µh	PROPN
ap-3989	73	46	∈	∈	PROPN
ap-3989	73	47	λh	λh	ADP
ap-3989	73	48	,	,	PUNCT
ap-3989	73	49	u(0	u(0	NOUN
ap-3989	73	50	)	)	PUNCT
ap-3989	73	51	=	=	SYM
ap-3989	73	52	u0	u0	ADJ
ap-3989	73	53	on	on	ADP
ap-3989	73	54	ω	ω	PROPN
ap-3989	73	55	.	.	PROPN
ap-3989	73	56	3.2	3.2	NUM
ap-3989	73	57	.	.	PUNCT
ap-3989	73	58	time	time	NOUN
ap-3989	73	59	discretization	discretization	NOUN
ap-3989	73	60	by	by	ADP
ap-3989	73	61	operator	operator	NOUN
ap-3989	73	62	splitting	splitting	NOUN
ap-3989	73	63	as	as	SCONJ
ap-3989	73	64	pointed	point	VERB
ap-3989	73	65	out	out	ADP
ap-3989	73	66	by	by	ADP
ap-3989	73	67	glowinski	glowinski	NOUN
ap-3989	73	68	[	[	PUNCT
ap-3989	73	69	11	11	NUM
ap-3989	73	70	]	]	PUNCT
ap-3989	73	71	,	,	PUNCT
ap-3989	73	72	numerical	numerical	ADJ
ap-3989	73	73	solutions	solution	NOUN
ap-3989	73	74	of	of	ADP
ap-3989	73	75	the	the	DET
ap-3989	73	76	nonlinear	nonlinear	ADJ
ap-3989	73	77	partial	partial	ADJ
ap-3989	73	78	differential	differential	NOUN
ap-3989	73	79	navier	navier	NOUN
ap-3989	73	80	-	-	PUNCT
ap-3989	73	81	stokes	stoke	NOUN
ap-3989	73	82	equations	equation	NOUN
ap-3989	73	83	are	be	AUX
ap-3989	73	84	not	not	PART
ap-3989	73	85	trivial	trivial	ADJ
ap-3989	73	86	,	,	PUNCT
ap-3989	73	87	mainly	mainly	ADV
ap-3989	73	88	due	due	ADP
ap-3989	73	89	to	to	ADP
ap-3989	73	90	the	the	DET
ap-3989	73	91	following	following	ADJ
ap-3989	73	92	reasons	reason	NOUN
ap-3989	73	93	:	:	PUNCT
ap-3989	73	94	(	(	PUNCT
ap-3989	73	95	i	i	NOUN
ap-3989	73	96	)	)	PUNCT
ap-3989	73	97	the	the	DET
ap-3989	73	98	above	above	ADJ
ap-3989	73	99	equations	equation	NOUN
ap-3989	73	100	are	be	AUX
ap-3989	73	101	nonlinear	nonlinear	ADJ
ap-3989	73	102	and	and	CCONJ
ap-3989	73	103	(	(	PUNCT
ap-3989	73	104	ii	ii	NOUN
ap-3989	73	105	)	)	PUNCT
ap-3989	73	106	the	the	DET
ap-3989	73	107	incompressibility	incompressibility	NOUN
ap-3989	73	108	condition	condition	NOUN
ap-3989	73	109	is	be	AUX
ap-3989	73	110	difficult	difficult	ADJ
ap-3989	73	111	to	to	PART
ap-3989	73	112	handle	handle	VERB
ap-3989	73	113	.	.	PUNCT
ap-3989	74	1	the	the	DET
ap-3989	74	2	above	above	ADJ
ap-3989	74	3	equations	equation	NOUN
ap-3989	74	4	represent	represent	VERB
ap-3989	74	5	a	a	DET
ap-3989	74	6	system	system	NOUN
ap-3989	74	7	of	of	ADP
ap-3989	74	8	partial	partial	ADJ
ap-3989	74	9	differential	differential	NOUN
ap-3989	74	10	equations	equation	NOUN
ap-3989	74	11	,	,	PUNCT
ap-3989	74	12	coupled	couple	VERB
ap-3989	74	13	through	through	ADP
ap-3989	74	14	the	the	DET
ap-3989	74	15	nonlinear	nonlinear	ADJ
ap-3989	74	16	term	term	NOUN
ap-3989	74	17	,	,	PUNCT
ap-3989	74	18	the	the	DET
ap-3989	74	19	incompressibility	incompressibility	NOUN
ap-3989	74	20	condition	condition	NOUN
ap-3989	74	21	∇	∇	X
ap-3989	74	22	·	·	PUNCT
ap-3989	74	23	u	u	NOUN
ap-3989	74	24	=	=	NOUN
ap-3989	74	25	0	0	NUM
ap-3989	74	26	,	,	PUNCT
ap-3989	74	27	and	and	CCONJ
ap-3989	74	28	sometimes	sometimes	ADV
ap-3989	74	29	through	through	ADP
ap-3989	74	30	the	the	DET
ap-3989	74	31	boundary	boundary	ADJ
ap-3989	74	32	conditions	condition	NOUN
ap-3989	74	33	.	.	PUNCT
ap-3989	75	1	the	the	DET
ap-3989	75	2	use	use	NOUN
ap-3989	75	3	of	of	ADP
ap-3989	75	4	time	time	NOUN
ap-3989	75	5	discretization	discretization	NOUN
ap-3989	75	6	by	by	ADP
ap-3989	75	7	operator	operator	NOUN
ap-3989	75	8	splitting	splitting	NOUN
ap-3989	75	9	will	will	AUX
ap-3989	75	10	partly	partly	ADV
ap-3989	75	11	overcome	overcome	VERB
ap-3989	75	12	the	the	DET
ap-3989	75	13	above	above	ADJ
ap-3989	75	14	difficulties	difficulty	NOUN
ap-3989	75	15	;	;	PUNCT
ap-3989	75	16	in	in	ADP
ap-3989	75	17	particular	particular	ADJ
ap-3989	75	18	,	,	PUNCT
ap-3989	75	19	decoupling	decouple	VERB
ap-3989	75	20	of	of	ADP
ap-3989	75	21	difficulties	difficulty	NOUN
ap-3989	75	22	associated	associate	VERB
ap-3989	75	23	with	with	ADP
ap-3989	75	24	the	the	DET
ap-3989	75	25	nonlinearity	nonlinearity	NOUN
ap-3989	75	26	from	from	ADP
ap-3989	75	27	those	those	PRON
ap-3989	75	28	associated	associate	VERB
ap-3989	75	29	with	with	ADP
ap-3989	75	30	the	the	DET
ap-3989	75	31	incompressibility	incompressibility	NOUN
ap-3989	75	32	condition	condition	NOUN
ap-3989	75	33	.	.	PUNCT
ap-3989	76	1	following	follow	VERB
ap-3989	76	2	the	the	DET
ap-3989	76	3	work	work	NOUN
ap-3989	76	4	of	of	ADP
ap-3989	76	5	glowinski	glowinski	NOUN
ap-3989	76	6	and	and	CCONJ
ap-3989	76	7	pironneau	pironneau	VERB
ap-3989	76	8	[	[	X
ap-3989	76	9	12	12	NUM
ap-3989	76	10	]	]	PUNCT
ap-3989	76	11	,	,	PUNCT
ap-3989	76	12	assuming	assume	VERB
ap-3989	76	13	the	the	DET
ap-3989	76	14	following	follow	VERB
ap-3989	76	15	initial	initial	ADJ
ap-3989	76	16	value	value	NOUN
ap-3989	76	17	problem	problem	NOUN
ap-3989	76	18	dϕ	dϕ	NOUN
ap-3989	76	19	dt	dt	X
ap-3989	76	20	+	+	NOUN
ap-3989	76	21	a(ϕ	a(ϕ	NOUN
ap-3989	76	22	)	)	PUNCT
ap-3989	76	23	=	=	SYM
ap-3989	76	24	0	0	NUM
ap-3989	76	25	,	,	PUNCT
ap-3989	76	26	ϕ(0	ϕ(0	PROPN
ap-3989	76	27	)	)	PUNCT
ap-3989	76	28	=	=	SYM
ap-3989	76	29	ϕ0	ϕ0	NOUN
ap-3989	76	30	,	,	PUNCT
ap-3989	76	31	where	where	SCONJ
ap-3989	76	32	a	a	PRON
ap-3989	76	33	is	be	AUX
ap-3989	76	34	an	an	DET
ap-3989	76	35	operator	operator	NOUN
ap-3989	76	36	(	(	PUNCT
ap-3989	76	37	possibly	possibly	ADV
ap-3989	76	38	nonlinear	nonlinear	ADJ
ap-3989	76	39	,	,	PUNCT
ap-3989	76	40	and	and	CCONJ
ap-3989	76	41	even	even	ADV
ap-3989	76	42	multivalued	multivalue	VERB
ap-3989	76	43	)	)	PUNCT
ap-3989	76	44	from	from	ADP
ap-3989	76	45	a	a	DET
ap-3989	76	46	hilbert	hilbert	NOUN
ap-3989	76	47	space	space	NOUN
ap-3989	76	48	h	h	NOUN
ap-3989	76	49	into	into	ADP
ap-3989	76	50	itself	itself	PRON
ap-3989	76	51	and	and	CCONJ
ap-3989	76	52	where	where	SCONJ
ap-3989	76	53	ϕ0	ϕ0	NOUN
ap-3989	76	54	∈	∈	PROPN
ap-3989	76	55	h.	h.	NOUN
ap-3989	76	56	a	a	DET
ap-3989	76	57	number	number	NOUN
ap-3989	76	58	of	of	ADP
ap-3989	76	59	splitting	splitting	NOUN
ap-3989	76	60	techniques	technique	NOUN
ap-3989	76	61	have	have	AUX
ap-3989	76	62	been	be	AUX
ap-3989	76	63	proposed	propose	VERB
ap-3989	76	64	,	,	PUNCT
ap-3989	76	65	for	for	ADP
ap-3989	76	66	an	an	DET
ap-3989	76	67	overview	overview	NOUN
ap-3989	76	68	,	,	PUNCT
ap-3989	76	69	we	we	PRON
ap-3989	76	70	refer	refer	VERB
ap-3989	76	71	to	to	ADP
ap-3989	76	72	[	[	X
ap-3989	76	73	5	5	NUM
ap-3989	76	74	]	]	PUNCT
ap-3989	76	75	.	.	PUNCT
ap-3989	77	1	in	in	ADP
ap-3989	77	2	this	this	DET
ap-3989	77	3	work	work	NOUN
ap-3989	77	4	,	,	PUNCT
ap-3989	77	5	we	we	PRON
ap-3989	77	6	have	have	AUX
ap-3989	77	7	used	use	VERB
ap-3989	77	8	the	the	DET
ap-3989	77	9	scheme	scheme	NOUN
ap-3989	77	10	proposed	propose	VERB
ap-3989	77	11	by	by	ADP
ap-3989	77	12	marchuk	marchuk	PROPN
ap-3989	78	1	[	[	X
ap-3989	78	2	5	5	NUM
ap-3989	78	3	]	]	PUNCT
ap-3989	78	4	,	,	PUNCT
ap-3989	78	5	which	which	PRON
ap-3989	78	6	is	be	AUX
ap-3989	78	7	described	describe	VERB
ap-3989	78	8	in	in	ADP
ap-3989	78	9	the	the	DET
ap-3989	78	10	next	next	ADJ
ap-3989	78	11	section	section	NOUN
ap-3989	78	12	.	.	PUNCT
ap-3989	79	1	3.3	3.3	NUM
ap-3989	79	2	.	.	PUNCT
ap-3989	80	1	marchuk	marchuk	PROPN
ap-3989	80	2	’s	’s	PART
ap-3989	80	3	fractional	fractional	ADJ
ap-3989	80	4	-	-	PUNCT
ap-3989	80	5	step	step	NOUN
ap-3989	80	6	scheme	scheme	NOUN
ap-3989	80	7	marchuk	marchuk	PROPN
ap-3989	80	8	assumed	assume	VERB
ap-3989	80	9	a	a	DET
ap-3989	80	10	decomposition	decomposition	NOUN
ap-3989	80	11	of	of	ADP
ap-3989	80	12	the	the	DET
ap-3989	80	13	operator	operator	NOUN
ap-3989	80	14	a	a	PRON
ap-3989	80	15	into	into	ADP
ap-3989	80	16	the	the	DET
ap-3989	80	17	following	follow	VERB
ap-3989	80	18	nontrivial	nontrivial	ADJ
ap-3989	80	19	decomposition	decomposition	NOUN
ap-3989	80	20	a	a	DET
ap-3989	80	21	=	=	NOUN
ap-3989	80	22	a1	a1	NOUN
ap-3989	80	23	+	+	PROPN
ap-3989	80	24	a2	a2	PROPN
ap-3989	80	25	+	+	NOUN
ap-3989	80	26	a3	a3	NOUN
ap-3989	80	27	(	(	PUNCT
ap-3989	80	28	14	14	NUM
ap-3989	80	29	)	)	PUNCT
ap-3989	80	30	(	(	PUNCT
ap-3989	80	31	by	by	ADP
ap-3989	80	32	nontrivial	nontrivial	NOUN
ap-3989	80	33	,	,	PUNCT
ap-3989	80	34	we	we	PRON
ap-3989	80	35	mean	mean	VERB
ap-3989	80	36	that	that	SCONJ
ap-3989	80	37	operators	operator	NOUN
ap-3989	80	38	a1	a1	VERB
ap-3989	80	39	,	,	PUNCT
ap-3989	80	40	a2	a2	PROPN
ap-3989	80	41	and	and	CCONJ
ap-3989	80	42	a3	a3	NOUN
ap-3989	80	43	are	be	AUX
ap-3989	80	44	individually	individually	ADV
ap-3989	80	45	simpler	simple	ADJ
ap-3989	80	46	than	than	ADP
ap-3989	80	47	a	a	PRON
ap-3989	80	48	)	)	PUNCT
ap-3989	80	49	.	.	PUNCT
ap-3989	81	1	by	by	ADP
ap-3989	81	2	assuming	assume	VERB
ap-3989	81	3	a	a	DET
ap-3989	81	4	time	time	NOUN
ap-3989	81	5	discretization	discretization	NOUN
ap-3989	81	6	with	with	ADP
ap-3989	81	7	the	the	DET
ap-3989	81	8	time	time	NOUN
ap-3989	81	9	step	step	NOUN
ap-3989	81	10	∆t	∆t	PROPN
ap-3989	81	11	,	,	PUNCT
ap-3989	81	12	the	the	DET
ap-3989	81	13	updated	update	VERB
ap-3989	81	14	value	value	NOUN
ap-3989	81	15	at	at	ADP
ap-3989	81	16	the	the	DET
ap-3989	81	17	end	end	NOUN
ap-3989	81	18	of	of	ADP
ap-3989	81	19	the	the	DET
ap-3989	81	20	time	time	NOUN
ap-3989	81	21	step	step	NOUN
ap-3989	81	22	can	can	AUX
ap-3989	81	23	be	be	AUX
ap-3989	81	24	computed	compute	VERB
ap-3989	81	25	using	use	VERB
ap-3989	81	26	a	a	DET
ap-3989	81	27	three	three	NUM
ap-3989	81	28	step	step	NOUN
ap-3989	81	29	integration	integration	NOUN
ap-3989	81	30	procedure	procedure	NOUN
ap-3989	81	31	as	as	SCONJ
ap-3989	81	32	follows	follow	VERB
ap-3989	81	33	:	:	PUNCT
ap-3989	81	34	ϕn+1/3	ϕn+1/3	INTJ
ap-3989	81	35	−	−	PROPN
ap-3989	81	36	ϕn	ϕn	INTJ
ap-3989	81	37	∆t	∆t	PROPN
ap-3989	82	1	+	+	PROPN
ap-3989	82	2	a1(ϕn+1/3	a1(ϕn+1/3	PROPN
ap-3989	82	3	)	)	PUNCT
ap-3989	82	4	=	=	SYM
ap-3989	82	5	fn+1	fn+1	NUM
ap-3989	82	6	1	1	NUM
ap-3989	82	7	,	,	PUNCT
ap-3989	83	1	ϕn+2/3	ϕn+2/3	ADJ
ap-3989	83	2	−	−	PUNCT
ap-3989	83	3	ϕn+1/3	ϕn+1/3	ADP
ap-3989	83	4	∆t	∆t	PROPN
ap-3989	83	5	+	+	NOUN
ap-3989	83	6	a2(ϕn+2/3	a2(ϕn+2/3	NOUN
ap-3989	83	7	)	)	PUNCT
ap-3989	83	8	=	=	SYM
ap-3989	83	9	fn+1	fn+1	NUM
ap-3989	83	10	2	2	NUM
ap-3989	83	11	,	,	PUNCT
ap-3989	83	12	ϕn+1	ϕn+1	ADJ
ap-3989	83	13	−	−	PROPN
ap-3989	83	14	ϕn+2/3	ϕn+2/3	ADJ
ap-3989	83	15	∆t	∆t	PROPN
ap-3989	83	16	+	+	NOUN
ap-3989	83	17	a3(ϕn+1	a3(ϕn+1	NOUN
ap-3989	83	18	)	)	PUNCT
ap-3989	84	1	=	=	SYM
ap-3989	84	2	fn+1	fn+1	NUM
ap-3989	84	3	3	3	X
ap-3989	84	4	.	.	PUNCT
ap-3989	85	1	by	by	ADP
ap-3989	85	2	applying	apply	VERB
ap-3989	85	3	an	an	DET
ap-3989	85	4	operator	operator	NOUN
ap-3989	85	5	splitting	splitting	NOUN
ap-3989	85	6	to	to	ADP
ap-3989	85	7	the	the	DET
ap-3989	85	8	problem	problem	NOUN
ap-3989	85	9	(	(	PUNCT
ap-3989	85	10	9	9	NUM
ap-3989	85	11	)	)	PUNCT
ap-3989	85	12	–	–	PUNCT
ap-3989	85	13	(	(	PUNCT
ap-3989	85	14	12	12	NUM
ap-3989	85	15	)	)	PUNCT
ap-3989	85	16	,	,	PUNCT
ap-3989	85	17	one	one	PRON
ap-3989	85	18	obtains	obtain	VERB
ap-3989	85	19	(	(	PUNCT
ap-3989	85	20	with	with	ADP
ap-3989	85	21	0	0	NUM
ap-3989	85	22	≤	≤	NUM
ap-3989	85	23	α	α	NOUN
ap-3989	85	24	,	,	PUNCT
ap-3989	85	25	β	β	X
ap-3989	85	26	≤	≤	ADV
ap-3989	85	27	1	1	NUM
ap-3989	85	28	and	and	CCONJ
ap-3989	85	29	α+	α+	PUNCT
ap-3989	85	30	β	β	X
ap-3989	85	31	=	=	SYM
ap-3989	85	32	1	1	NUM
ap-3989	85	33	):	):	PUNCT
ap-3989	85	34	find	find	VERB
ap-3989	85	35	un+1/3	un+1/3	ADJ
ap-3989	85	36	h	h	NOUN
ap-3989	85	37	wh	wh	NOUN
ap-3989	85	38	and	and	CCONJ
ap-3989	85	39	pn+1/3	pn+1/3	PROPN
ap-3989	85	40	∈	∈	PROPN
ap-3989	86	1	lh	lh	PROPN
ap-3989	86	2	such	such	ADJ
ap-3989	87	1	that	that	DET
ap-3989	87	2	%	%	NOUN
ap-3989	88	1	∫	∫	PROPN
ap-3989	88	2	ω	ω	NUM
ap-3989	88	3	u	u	NOUN
ap-3989	88	4	n+1/3	n+1/3	PROPN
ap-3989	88	5	h	h	NOUN
ap-3989	88	6	−	−	PROPN
ap-3989	88	7	un	un	PROPN
ap-3989	88	8	h	h	PROPN
ap-3989	88	9	∆t	∆t	PROPN
ap-3989	88	10	·	·	PUNCT
ap-3989	88	11	vh	vh	PROPN
ap-3989	88	12	dx−	dx−	NUM
ap-3989	88	13	∫	∫	PROPN
ap-3989	88	14	ω	ω	PROPN
ap-3989	89	1	p	p	X
ap-3989	89	2	n+1/3	n+1/3	PROPN
ap-3989	89	3	h	h	NOUN
ap-3989	89	4	∇	∇	X
ap-3989	89	5	·	·	PUNCT
ap-3989	89	6	vh	vh	PROPN
ap-3989	89	7	dx	dx	PROPN
ap-3989	90	1	=	=	SYM
ap-3989	90	2	0	0	PROPN
ap-3989	90	3	for	for	ADP
ap-3989	90	4	all	all	DET
ap-3989	90	5	vh	vh	PROPN
ap-3989	90	6	∈	∈	PROPN
ap-3989	90	7	vh	vh	PROPN
ap-3989	90	8	,	,	PUNCT
ap-3989	90	9	(	(	PUNCT
ap-3989	90	10	15)∫	15)∫	NUM
ap-3989	90	11	ω	ω	NUM
ap-3989	90	12	qh∇	qh∇	NUM
ap-3989	91	1	·	·	PUNCT
ap-3989	91	2	un+1/3	un+1/3	NUM
ap-3989	91	3	h	h	NOUN
ap-3989	91	4	dx	dx	PROPN
ap-3989	91	5	=	=	SYM
ap-3989	91	6	0	0	PROPN
ap-3989	91	7	for	for	ADP
ap-3989	91	8	all	all	DET
ap-3989	91	9	qh	qh	NOUN
ap-3989	91	10	∈	∈	PROPN
ap-3989	91	11	l2	l2	NOUN
ap-3989	91	12	h.	h.	NOUN
ap-3989	91	13	(	(	PUNCT
ap-3989	91	14	16	16	NUM
ap-3989	91	15	)	)	SYM
ap-3989	91	16	247	247	NUM
ap-3989	91	17	matej	matej	PROPN
ap-3989	91	18	beňo	beňo	NOUN
ap-3989	91	19	,	,	PUNCT
ap-3989	91	20	bořek	bořek	PROPN
ap-3989	91	21	patzák	patzák	VERB
ap-3989	91	22	acta	acta	PROPN
ap-3989	91	23	polytechnica	polytechnica	PROPN
ap-3989	91	24	figure	figure	NOUN
ap-3989	91	25	2	2	NUM
ap-3989	91	26	.	.	PUNCT
ap-3989	92	1	the	the	DET
ap-3989	92	2	different	different	ADJ
ap-3989	92	3	strategies	strategy	NOUN
ap-3989	92	4	for	for	ADP
ap-3989	92	5	selection	selection	NOUN
ap-3989	92	6	of	of	ADP
ap-3989	92	7	sampling	sample	VERB
ap-3989	92	8	points	point	NOUN
ap-3989	92	9	.	.	PUNCT
ap-3989	93	1	the	the	DET
ap-3989	93	2	boxed	box	VERB
ap-3989	93	3	cross	cross	NOUN
ap-3989	93	4	represents	represent	VERB
ap-3989	93	5	boundary	boundary	ADJ
ap-3989	93	6	condition	condition	NOUN
ap-3989	93	7	application	application	NOUN
ap-3989	93	8	(	(	PUNCT
ap-3989	93	9	zero	zero	NUM
ap-3989	93	10	velocity	velocity	NOUN
ap-3989	93	11	)	)	PUNCT
ap-3989	93	12	in	in	ADP
ap-3989	93	13	case	case	NOUN
ap-3989	93	14	of	of	ADP
ap-3989	93	15	fixed	fix	VERB
ap-3989	93	16	particle	particle	NOUN
ap-3989	93	17	,	,	PUNCT
ap-3989	93	18	the	the	DET
ap-3989	93	19	open	open	PROPN
ap-3989	93	20	cross	cross	PROPN
ap-3989	93	21	indicate	indicate	VERB
ap-3989	93	22	location	location	NOUN
ap-3989	93	23	of	of	ADP
ap-3989	93	24	sampling	sample	VERB
ap-3989	93	25	point	point	NOUN
ap-3989	93	26	.	.	PUNCT
ap-3989	94	1	find	find	VERB
ap-3989	94	2	un+2/3	un+2/3	ADJ
ap-3989	94	3	h	h	NOUN
ap-3989	94	4	∈wh	∈wh	NOUN
ap-3989	94	5	such	such	ADJ
ap-3989	94	6	that	that	DET
ap-3989	94	7	%	%	NOUN
ap-3989	94	8	∫	∫	PROPN
ap-3989	94	9	ω	ω	NUM
ap-3989	94	10	u	u	PROPN
ap-3989	94	11	n+2/3	n+2/3	PROPN
ap-3989	94	12	h	h	NOUN
ap-3989	94	13	−	−	PUNCT
ap-3989	94	14	un+1/3	un+1/3	ADJ
ap-3989	94	15	h	h	NOUN
ap-3989	94	16	∆t	∆t	PROPN
ap-3989	94	17	·	·	PUNCT
ap-3989	94	18	vh	vh	PROPN
ap-3989	94	19	dx	dx	PROPN
ap-3989	94	20	−	−	PROPN
ap-3989	94	21	%	%	INTJ
ap-3989	94	22	∫	∫	PROPN
ap-3989	94	23	ω	ω	INTJ
ap-3989	94	24	(	(	PUNCT
ap-3989	94	25	un+1/3	un+1/3	PROPN
ap-3989	94	26	h	h	NOUN
ap-3989	94	27	·	·	PUNCT
ap-3989	95	1	∇)un+2/3	∇)un+2/3	NUM
ap-3989	95	2	h	h	NOUN
ap-3989	95	3	·	·	SYM
ap-3989	95	4	vh	vh	X
ap-3989	95	5	dx	dx	PROPN
ap-3989	95	6	+	+	CCONJ
ap-3989	95	7	2αη	2αη	ADJ
ap-3989	95	8	∫	∫	PROPN
ap-3989	96	1	ω	ω	NUM
ap-3989	96	2	d[un+2/3	d[un+2/3	PROPN
ap-3989	96	3	h	h	NOUN
ap-3989	96	4	]	]	X
ap-3989	96	5	:	:	PUNCT
ap-3989	96	6	d[vh	d[vh	PROPN
ap-3989	96	7	]	]	PUNCT
ap-3989	96	8	dx	dx	PROPN
ap-3989	97	1	=	=	SYM
ap-3989	97	2	0	0	PROPN
ap-3989	97	3	for	for	ADP
ap-3989	97	4	all	all	DET
ap-3989	97	5	vh	vh	PROPN
ap-3989	97	6	∈	∈	PROPN
ap-3989	97	7	vh	vh	PROPN
ap-3989	97	8	.	.	PUNCT
ap-3989	98	1	(	(	PUNCT
ap-3989	98	2	17	17	NUM
ap-3989	98	3	)	)	PUNCT
ap-3989	98	4	finally	finally	ADV
ap-3989	98	5	find	find	VERB
ap-3989	98	6	un+1	un+1	NOUN
ap-3989	98	7	h	h	NOUN
ap-3989	98	8	∈wh	∈wh	NOUN
ap-3989	98	9	,	,	PUNCT
ap-3989	98	10	λn+1	λn+1	ADP
ap-3989	98	11	h	h	NOUN
ap-3989	98	12	∈	∈	PROPN
ap-3989	98	13	λh	λh	ADP
ap-3989	98	14	such	such	DET
ap-3989	98	15	that	that	DET
ap-3989	98	16	%	%	NOUN
ap-3989	99	1	∫	∫	PROPN
ap-3989	99	2	ω	ω	NUM
ap-3989	99	3	un+1	un+1	PROPN
ap-3989	99	4	h	h	NOUN
ap-3989	99	5	−	−	PROPN
ap-3989	100	1	un+2/3	un+2/3	ADJ
ap-3989	100	2	h	h	NOUN
ap-3989	100	3	∆t	∆t	PROPN
ap-3989	100	4	·	·	PUNCT
ap-3989	100	5	vh	vh	PROPN
ap-3989	100	6	dx	dx	PROPN
ap-3989	100	7	+	+	CCONJ
ap-3989	100	8	2βη	2βη	ADJ
ap-3989	100	9	∫	∫	PROPN
ap-3989	100	10	ω	ω	NUM
ap-3989	100	11	d[un+1	d[un+1	PROPN
ap-3989	100	12	h	h	NOUN
ap-3989	100	13	]	]	X
ap-3989	100	14	:	:	PUNCT
ap-3989	100	15	d[vh	d[vh	PROPN
ap-3989	100	16	]	]	PUNCT
ap-3989	100	17	dx	dx	PROPN
ap-3989	100	18	=	=	SYM
ap-3989	100	19	〈	〈	PROPN
ap-3989	100	20	λn+1	λn+1	PROPN
ap-3989	100	21	h	h	PROPN
ap-3989	100	22	,	,	PUNCT
ap-3989	100	23	vh	vh	PROPN
ap-3989	100	24	〉	〉	PROPN
ap-3989	100	25	for	for	ADP
ap-3989	100	26	all	all	DET
ap-3989	100	27	vh	vh	PROPN
ap-3989	100	28	∈	∈	PROPN
ap-3989	100	29	vh	vh	PROPN
ap-3989	100	30	,	,	PUNCT
ap-3989	100	31	(	(	PUNCT
ap-3989	100	32	18	18	NUM
ap-3989	100	33	)	)	PUNCT
ap-3989	100	34	〈	〈	PROPN
ap-3989	100	35	µh	µh	PROPN
ap-3989	100	36	,	,	PUNCT
ap-3989	100	37	u	u	PROPN
ap-3989	100	38	n+1	n+1	PROPN
ap-3989	100	39	h	h	NOUN
ap-3989	100	40	〉	〉	PROPN
ap-3989	100	41	p	p	NOUN
ap-3989	100	42	=	=	NOUN
ap-3989	100	43	0	0	NUM
ap-3989	100	44	for	for	ADP
ap-3989	100	45	all	all	DET
ap-3989	100	46	µh	µh	PROPN
ap-3989	100	47	∈	∈	PROPN
ap-3989	100	48	λh	λh	VERB
ap-3989	100	49	.	.	PUNCT
ap-3989	100	50	(	(	PUNCT
ap-3989	100	51	19	19	NUM
ap-3989	100	52	)	)	PUNCT
ap-3989	100	53	this	this	DET
ap-3989	100	54	scheme	scheme	NOUN
ap-3989	100	55	is	be	AUX
ap-3989	100	56	only	only	ADV
ap-3989	100	57	first	first	ADJ
ap-3989	100	58	order	order	NOUN
ap-3989	100	59	accurate	accurate	ADJ
ap-3989	100	60	,	,	PUNCT
ap-3989	100	61	but	but	CCONJ
ap-3989	100	62	with	with	ADP
ap-3989	100	63	good	good	ADJ
ap-3989	100	64	stability	stability	NOUN
ap-3989	100	65	properties	property	NOUN
ap-3989	100	66	,	,	PUNCT
ap-3989	100	67	see	see	VERB
ap-3989	100	68	[	[	X
ap-3989	100	69	5	5	NUM
ap-3989	100	70	]	]	PUNCT
ap-3989	100	71	.	.	PUNCT
ap-3989	101	1	the	the	DET
ap-3989	101	2	described	describe	VERB
ap-3989	101	3	method	method	NOUN
ap-3989	101	4	has	have	AUX
ap-3989	101	5	also	also	ADV
ap-3989	101	6	been	be	AUX
ap-3989	101	7	used	use	VERB
ap-3989	101	8	in	in	ADP
ap-3989	101	9	[	[	X
ap-3989	101	10	6	6	NUM
ap-3989	101	11	]	]	PUNCT
ap-3989	101	12	.	.	PUNCT
ap-3989	102	1	4	4	X
ap-3989	102	2	.	.	X
ap-3989	102	3	sampling	sample	VERB
ap-3989	102	4	point	point	NOUN
ap-3989	102	5	selection	selection	NOUN
ap-3989	102	6	as	as	SCONJ
ap-3989	102	7	already	already	ADV
ap-3989	102	8	mentioned	mention	VERB
ap-3989	102	9	,	,	PUNCT
ap-3989	102	10	the	the	DET
ap-3989	102	11	rigid	rigid	ADJ
ap-3989	102	12	body	body	NOUN
ap-3989	102	13	or	or	CCONJ
ap-3989	102	14	no	no	DET
ap-3989	102	15	flow	flow	NOUN
ap-3989	102	16	constraints	constraint	NOUN
ap-3989	102	17	are	be	AUX
ap-3989	102	18	imposed	impose	VERB
ap-3989	102	19	in	in	ADP
ap-3989	102	20	a	a	DET
ap-3989	102	21	weak	weak	ADJ
ap-3989	102	22	sense	sense	NOUN
ap-3989	102	23	using	use	VERB
ap-3989	102	24	lagrange	lagrange	NOUN
ap-3989	102	25	multipliers	multiplier	NOUN
ap-3989	102	26	.	.	PUNCT
ap-3989	103	1	in	in	ADP
ap-3989	103	2	a	a	DET
ap-3989	103	3	practical	practical	ADJ
ap-3989	103	4	implementation	implementation	NOUN
ap-3989	103	5	,	,	PUNCT
ap-3989	103	6	the	the	DET
ap-3989	103	7	corresponding	corresponding	ADJ
ap-3989	103	8	integral	integral	NOUN
ap-3989	103	9	in	in	ADP
ap-3989	103	10	a	a	DET
ap-3989	103	11	weak	weak	ADJ
ap-3989	103	12	form	form	NOUN
ap-3989	103	13	is	be	AUX
ap-3989	103	14	evaluated	evaluate	VERB
ap-3989	103	15	as	as	ADP
ap-3989	103	16	a	a	DET
ap-3989	103	17	sum	sum	NOUN
ap-3989	103	18	over	over	ADP
ap-3989	103	19	a	a	DET
ap-3989	103	20	set	set	NOUN
ap-3989	103	21	of	of	ADP
ap-3989	103	22	discrete	discrete	ADJ
ap-3989	103	23	sampling	sampling	NOUN
ap-3989	103	24	points	point	NOUN
ap-3989	103	25	.	.	PUNCT
ap-3989	104	1	in	in	ADP
ap-3989	104	2	this	this	DET
ap-3989	104	3	paper	paper	NOUN
ap-3989	104	4	,	,	PUNCT
ap-3989	104	5	we	we	PRON
ap-3989	104	6	have	have	AUX
ap-3989	104	7	proposed	propose	VERB
ap-3989	104	8	and	and	CCONJ
ap-3989	104	9	tested	test	VERB
ap-3989	104	10	several	several	ADJ
ap-3989	104	11	strategies	strategy	NOUN
ap-3989	104	12	to	to	PART
ap-3989	104	13	enforce	enforce	VERB
ap-3989	104	14	constrains	constrain	NOUN
ap-3989	104	15	by	by	ADP
ap-3989	104	16	combining	combine	VERB
ap-3989	104	17	one	one	NUM
ap-3989	104	18	or	or	CCONJ
ap-3989	104	19	more	more	ADJ
ap-3989	104	20	lagrange	lagrange	NOUN
ap-3989	104	21	multipliers	multiplier	NOUN
ap-3989	104	22	per	per	ADP
ap-3989	104	23	particle	particle	NOUN
ap-3989	104	24	and	and	CCONJ
ap-3989	104	25	using	use	VERB
ap-3989	104	26	different	different	ADJ
ap-3989	104	27	strategies	strategy	NOUN
ap-3989	104	28	for	for	ADP
ap-3989	104	29	the	the	DET
ap-3989	104	30	sampling	sampling	NOUN
ap-3989	104	31	point	point	NOUN
ap-3989	104	32	selection	selection	NOUN
ap-3989	104	33	.	.	PUNCT
ap-3989	105	1	for	for	ADP
ap-3989	105	2	the	the	DET
ap-3989	105	3	considered	considered	ADJ
ap-3989	105	4	figure	figure	NOUN
ap-3989	105	5	3	3	NUM
ap-3989	105	6	.	.	PUNCT
ap-3989	106	1	the	the	DET
ap-3989	106	2	problem	problem	NOUN
ap-3989	106	3	of	of	ADP
ap-3989	106	4	2d	2d	NUM
ap-3989	106	5	flow	flow	NOUN
ap-3989	106	6	around	around	ADP
ap-3989	106	7	single	single	ADJ
ap-3989	106	8	obstacle	obstacle	NOUN
ap-3989	106	9	.	.	PUNCT
ap-3989	107	1	figure	figure	VERB
ap-3989	107	2	4	4	NUM
ap-3989	107	3	.	.	PUNCT
ap-3989	108	1	the	the	DET
ap-3989	108	2	mesh	mesh	NOUN
ap-3989	108	3	of	of	ADP
ap-3989	108	4	2d	2d	NUM
ap-3989	108	5	flow	flow	NOUN
ap-3989	108	6	with	with	ADP
ap-3989	108	7	single	single	ADJ
ap-3989	108	8	obstacle	obstacle	NOUN
ap-3989	108	9	.	.	PUNCT
ap-3989	109	1	circular	circular	ADJ
ap-3989	109	2	geometry	geometry	NOUN
ap-3989	109	3	of	of	ADP
ap-3989	109	4	particle	particle	NOUN
ap-3989	109	5	,	,	PUNCT
ap-3989	109	6	the	the	DET
ap-3989	109	7	proposed	propose	VERB
ap-3989	109	8	strategies	strategy	NOUN
ap-3989	109	9	consist	consist	VERB
ap-3989	109	10	of	of	ADP
ap-3989	109	11	generating	generate	VERB
ap-3989	109	12	the	the	DET
ap-3989	109	13	different	different	ADJ
ap-3989	109	14	patterns	pattern	NOUN
ap-3989	109	15	of	of	ADP
ap-3989	109	16	sampling	sample	VERB
ap-3989	109	17	points	point	NOUN
ap-3989	109	18	in	in	ADP
ap-3989	109	19	radial	radial	ADJ
ap-3989	109	20	and	and	CCONJ
ap-3989	109	21	longitudinal	longitudinal	ADJ
ap-3989	109	22	directions	direction	NOUN
ap-3989	109	23	,	,	PUNCT
ap-3989	109	24	see	see	VERB
ap-3989	109	25	figure	figure	NOUN
ap-3989	109	26	2	2	NUM
ap-3989	109	27	.	.	PUNCT
ap-3989	110	1	these	these	DET
ap-3989	110	2	results	result	NOUN
ap-3989	110	3	of	of	ADP
ap-3989	110	4	these	these	DET
ap-3989	110	5	strategies	strategy	NOUN
ap-3989	110	6	are	be	AUX
ap-3989	110	7	compared	compare	VERB
ap-3989	110	8	using	use	VERB
ap-3989	110	9	two	two	NUM
ap-3989	110	10	test	test	NOUN
ap-3989	110	11	scenarios	scenario	NOUN
ap-3989	110	12	to	to	ADP
ap-3989	110	13	results	result	NOUN
ap-3989	110	14	obtained	obtain	VERB
ap-3989	110	15	with	with	ADP
ap-3989	110	16	fully	fully	ADV
ap-3989	110	17	resolved	resolve	VERB
ap-3989	110	18	simulations	simulation	NOUN
ap-3989	110	19	,	,	PUNCT
ap-3989	110	20	where	where	SCONJ
ap-3989	110	21	the	the	DET
ap-3989	110	22	geometry	geometry	NOUN
ap-3989	110	23	of	of	ADP
ap-3989	110	24	each	each	DET
ap-3989	110	25	individual	individual	ADJ
ap-3989	110	26	particle	particle	NOUN
ap-3989	110	27	is	be	AUX
ap-3989	110	28	represented	represent	VERB
ap-3989	110	29	exactly	exactly	ADV
ap-3989	110	30	by	by	ADP
ap-3989	110	31	the	the	DET
ap-3989	110	32	mesh	mesh	NOUN
ap-3989	110	33	and	and	CCONJ
ap-3989	110	34	corresponding	correspond	VERB
ap-3989	110	35	no	no	DET
ap-3989	110	36	-	-	PUNCT
ap-3989	110	37	flow	flow	NOUN
ap-3989	110	38	constraints	constraint	NOUN
ap-3989	110	39	are	be	AUX
ap-3989	110	40	exactly	exactly	ADV
ap-3989	110	41	satisfied	satisfied	ADJ
ap-3989	110	42	.	.	PUNCT
ap-3989	111	1	5	5	X
ap-3989	111	2	.	.	X
ap-3989	111	3	numerical	numerical	ADJ
ap-3989	111	4	tests	test	NOUN
ap-3989	111	5	5.1	5.1	NUM
ap-3989	111	6	.	.	PUNCT
ap-3989	112	1	flow	flow	VERB
ap-3989	112	2	around	around	ADP
ap-3989	112	3	single	single	ADJ
ap-3989	112	4	obstacle	obstacle	NOUN
ap-3989	112	5	the	the	DET
ap-3989	112	6	first	first	ADJ
ap-3989	112	7	example	example	NOUN
ap-3989	112	8	to	to	PART
ap-3989	112	9	evaluate	evaluate	VERB
ap-3989	112	10	proposed	propose	VERB
ap-3989	112	11	strategies	strategy	NOUN
ap-3989	112	12	solves	solve	VERB
ap-3989	112	13	the	the	DET
ap-3989	112	14	2d	2d	NUM
ap-3989	112	15	flow	flow	VERB
ap-3989	112	16	around	around	ADP
ap-3989	112	17	a	a	DET
ap-3989	112	18	single	single	ADJ
ap-3989	112	19	,	,	PUNCT
ap-3989	112	20	rigid	rigid	ADJ
ap-3989	112	21	particle	particle	NOUN
ap-3989	112	22	.	.	PUNCT
ap-3989	113	1	the	the	DET
ap-3989	113	2	geometry	geometry	NOUN
ap-3989	113	3	of	of	ADP
ap-3989	113	4	the	the	DET
ap-3989	113	5	problem	problem	NOUN
ap-3989	113	6	is	be	AUX
ap-3989	113	7	depicted	depict	VERB
ap-3989	113	8	in	in	ADP
ap-3989	113	9	figure	figure	NOUN
ap-3989	113	10	3	3	NUM
ap-3989	113	11	,	,	PUNCT
ap-3989	113	12	together	together	ADV
ap-3989	113	13	with	with	ADP
ap-3989	113	14	initial	initial	ADJ
ap-3989	113	15	and	and	CCONJ
ap-3989	113	16	boundary	boundary	ADJ
ap-3989	113	17	conditions	condition	NOUN
ap-3989	113	18	.	.	PUNCT
ap-3989	114	1	the	the	DET
ap-3989	114	2	perfect	perfect	ADJ
ap-3989	114	3	friction	friction	NOUN
ap-3989	114	4	(	(	PUNCT
ap-3989	114	5	no	no	DET
ap-3989	114	6	slip	slip	NOUN
ap-3989	114	7	)	)	PUNCT
ap-3989	114	8	boundary	boundary	ADJ
ap-3989	114	9	condition	condition	NOUN
ap-3989	114	10	has	have	AUX
ap-3989	114	11	been	be	AUX
ap-3989	114	12	assumed	assume	VERB
ap-3989	114	13	on	on	ADP
ap-3989	114	14	horizontal	horizontal	ADJ
ap-3989	114	15	edges	edge	NOUN
ap-3989	114	16	.	.	PUNCT
ap-3989	115	1	the	the	DET
ap-3989	115	2	domain	domain	NOUN
ap-3989	115	3	has	have	AUX
ap-3989	115	4	been	be	AUX
ap-3989	115	5	discretized	discretize	VERB
ap-3989	115	6	into	into	ADP
ap-3989	115	7	1820	1820	NUM
ap-3989	115	8	triangular	triangular	NOUN
ap-3989	115	9	taylor	taylor	PROPN
ap-3989	115	10	-	-	PUNCT
ap-3989	115	11	hood	hood	NOUN
ap-3989	115	12	elements	element	NOUN
ap-3989	115	13	,	,	PUNCT
ap-3989	115	14	see	see	VERB
ap-3989	115	15	figure	figure	NOUN
ap-3989	115	16	4	4	NUM
ap-3989	115	17	top	top	NOUN
ap-3989	115	18	.	.	PUNCT
ap-3989	116	1	the	the	DET
ap-3989	116	2	values	value	NOUN
ap-3989	116	3	of	of	ADP
ap-3989	116	4	mass	mass	ADJ
ap-3989	116	5	density	density	NOUN
ap-3989	116	6	%	%	NOUN
ap-3989	116	7	=	=	NOUN
ap-3989	116	8	1.0	1.0	NUM
ap-3989	116	9	kg	kg	NOUN
ap-3989	116	10	/	/	SYM
ap-3989	116	11	m3	m3	PROPN
ap-3989	116	12	,	,	PUNCT
ap-3989	116	13	viscosity	viscosity	NOUN
ap-3989	116	14	η	η	PROPN
ap-3989	116	15	=	=	PROPN
ap-3989	116	16	10−1	10−1	PROPN
ap-3989	116	17	pa	pa	PROPN
ap-3989	116	18	s	s	PROPN
ap-3989	116	19	,	,	PUNCT
ap-3989	116	20	and	and	CCONJ
ap-3989	116	21	time	time	NOUN
ap-3989	116	22	step	step	NOUN
ap-3989	116	23	∆t	∆t	PROPN
ap-3989	116	24	=	=	SYM
ap-3989	116	25	0.001	0.001	NUM
ap-3989	116	26	s	s	NOUN
ap-3989	116	27	have	have	AUX
ap-3989	116	28	been	be	AUX
ap-3989	116	29	used	use	VERB
ap-3989	116	30	in	in	ADP
ap-3989	116	31	this	this	DET
ap-3989	116	32	study	study	NOUN
ap-3989	116	33	.	.	PUNCT
ap-3989	117	1	the	the	DET
ap-3989	117	2	described	describe	VERB
ap-3989	117	3	model	model	NOUN
ap-3989	117	4	has	have	AUX
ap-3989	117	5	been	be	AUX
ap-3989	117	6	implemented	implement	VERB
ap-3989	117	7	into	into	ADP
ap-3989	117	8	248	248	NUM
ap-3989	117	9	vol	vol	NOUN
ap-3989	117	10	.	.	PUNCT
ap-3989	118	1	57	57	NUM
ap-3989	119	1	no	no	NOUN
ap-3989	119	2	.	.	PUNCT
ap-3989	120	1	4/2017	4/2017	NUM
ap-3989	120	2	fictitious	fictitious	ADJ
ap-3989	120	3	domain	domain	NOUN
ap-3989	120	4	method	method	NOUN
ap-3989	120	5	for	for	ADP
ap-3989	120	6	a	a	DET
ap-3989	120	7	numerical	numerical	ADJ
ap-3989	120	8	simulation	simulation	NOUN
ap-3989	120	9	figure	figure	NOUN
ap-3989	120	10	5	5	NUM
ap-3989	120	11	.	.	PUNCT
ap-3989	120	12	velocity	velocity	NOUN
ap-3989	120	13	profiles	profile	NOUN
ap-3989	120	14	through	through	ADP
ap-3989	120	15	obstacle	obstacle	NOUN
ap-3989	120	16	.	.	PUNCT
ap-3989	121	1	figure	figure	VERB
ap-3989	121	2	6	6	NUM
ap-3989	121	3	.	.	PUNCT
ap-3989	122	1	the	the	DET
ap-3989	122	2	geometry	geometry	NOUN
ap-3989	122	3	and	and	CCONJ
ap-3989	122	4	the	the	DET
ap-3989	122	5	boundary	boundary	ADJ
ap-3989	122	6	conditions	condition	NOUN
ap-3989	122	7	of	of	ADP
ap-3989	122	8	the	the	DET
ap-3989	122	9	flow	flow	NOUN
ap-3989	122	10	in	in	ADP
ap-3989	122	11	tube	tube	NOUN
ap-3989	122	12	with	with	ADP
ap-3989	122	13	obstacle	obstacle	NOUN
ap-3989	122	14	(	(	PUNCT
ap-3989	122	15	448	448	NUM
ap-3989	122	16	el	el	NOUN
ap-3989	122	17	.	.	PROPN
ap-3989	122	18	)	)	PUNCT
ap-3989	122	19	.	.	PUNCT
ap-3989	123	1	an	an	DET
ap-3989	123	2	object	object	NOUN
ap-3989	123	3	oriented	orient	VERB
ap-3989	123	4	fe	fe	X
ap-3989	123	5	code	code	NOUN
ap-3989	123	6	oofem	oofem	NOUN
ap-3989	124	1	[	[	X
ap-3989	124	2	13	13	NUM
ap-3989	124	3	]	]	PUNCT
ap-3989	124	4	.	.	PUNCT
ap-3989	125	1	the	the	DET
ap-3989	125	2	different	different	ADJ
ap-3989	125	3	strategies	strategy	NOUN
ap-3989	125	4	for	for	ADP
ap-3989	125	5	a	a	DET
ap-3989	125	6	selection	selection	NOUN
ap-3989	125	7	of	of	ADP
ap-3989	125	8	sampling	sample	VERB
ap-3989	125	9	points	point	NOUN
ap-3989	125	10	have	have	AUX
ap-3989	125	11	been	be	AUX
ap-3989	125	12	evaluated	evaluate	VERB
ap-3989	125	13	and	and	CCONJ
ap-3989	125	14	compared	compare	VERB
ap-3989	125	15	to	to	ADP
ap-3989	125	16	results	result	NOUN
ap-3989	125	17	obtained	obtain	VERB
ap-3989	125	18	by	by	ADP
ap-3989	125	19	fully	fully	ADV
ap-3989	125	20	resolved	resolve	VERB
ap-3989	125	21	simulation	simulation	NOUN
ap-3989	125	22	(	(	PUNCT
ap-3989	125	23	see	see	VERB
ap-3989	125	24	figure	figure	NOUN
ap-3989	125	25	4	4	NUM
ap-3989	125	26	bottom	bottom	NOUN
ap-3989	125	27	for	for	ADP
ap-3989	125	28	discretization	discretization	NOUN
ap-3989	125	29	,	,	PUNCT
ap-3989	125	30	consisting	consist	VERB
ap-3989	125	31	of	of	ADP
ap-3989	125	32	1656	1656	NUM
ap-3989	125	33	elements	element	NOUN
ap-3989	125	34	and	and	CCONJ
ap-3989	125	35	3462	3462	NUM
ap-3989	125	36	nodes	node	NOUN
ap-3989	125	37	)	)	PUNCT
ap-3989	125	38	.	.	PUNCT
ap-3989	126	1	the	the	DET
ap-3989	126	2	comparison	comparison	NOUN
ap-3989	126	3	with	with	ADP
ap-3989	126	4	fully	fully	ADV
ap-3989	126	5	resolved	resolve	VERB
ap-3989	126	6	simulation	simulation	NOUN
ap-3989	126	7	has	have	AUX
ap-3989	126	8	been	be	AUX
ap-3989	126	9	made	make	VERB
ap-3989	126	10	at	at	ADP
ap-3989	126	11	a	a	DET
ap-3989	126	12	steady	steady	ADJ
ap-3989	126	13	state	state	NOUN
ap-3989	126	14	.	.	PUNCT
ap-3989	127	1	the	the	DET
ap-3989	127	2	individual	individual	ADJ
ap-3989	127	3	strategies	strategy	NOUN
ap-3989	127	4	considered	consider	VERB
ap-3989	127	5	are	be	AUX
ap-3989	127	6	described	describe	VERB
ap-3989	127	7	in	in	ADP
ap-3989	127	8	table	table	NOUN
ap-3989	127	9	1	1	NUM
ap-3989	127	10	.	.	PUNCT
ap-3989	128	1	the	the	DET
ap-3989	128	2	figure	figure	NOUN
ap-3989	128	3	5	5	NUM
ap-3989	128	4	shows	show	VERB
ap-3989	128	5	the	the	DET
ap-3989	128	6	profiles	profile	NOUN
ap-3989	128	7	of	of	ADP
ap-3989	128	8	velocity	velocity	NOUN
ap-3989	128	9	(	(	PUNCT
ap-3989	128	10	horizontal	horizontal	ADJ
ap-3989	128	11	component	component	NOUN
ap-3989	128	12	)	)	PUNCT
ap-3989	128	13	in	in	ADP
ap-3989	128	14	a	a	DET
ap-3989	128	15	vertical	vertical	ADJ
ap-3989	128	16	section	section	NOUN
ap-3989	128	17	passing	pass	VERB
ap-3989	128	18	through	through	ADP
ap-3989	128	19	the	the	DET
ap-3989	128	20	particle	particle	NOUN
ap-3989	128	21	center	center	NOUN
ap-3989	128	22	.	.	PUNCT
ap-3989	129	1	table	table	NOUN
ap-3989	129	2	1	1	NUM
ap-3989	129	3	also	also	ADV
ap-3989	129	4	contains	contain	VERB
ap-3989	129	5	the	the	DET
ap-3989	129	6	l2	l2	NOUN
ap-3989	129	7	norm	norm	NOUN
ap-3989	129	8	of	of	ADP
ap-3989	129	9	the	the	DET
ap-3989	129	10	difference	difference	NOUN
ap-3989	129	11	of	of	ADP
ap-3989	129	12	the	the	DET
ap-3989	129	13	obtained	obtain	VERB
ap-3989	129	14	velocity	velocity	NOUN
ap-3989	129	15	and	and	CCONJ
ap-3989	129	16	velocity	velocity	NOUN
ap-3989	129	17	from	from	ADP
ap-3989	129	18	fully	fully	ADV
ap-3989	129	19	resolved	resolve	VERB
ap-3989	129	20	simulation	simulation	NOUN
ap-3989	129	21	along	along	ADP
ap-3989	129	22	the	the	DET
ap-3989	129	23	vertical	vertical	ADJ
ap-3989	129	24	profile	profile	NOUN
ap-3989	129	25	passing	pass	VERB
ap-3989	129	26	the	the	DET
ap-3989	129	27	center	center	NOUN
ap-3989	129	28	of	of	ADP
ap-3989	129	29	the	the	DET
ap-3989	129	30	particle	particle	NOUN
ap-3989	129	31	.	.	PUNCT
ap-3989	130	1	the	the	DET
ap-3989	130	2	obtained	obtain	VERB
ap-3989	130	3	results	result	NOUN
ap-3989	130	4	indicate	indicate	VERB
ap-3989	130	5	that	that	SCONJ
ap-3989	130	6	an	an	DET
ap-3989	130	7	optimum	optimum	ADJ
ap-3989	130	8	strategy	strategy	NOUN
ap-3989	130	9	for	for	ADP
ap-3989	130	10	sampling	sample	VERB
ap-3989	130	11	point	point	NOUN
ap-3989	130	12	selection	selection	NOUN
ap-3989	130	13	is	be	AUX
ap-3989	130	14	to	to	PART
ap-3989	130	15	have	have	VERB
ap-3989	130	16	multiple	multiple	ADJ
ap-3989	130	17	rings	ring	NOUN
ap-3989	130	18	with	with	ADP
ap-3989	130	19	a	a	DET
ap-3989	130	20	dedicated	dedicated	ADJ
ap-3989	130	21	multiplier	multipli	ADJ
ap-3989	130	22	for	for	ADP
ap-3989	130	23	each	each	DET
ap-3989	130	24	ring	ring	NOUN
ap-3989	130	25	.	.	PUNCT
ap-3989	131	1	the	the	DET
ap-3989	131	2	best	good	ADJ
ap-3989	131	3	result	result	NOUN
ap-3989	131	4	(	(	PUNCT
ap-3989	131	5	in	in	ADP
ap-3989	131	6	terms	term	NOUN
ap-3989	131	7	of	of	ADP
ap-3989	131	8	smaller	small	ADJ
ap-3989	131	9	difference	difference	NOUN
ap-3989	131	10	)	)	PUNCT
ap-3989	131	11	has	have	AUX
ap-3989	131	12	been	be	AUX
ap-3989	131	13	obtained	obtain	VERB
ap-3989	131	14	for	for	ADP
ap-3989	131	15	strategy	strategy	NOUN
ap-3989	131	16	05	05	NUM
ap-3989	131	17	consisting	consist	VERB
ap-3989	131	18	of	of	ADP
ap-3989	131	19	12	12	NUM
ap-3989	131	20	rings	ring	NOUN
ap-3989	131	21	and	and	CCONJ
ap-3989	131	22	12	12	NUM
ap-3989	131	23	multipliers	multiplier	NOUN
ap-3989	131	24	for	for	ADP
ap-3989	131	25	each	each	DET
ap-3989	131	26	ring	ring	NOUN
ap-3989	131	27	.	.	PUNCT
ap-3989	132	1	however	however	ADV
ap-3989	132	2	,	,	PUNCT
ap-3989	132	3	it	it	PRON
ap-3989	132	4	is	be	AUX
ap-3989	132	5	necessary	necessary	ADJ
ap-3989	132	6	to	to	PART
ap-3989	132	7	balance	balance	VERB
ap-3989	132	8	the	the	DET
ap-3989	132	9	computational	computational	ADJ
ap-3989	132	10	effort	effort	NOUN
ap-3989	132	11	(	(	PUNCT
ap-3989	132	12	related	relate	VERB
ap-3989	132	13	to	to	ADP
ap-3989	132	14	number	number	NOUN
ap-3989	132	15	of	of	ADP
ap-3989	132	16	rings	ring	NOUN
ap-3989	132	17	and	and	CCONJ
ap-3989	132	18	number	number	NOUN
ap-3989	132	19	of	of	ADP
ap-3989	132	20	multipliers	multiplier	NOUN
ap-3989	132	21	)	)	PUNCT
ap-3989	132	22	and	and	CCONJ
ap-3989	132	23	obtained	obtain	VERB
ap-3989	132	24	error	error	NOUN
ap-3989	132	25	.	.	PUNCT
ap-3989	133	1	from	from	ADP
ap-3989	133	2	this	this	DET
ap-3989	133	3	point	point	NOUN
ap-3989	133	4	of	of	ADP
ap-3989	133	5	view	view	NOUN
ap-3989	133	6	,	,	PUNCT
ap-3989	133	7	the	the	DET
ap-3989	133	8	optimal	optimal	ADJ
ap-3989	133	9	seems	seem	VERB
ap-3989	133	10	to	to	PART
ap-3989	133	11	be	be	AUX
ap-3989	133	12	the	the	DET
ap-3989	133	13	strategy	strategy	NOUN
ap-3989	133	14	03	03	NUM
ap-3989	133	15	with	with	ADP
ap-3989	133	16	4	4	NUM
ap-3989	133	17	rings	ring	NOUN
ap-3989	133	18	.	.	PUNCT
ap-3989	134	1	5.2	5.2	NUM
ap-3989	134	2	.	.	PUNCT
ap-3989	135	1	flow	flow	VERB
ap-3989	135	2	around	around	ADP
ap-3989	135	3	two	two	NUM
ap-3989	135	4	obstacles	obstacle	NOUN
ap-3989	135	5	the	the	DET
ap-3989	135	6	second	second	ADJ
ap-3989	135	7	example	example	NOUN
ap-3989	135	8	represents	represent	VERB
ap-3989	135	9	a	a	DET
ap-3989	135	10	flow	flow	NOUN
ap-3989	135	11	in	in	ADP
ap-3989	135	12	a	a	DET
ap-3989	135	13	tube	tube	NOUN
ap-3989	135	14	with	with	ADP
ap-3989	135	15	two	two	NUM
ap-3989	135	16	particles	particle	NOUN
ap-3989	135	17	,	,	PUNCT
ap-3989	135	18	as	as	SCONJ
ap-3989	135	19	illustrated	illustrate	VERB
ap-3989	135	20	in	in	ADP
ap-3989	135	21	figure	figure	NOUN
ap-3989	135	22	6	6	NUM
ap-3989	135	23	.	.	PUNCT
ap-3989	136	1	in	in	ADP
ap-3989	136	2	this	this	DET
ap-3989	136	3	test	test	NOUN
ap-3989	136	4	,	,	PUNCT
ap-3989	136	5	three	three	NUM
ap-3989	136	6	different	different	ADJ
ap-3989	136	7	discretizations	discretization	NOUN
ap-3989	136	8	of	of	ADP
ap-3989	136	9	the	the	DET
ap-3989	136	10	fictitious	fictitious	ADJ
ap-3989	136	11	domain	domain	NOUN
ap-3989	136	12	have	have	AUX
ap-3989	136	13	been	be	AUX
ap-3989	136	14	used	use	VERB
ap-3989	136	15	with	with	ADP
ap-3989	136	16	an	an	DET
ap-3989	136	17	increasing	increase	VERB
ap-3989	136	18	mesh	mesh	NOUN
ap-3989	136	19	density	density	NOUN
ap-3989	136	20	,	,	PUNCT
ap-3989	136	21	containing	contain	VERB
ap-3989	136	22	448	448	NUM
ap-3989	136	23	,	,	PUNCT
ap-3989	136	24	1792	1792	NUM
ap-3989	136	25	,	,	PUNCT
ap-3989	136	26	and	and	CCONJ
ap-3989	136	27	7168	7168	NUM
ap-3989	136	28	elements	element	NOUN
ap-3989	136	29	.	.	PUNCT
ap-3989	137	1	the	the	DET
ap-3989	137	2	perfect	perfect	ADJ
ap-3989	137	3	friction	friction	NOUN
ap-3989	137	4	on	on	ADP
ap-3989	137	5	both	both	DET
ap-3989	137	6	horizontal	horizontal	ADJ
ap-3989	137	7	edges	edge	NOUN
ap-3989	137	8	(	(	PUNCT
ap-3989	137	9	no	no	DET
ap-3989	137	10	slip	slip	NOUN
ap-3989	137	11	condition	condition	NOUN
ap-3989	137	12	)	)	PUNCT
ap-3989	137	13	has	have	AUX
ap-3989	137	14	been	be	AUX
ap-3989	137	15	assumed	assume	VERB
ap-3989	137	16	.	.	PUNCT
ap-3989	138	1	the	the	DET
ap-3989	138	2	results	result	NOUN
ap-3989	138	3	are	be	AUX
ap-3989	138	4	again	again	ADV
ap-3989	138	5	compared	compare	VERB
ap-3989	138	6	by	by	ADP
ap-3989	138	7	means	mean	NOUN
ap-3989	138	8	of	of	ADP
ap-3989	138	9	comparing	compare	VERB
ap-3989	138	10	the	the	DET
ap-3989	138	11	velocity	velocity	NOUN
ap-3989	138	12	profiles	profile	NOUN
ap-3989	138	13	along	along	ADP
ap-3989	138	14	the	the	DET
ap-3989	138	15	249	249	NUM
ap-3989	138	16	matej	matej	PROPN
ap-3989	138	17	beňo	beňo	PROPN
ap-3989	138	18	,	,	PUNCT
ap-3989	138	19	bořek	bořek	PROPN
ap-3989	138	20	patzák	patzák	VERB
ap-3989	138	21	acta	acta	PROPN
ap-3989	138	22	polytechnica	polytechnica	PROPN
ap-3989	138	23	no	no	PROPN
ap-3989	138	24	.	.	PUNCT
ap-3989	139	1	lagrange	lagrange	PROPN
ap-3989	139	2	multipliers	multiplier	NOUN
ap-3989	139	3	figure	figure	VERB
ap-3989	139	4	error	error	NOUN
ap-3989	139	5	l2	l2	NOUN
ap-3989	139	6	-	-	PUNCT
ap-3989	139	7	norm	norm	NOUN
ap-3989	139	8	10	10	NUM
ap-3989	139	9	fully	fully	ADV
ap-3989	139	10	resolved	resolve	VERB
ap-3989	139	11	simulation	simulation	NOUN
ap-3989	139	12	0	0	NUM
ap-3989	139	13	01	01	NUM
ap-3989	139	14	1	1	NUM
ap-3989	139	15	multiplier	multipli	ADJ
ap-3989	139	16	per	per	ADP
ap-3989	139	17	ring	ring	NOUN
ap-3989	139	18	–	–	PUNCT
ap-3989	139	19	1	1	NUM
ap-3989	139	20	ring	ring	NOUN
ap-3989	139	21	15	15	NUM
ap-3989	139	22	a	a	DET
ap-3989	139	23	58.10	58.10	NUM
ap-3989	139	24	02	02	NUM
ap-3989	139	25	1	1	NUM
ap-3989	139	26	multiplier	multipli	ADJ
ap-3989	139	27	per	per	ADP
ap-3989	139	28	ring	ring	NOUN
ap-3989	139	29	–	–	PUNCT
ap-3989	139	30	2	2	NUM
ap-3989	139	31	rings	ring	NOUN
ap-3989	139	32	15	15	NUM
ap-3989	139	33	b	b	NOUN
ap-3989	139	34	9.36	9.36	NUM
ap-3989	139	35	03	03	NUM
ap-3989	139	36	1	1	NUM
ap-3989	139	37	multiplier	multipli	ADJ
ap-3989	139	38	per	per	ADP
ap-3989	139	39	ring	ring	NOUN
ap-3989	139	40	–	–	PUNCT
ap-3989	139	41	4	4	NUM
ap-3989	139	42	rings	ring	NOUN
ap-3989	139	43	15	15	NUM
ap-3989	139	44	b	b	NOUN
ap-3989	139	45	1.13	1.13	NUM
ap-3989	139	46	04	04	NUM
ap-3989	139	47	1	1	NUM
ap-3989	139	48	multiplier	multipli	ADJ
ap-3989	139	49	per	per	ADP
ap-3989	139	50	ring	ring	NOUN
ap-3989	139	51	–	–	PUNCT
ap-3989	139	52	8	8	NUM
ap-3989	139	53	rings	ring	NOUN
ap-3989	139	54	15	15	NUM
ap-3989	139	55	b	b	NOUN
ap-3989	139	56	0.93	0.93	NUM
ap-3989	139	57	05	05	NUM
ap-3989	139	58	1	1	NUM
ap-3989	139	59	multiplier	multipli	ADJ
ap-3989	139	60	per	per	ADP
ap-3989	139	61	ring	ring	NOUN
ap-3989	139	62	–	–	PUNCT
ap-3989	139	63	12	12	NUM
ap-3989	139	64	rings	ring	NOUN
ap-3989	139	65	15	15	NUM
ap-3989	139	66	b	b	SYM
ap-3989	139	67	0.89	0.89	NUM
ap-3989	139	68	001	001	NUM
ap-3989	139	69	1	1	NUM
ap-3989	139	70	multiplier	multipli	ADJ
ap-3989	139	71	for	for	ADP
ap-3989	139	72	2	2	NUM
ap-3989	139	73	rings	ring	NOUN
ap-3989	139	74	15	15	NUM
ap-3989	139	75	c	c	NOUN
ap-3989	139	76	22.66	22.66	NUM
ap-3989	139	77	002	002	NUM
ap-3989	139	78	1	1	NUM
ap-3989	139	79	multiplier	multipli	ADJ
ap-3989	139	80	for	for	ADP
ap-3989	139	81	4	4	NUM
ap-3989	139	82	rings	ring	NOUN
ap-3989	139	83	15	15	NUM
ap-3989	139	84	c	c	NOUN
ap-3989	139	85	7.48	7.48	NUM
ap-3989	139	86	003	003	NUM
ap-3989	139	87	1	1	NUM
ap-3989	139	88	multiplier	multipli	ADJ
ap-3989	139	89	for	for	ADP
ap-3989	139	90	8	8	NUM
ap-3989	139	91	rings	ring	NOUN
ap-3989	139	92	15	15	NUM
ap-3989	139	93	c	c	NOUN
ap-3989	139	94	4.45	4.45	NUM
ap-3989	139	95	004	004	NUM
ap-3989	139	96	1	1	NUM
ap-3989	139	97	multiplier	multipli	ADJ
ap-3989	139	98	for	for	ADP
ap-3989	139	99	12	12	NUM
ap-3989	139	100	rings	ring	NOUN
ap-3989	139	101	15	15	NUM
ap-3989	139	102	c	c	NOUN
ap-3989	139	103	4.04	4.04	NUM
ap-3989	139	104	01	01	NUM
ap-3989	139	105	-	-	PUNCT
ap-3989	139	106	p1	p1	NOUN
ap-3989	139	107	same	same	ADJ
ap-3989	139	108	as	as	ADP
ap-3989	139	109	01	01	NUM
ap-3989	139	110	–	–	PUNCT
ap-3989	139	111	sporadic	sporadic	ADJ
ap-3989	139	112	points	point	NOUN
ap-3989	139	113	15	15	NUM
ap-3989	139	114	d	d	NOUN
ap-3989	139	115	56.33	56.33	NUM
ap-3989	139	116	02	02	NUM
ap-3989	139	117	-	-	PUNCT
ap-3989	139	118	p1	p1	NOUN
ap-3989	139	119	same	same	ADJ
ap-3989	139	120	as	as	ADP
ap-3989	139	121	02	02	NUM
ap-3989	139	122	–	–	PUNCT
ap-3989	139	123	sporadic	sporadic	ADJ
ap-3989	139	124	points	point	NOUN
ap-3989	139	125	15	15	NUM
ap-3989	139	126	d	d	NOUN
ap-3989	139	127	21.10	21.10	NUM
ap-3989	139	128	03	03	NUM
ap-3989	139	129	-	-	PUNCT
ap-3989	139	130	p1	p1	NOUN
ap-3989	139	131	same	same	ADJ
ap-3989	139	132	as	as	ADP
ap-3989	139	133	03	03	NUM
ap-3989	139	134	–	–	PUNCT
ap-3989	139	135	sporadic	sporadic	ADJ
ap-3989	139	136	points	point	NOUN
ap-3989	139	137	15	15	NUM
ap-3989	139	138	d	d	SYM
ap-3989	139	139	13.92	13.92	NUM
ap-3989	139	140	04	04	NUM
ap-3989	139	141	-	-	PUNCT
ap-3989	139	142	p1	p1	NOUN
ap-3989	139	143	same	same	ADJ
ap-3989	139	144	as	as	ADP
ap-3989	139	145	04	04	NUM
ap-3989	139	146	–	–	PUNCT
ap-3989	139	147	sporadic	sporadic	ADJ
ap-3989	139	148	points	point	NOUN
ap-3989	139	149	15	15	NUM
ap-3989	139	150	d	d	SYM
ap-3989	139	151	9.76	9.76	NUM
ap-3989	139	152	05	05	NUM
ap-3989	139	153	-	-	PUNCT
ap-3989	139	154	p1	p1	NOUN
ap-3989	139	155	same	same	ADJ
ap-3989	139	156	as	as	ADP
ap-3989	139	157	05	05	NUM
ap-3989	139	158	–	–	PUNCT
ap-3989	139	159	sporadic	sporadic	ADJ
ap-3989	139	160	points	point	NOUN
ap-3989	139	161	15	15	NUM
ap-3989	139	162	d	d	SYM
ap-3989	139	163	8.88	8.88	NUM
ap-3989	139	164	table	table	NOUN
ap-3989	139	165	1	1	NUM
ap-3989	139	166	.	.	PUNCT
ap-3989	139	167	different	different	ADJ
ap-3989	139	168	ways	way	NOUN
ap-3989	139	169	of	of	ADP
ap-3989	139	170	introducing	introduce	VERB
ap-3989	139	171	of	of	ADP
ap-3989	139	172	sample	sample	NOUN
ap-3989	139	173	points	point	NOUN
ap-3989	139	174	with	with	ADP
ap-3989	139	175	l2	l2	NOUN
ap-3989	139	176	norm	norm	NOUN
ap-3989	139	177	of	of	ADP
ap-3989	139	178	velocity	velocity	NOUN
ap-3989	139	179	difference	difference	NOUN
ap-3989	139	180	in	in	ADP
ap-3989	139	181	vertical	vertical	ADJ
ap-3989	139	182	profile	profile	NOUN
ap-3989	139	183	passing	pass	VERB
ap-3989	139	184	the	the	DET
ap-3989	139	185	center	center	NOUN
ap-3989	139	186	of	of	ADP
ap-3989	139	187	obstacle	obstacle	NOUN
ap-3989	139	188	.	.	PUNCT
ap-3989	140	1	figure	figure	VERB
ap-3989	140	2	7	7	NUM
ap-3989	140	3	.	.	PUNCT
ap-3989	141	1	vertical	vertical	ADJ
ap-3989	141	2	profiles	profile	NOUN
ap-3989	141	3	of	of	ADP
ap-3989	141	4	velocity	velocity	NOUN
ap-3989	141	5	passing	pass	VERB
ap-3989	141	6	the	the	DET
ap-3989	141	7	centers	center	NOUN
ap-3989	141	8	of	of	ADP
ap-3989	141	9	both	both	DET
ap-3989	141	10	particles	particle	NOUN
ap-3989	141	11	.	.	PUNCT
ap-3989	142	1	vertical	vertical	ADJ
ap-3989	142	2	section	section	NOUN
ap-3989	142	3	,	,	PUNCT
ap-3989	142	4	indicated	indicate	VERB
ap-3989	142	5	in	in	ADP
ap-3989	142	6	figure	figure	NOUN
ap-3989	142	7	6	6	NUM
ap-3989	142	8	.	.	NOUN
ap-3989	142	9	four	four	NUM
ap-3989	142	10	(	(	PUNCT
ap-3989	142	11	eight	eight	NUM
ap-3989	142	12	,	,	PUNCT
ap-3989	142	13	twenty	twenty	NUM
ap-3989	142	14	-	-	PUNCT
ap-3989	142	15	four	four	NUM
ap-3989	142	16	)	)	PUNCT
ap-3989	142	17	lagrange	lagrange	NOUN
ap-3989	142	18	multipliers	multiplier	NOUN
ap-3989	142	19	per	per	ADP
ap-3989	142	20	obstacle	obstacle	NOUN
ap-3989	142	21	hav	hav	AUX
ap-3989	142	22	been	be	AUX
ap-3989	142	23	used	use	VERB
ap-3989	142	24	.	.	PUNCT
ap-3989	143	1	figure	figure	NOUN
ap-3989	143	2	6	6	NUM
ap-3989	143	3	shows	show	NOUN
ap-3989	143	4	obtained	obtain	VERB
ap-3989	143	5	velocity	velocity	NOUN
ap-3989	143	6	profiles	profile	NOUN
ap-3989	143	7	using	use	VERB
ap-3989	143	8	the	the	DET
ap-3989	143	9	fictitious	fictitious	ADJ
ap-3989	143	10	domain	domain	NOUN
ap-3989	143	11	method	method	NOUN
ap-3989	143	12	and	and	CCONJ
ap-3989	143	13	using	use	VERB
ap-3989	143	14	the	the	DET
ap-3989	143	15	fully	fully	ADV
ap-3989	143	16	resolved	resolve	VERB
ap-3989	143	17	simulation	simulation	NOUN
ap-3989	143	18	.	.	PUNCT
ap-3989	144	1	the	the	DET
ap-3989	144	2	obtained	obtain	VERB
ap-3989	144	3	results	result	NOUN
ap-3989	144	4	show	show	VERB
ap-3989	144	5	excellent	excellent	ADJ
ap-3989	144	6	agreement	agreement	NOUN
ap-3989	144	7	to	to	ADP
ap-3989	144	8	the	the	DET
ap-3989	144	9	results	result	NOUN
ap-3989	144	10	obtained	obtain	VERB
ap-3989	144	11	by	by	ADP
ap-3989	144	12	the	the	DET
ap-3989	144	13	fully	fully	ADV
ap-3989	144	14	resolved	resolve	VERB
ap-3989	144	15	simulation	simulation	NOUN
ap-3989	144	16	.	.	PUNCT
ap-3989	145	1	6	6	NUM
ap-3989	145	2	.	.	X
ap-3989	145	3	conclusion	conclusion	NOUN
ap-3989	145	4	the	the	DET
ap-3989	145	5	presented	present	VERB
ap-3989	145	6	paper	paper	NOUN
ap-3989	145	7	deals	deal	NOUN
ap-3989	145	8	with	with	ADP
ap-3989	145	9	the	the	DET
ap-3989	145	10	modelling	modelling	NOUN
ap-3989	145	11	of	of	ADP
ap-3989	145	12	incompressible	incompressible	ADJ
ap-3989	145	13	flow	flow	NOUN
ap-3989	145	14	around	around	ADP
ap-3989	145	15	fixed	fix	VERB
ap-3989	145	16	(	(	PUNCT
ap-3989	145	17	or	or	CCONJ
ap-3989	145	18	moving	move	VERB
ap-3989	145	19	,	,	PUNCT
ap-3989	145	20	rigid	rigid	ADJ
ap-3989	145	21	)	)	PUNCT
ap-3989	145	22	particles	particle	NOUN
ap-3989	145	23	using	use	VERB
ap-3989	145	24	the	the	DET
ap-3989	145	25	concept	concept	NOUN
ap-3989	145	26	of	of	ADP
ap-3989	145	27	fictitious	fictitious	ADJ
ap-3989	145	28	domain	domain	NOUN
ap-3989	145	29	method	method	NOUN
ap-3989	145	30	and	and	CCONJ
ap-3989	145	31	demonstrates	demonstrate	VERB
ap-3989	145	32	the	the	DET
ap-3989	145	33	capability	capability	NOUN
ap-3989	145	34	of	of	ADP
ap-3989	145	35	this	this	DET
ap-3989	145	36	method	method	NOUN
ap-3989	145	37	to	to	PART
ap-3989	145	38	describe	describe	VERB
ap-3989	145	39	the	the	DET
ap-3989	145	40	flow	flow	NOUN
ap-3989	145	41	with	with	ADP
ap-3989	145	42	solid	solid	ADJ
ap-3989	145	43	obstacles	obstacle	NOUN
ap-3989	145	44	.	.	PUNCT
ap-3989	146	1	the	the	DET
ap-3989	146	2	paper	paper	NOUN
ap-3989	146	3	demonstrates	demonstrate	VERB
ap-3989	146	4	that	that	SCONJ
ap-3989	146	5	the	the	DET
ap-3989	146	6	accuracy	accuracy	NOUN
ap-3989	146	7	of	of	ADP
ap-3989	146	8	the	the	DET
ap-3989	146	9	method	method	NOUN
ap-3989	146	10	depends	depend	VERB
ap-3989	146	11	on	on	ADP
ap-3989	146	12	the	the	DET
ap-3989	146	13	strategy	strategy	NOUN
ap-3989	146	14	of	of	ADP
ap-3989	146	15	choosing	choose	VERB
ap-3989	146	16	sampling	sample	VERB
ap-3989	146	17	points	point	NOUN
ap-3989	146	18	in	in	ADP
ap-3989	146	19	addition	addition	NOUN
ap-3989	146	20	to	to	ADP
ap-3989	146	21	traditional	traditional	ADJ
ap-3989	146	22	aspects	aspect	NOUN
ap-3989	146	23	,	,	PUNCT
ap-3989	146	24	such	such	ADJ
ap-3989	146	25	as	as	ADP
ap-3989	146	26	time	time	NOUN
ap-3989	146	27	stepping	stepping	ADJ
ap-3989	146	28	and	and	CCONJ
ap-3989	146	29	integration	integration	NOUN
ap-3989	146	30	or	or	CCONJ
ap-3989	146	31	space	space	NOUN
ap-3989	146	32	discretization	discretization	NOUN
ap-3989	146	33	.	.	PUNCT
ap-3989	147	1	from	from	ADP
ap-3989	147	2	the	the	DET
ap-3989	147	3	simulations	simulation	NOUN
ap-3989	147	4	performed	perform	VERB
ap-3989	147	5	using	use	VERB
ap-3989	147	6	different	different	ADJ
ap-3989	147	7	strategies	strategy	NOUN
ap-3989	147	8	,	,	PUNCT
ap-3989	147	9	the	the	DET
ap-3989	147	10	uniform	uniform	ADJ
ap-3989	147	11	distribution	distribution	NOUN
ap-3989	147	12	of	of	ADP
ap-3989	147	13	sampling	sample	VERB
ap-3989	147	14	points	point	NOUN
ap-3989	147	15	is	be	AUX
ap-3989	147	16	strongly	strongly	ADV
ap-3989	147	17	recommended	recommend	VERB
ap-3989	147	18	,	,	PUNCT
ap-3989	147	19	while	while	SCONJ
ap-3989	147	20	each	each	DET
ap-3989	147	21	element	element	NOUN
ap-3989	147	22	should	should	AUX
ap-3989	147	23	contain	contain	VERB
ap-3989	147	24	at	at	ADV
ap-3989	147	25	least	least	ADJ
ap-3989	147	26	1	1	NUM
ap-3989	147	27	sampling	sampling	NOUN
ap-3989	147	28	point	point	NOUN
ap-3989	147	29	.	.	PUNCT
ap-3989	148	1	although	although	SCONJ
ap-3989	148	2	the	the	DET
ap-3989	148	3	obtained	obtain	VERB
ap-3989	148	4	results	result	NOUN
ap-3989	148	5	are	be	AUX
ap-3989	148	6	problem	problem	NOUN
ap-3989	148	7	and	and	CCONJ
ap-3989	148	8	grid	grid	VERB
ap-3989	148	9	dependent	dependent	ADJ
ap-3989	148	10	,	,	PUNCT
ap-3989	148	11	they	they	PRON
ap-3989	148	12	demonstrate	demonstrate	VERB
ap-3989	148	13	the	the	DET
ap-3989	148	14	clear	clear	ADJ
ap-3989	148	15	dependence	dependence	NOUN
ap-3989	148	16	of	of	ADP
ap-3989	148	17	the	the	DET
ap-3989	148	18	sampling	sampling	NOUN
ap-3989	148	19	point	point	NOUN
ap-3989	148	20	selection	selection	NOUN
ap-3989	148	21	on	on	ADP
ap-3989	148	22	the	the	DET
ap-3989	148	23	quality	quality	NOUN
ap-3989	148	24	of	of	ADP
ap-3989	148	25	the	the	DET
ap-3989	148	26	solution	solution	NOUN
ap-3989	148	27	.	.	PUNCT
ap-3989	149	1	acknowledgements	acknowledgement	NOUN
ap-3989	149	2	the	the	DET
ap-3989	149	3	authors	author	NOUN
ap-3989	149	4	would	would	AUX
ap-3989	149	5	like	like	VERB
ap-3989	149	6	to	to	PART
ap-3989	149	7	acknowledge	acknowledge	VERB
ap-3989	149	8	the	the	DET
ap-3989	149	9	support	support	NOUN
ap-3989	149	10	of	of	ADP
ap-3989	149	11	the	the	DET
ap-3989	149	12	czech	czech	PROPN
ap-3989	149	13	science	science	NOUN
ap-3989	149	14	foundation	foundation	NOUN
ap-3989	149	15	under	under	ADP
ap-3989	149	16	the	the	DET
ap-3989	149	17	project	project	NOUN
ap-3989	149	18	13	13	NUM
ap-3989	149	19	-	-	SYM
ap-3989	149	20	23584s	23584s	NUM
ap-3989	149	21	.	.	PUNCT
ap-3989	150	1	250	250	NUM
ap-3989	150	2	vol	vol	NOUN
ap-3989	150	3	.	.	PUNCT
ap-3989	150	4	57	57	NUM
ap-3989	150	5	no	no	NOUN
ap-3989	150	6	.	.	PUNCT
ap-3989	151	1	4/2017	4/2017	NUM
ap-3989	151	2	fictitious	fictitious	ADJ
ap-3989	151	3	domain	domain	NOUN
ap-3989	151	4	method	method	NOUN
ap-3989	151	5	for	for	ADP
ap-3989	151	6	a	a	DET
ap-3989	151	7	numerical	numerical	ADJ
ap-3989	151	8	simulation	simulation	NOUN
ap-3989	151	9	references	reference	NOUN
ap-3989	151	10	[	[	X
ap-3989	151	11	1	1	NUM
ap-3989	151	12	]	]	PUNCT
ap-3989	151	13	h.	h.	PROPN
ap-3989	151	14	mori	mori	PROPN
ap-3989	151	15	,	,	PUNCT
ap-3989	151	16	y.	y.	PROPN
ap-3989	151	17	tanigawa	tanigawa	PROPN
ap-3989	151	18	.	.	PUNCT
ap-3989	152	1	simulation	simulation	NOUN
ap-3989	152	2	methods	method	NOUN
ap-3989	152	3	for	for	ADP
ap-3989	152	4	fluidity	fluidity	NOUN
ap-3989	152	5	of	of	ADP
ap-3989	152	6	fresh	fresh	ADJ
ap-3989	152	7	concrete	concrete	NOUN
ap-3989	152	8	.	.	PUNCT
ap-3989	153	1	memoirs	memoir	NOUN
ap-3989	153	2	of	of	ADP
ap-3989	153	3	the	the	DET
ap-3989	153	4	school	school	NOUN
ap-3989	153	5	of	of	ADP
ap-3989	153	6	engineering	engineering	NOUN
ap-3989	153	7	.	.	PUNCT
ap-3989	154	1	1992	1992	NUM
ap-3989	154	2	,	,	PUNCT
ap-3989	154	3	vol	vol	NOUN
ap-3989	154	4	.	.	PROPN
ap-3989	154	5	1	1	NUM
ap-3989	154	6	,	,	PUNCT
ap-3989	154	7	44	44	NUM
ap-3989	154	8	.	.	PUNCT
ap-3989	155	1	[	[	X
ap-3989	155	2	2	2	NUM
ap-3989	155	3	]	]	PUNCT
ap-3989	155	4	f.	f.	PROPN
ap-3989	155	5	kolařík	kolařík	PROPN
ap-3989	155	6	,	,	PUNCT
ap-3989	155	7	b.	b.	PROPN
ap-3989	155	8	patzák	patzák	PROPN
ap-3989	155	9	,	,	PUNCT
ap-3989	155	10	l.n	l.n	PROPN
ap-3989	155	11	.	.	PROPN
ap-3989	155	12	thrane	thrane	NOUN
ap-3989	155	13	.	.	PUNCT
ap-3989	156	1	modeling	modeling	NOUN
ap-3989	156	2	of	of	ADP
ap-3989	156	3	fiber	fiber	NOUN
ap-3989	156	4	orientation	orientation	NOUN
ap-3989	156	5	in	in	ADP
ap-3989	156	6	viscous	viscous	ADJ
ap-3989	156	7	fluid	fluid	NOUN
ap-3989	156	8	flow	flow	NOUN
ap-3989	156	9	with	with	ADP
ap-3989	156	10	application	application	NOUN
ap-3989	156	11	to	to	ADP
ap-3989	156	12	self	self	NOUN
ap-3989	156	13	-	-	PUNCT
ap-3989	156	14	compacting	compact	VERB
ap-3989	156	15	concrete	concrete	NOUN
ap-3989	156	16	.	.	PUNCT
ap-3989	157	1	computers	computer	NOUN
ap-3989	157	2	&	&	CCONJ
ap-3989	157	3	structures	structure	NOUN
ap-3989	157	4	.	.	PUNCT
ap-3989	158	1	2015	2015	NUM
ap-3989	158	2	,	,	PUNCT
ap-3989	158	3	vol	vol	NOUN
ap-3989	158	4	.	.	PROPN
ap-3989	158	5	154	154	NUM
ap-3989	158	6	,	,	PUNCT
ap-3989	159	1	pp	pp	ADJ
ap-3989	159	2	.	.	PUNCT
ap-3989	160	1	91	91	NUM
ap-3989	160	2	-	-	SYM
ap-3989	160	3	100	100	NUM
ap-3989	160	4	.	.	PUNCT
ap-3989	161	1	[	[	X
ap-3989	161	2	3	3	X
ap-3989	161	3	]	]	X
ap-3989	161	4	k.	k.	PROPN
ap-3989	161	5	vassilic	vassilic	PROPN
ap-3989	161	6	,	,	PUNCT
ap-3989	161	7	b.	b.	PROPN
ap-3989	161	8	meng	meng	PROPN
ap-3989	161	9	,	,	PUNCT
ap-3989	161	10	h.c	h.c	PROPN
ap-3989	161	11	.	.	PUNCT
ap-3989	161	12	kühne	kühne	PROPN
ap-3989	161	13	,	,	PUNCT
ap-3989	161	14	n.	n.	NOUN
ap-3989	161	15	roussel	roussel	PROPN
ap-3989	161	16	.	.	PUNCT
ap-3989	162	1	flow	flow	NOUN
ap-3989	162	2	of	of	ADP
ap-3989	162	3	fresh	fresh	ADJ
ap-3989	162	4	concrete	concrete	NOUN
ap-3989	162	5	through	through	ADP
ap-3989	162	6	steel	steel	NOUN
ap-3989	162	7	bars	bar	NOUN
ap-3989	162	8	:	:	PUNCT
ap-3989	162	9	a	a	DET
ap-3989	162	10	porous	porous	ADJ
ap-3989	162	11	medium	medium	ADJ
ap-3989	162	12	analogy	analogy	NOUN
ap-3989	162	13	.	.	PUNCT
ap-3989	163	1	cement	cement	NOUN
ap-3989	163	2	and	and	CCONJ
ap-3989	163	3	concrete	concrete	ADJ
ap-3989	163	4	research	research	NOUN
ap-3989	163	5	.	.	PUNCT
ap-3989	164	1	may	may	AUX
ap-3989	164	2	2011	2011	NUM
ap-3989	164	3	,	,	PUNCT
ap-3989	164	4	vol	vol	NOUN
ap-3989	164	5	.	.	PROPN
ap-3989	164	6	41	41	NUM
ap-3989	164	7	,	,	PUNCT
ap-3989	164	8	5	5	NUM
ap-3989	164	9	,	,	PUNCT
ap-3989	164	10	pp	pp	ADJ
ap-3989	164	11	.	.	PUNCT
ap-3989	165	1	496	496	NUM
ap-3989	165	2	-	-	SYM
ap-3989	165	3	503	503	NUM
ap-3989	165	4	.	.	PUNCT
ap-3989	166	1	[	[	X
ap-3989	166	2	4	4	NUM
ap-3989	166	3	]	]	SYM
ap-3989	166	4	babuška	babuška	PROPN
ap-3989	166	5	,	,	PUNCT
ap-3989	166	6	i.	i.	PROPN
ap-3989	166	7	the	the	DET
ap-3989	166	8	finite	finite	PROPN
ap-3989	166	9	element	element	NOUN
ap-3989	166	10	method	method	NOUN
ap-3989	166	11	with	with	ADP
ap-3989	166	12	lagrangian	lagrangian	ADJ
ap-3989	166	13	multipliers	multiplier	NOUN
ap-3989	166	14	.	.	PUNCT
ap-3989	167	1	numerische	numerische	PROPN
ap-3989	167	2	mathematik	mathematik	PROPN
ap-3989	167	3	.	.	PROPN
ap-3989	168	1	20	20	NUM
ap-3989	168	2	,	,	PUNCT
ap-3989	168	3	pp	pp	ADJ
ap-3989	168	4	.	.	PUNCT
ap-3989	169	1	179	179	NUM
ap-3989	169	2	-	-	SYM
ap-3989	169	3	192	192	NUM
ap-3989	169	4	.	.	PUNCT
ap-3989	170	1	[	[	X
ap-3989	170	2	5	5	NUM
ap-3989	170	3	]	]	X
ap-3989	170	4	marchuk	marchuk	NOUN
ap-3989	170	5	,	,	PUNCT
ap-3989	170	6	g.i	g.i	PROPN
ap-3989	170	7	.	.	PUNCT
ap-3989	170	8	splitting	splitting	NOUN
ap-3989	170	9	and	and	CCONJ
ap-3989	170	10	alternating	alternate	VERB
ap-3989	170	11	direction	direction	NOUN
ap-3989	170	12	methods	method	NOUN
ap-3989	170	13	.	.	PUNCT
ap-3989	171	1	[	[	X
ap-3989	171	2	book	book	NOUN
ap-3989	171	3	auth	auth	ADV
ap-3989	171	4	.	.	PUNCT
ap-3989	171	5	]	]	PUNCT
ap-3989	172	1	j.l	j.l	PROPN
ap-3989	172	2	.	.	PROPN
ap-3989	172	3	lions	lions	PROPN
ap-3989	172	4	p.g	p.g	PROPN
ap-3989	172	5	.	.	PROPN
ap-3989	172	6	ciarlet	ciarlet	PROPN
ap-3989	172	7	.	.	PUNCT
ap-3989	173	1	handbook	handbook	NOUN
ap-3989	173	2	of	of	ADP
ap-3989	173	3	numerical	numerical	ADJ
ap-3989	173	4	analysis	analysis	NOUN
ap-3989	173	5	.	.	PUNCT
ap-3989	174	1	amsterdam	amsterdam	PROPN
ap-3989	174	2	,	,	PUNCT
ap-3989	174	3	north	north	NOUN
ap-3989	174	4	-	-	PUNCT
ap-3989	174	5	holland	holland	NOUN
ap-3989	174	6	,	,	PUNCT
ap-3989	174	7	1990	1990	NUM
ap-3989	174	8	,	,	PUNCT
ap-3989	174	9	vol	vol	NOUN
ap-3989	174	10	.	.	PROPN
ap-3989	174	11	1	1	NUM
ap-3989	174	12	,	,	PUNCT
ap-3989	174	13	pp	pp	ADJ
ap-3989	174	14	.	.	PUNCT
ap-3989	175	1	197	197	NUM
ap-3989	175	2	-	-	SYM
ap-3989	175	3	461	461	NUM
ap-3989	175	4	.	.	PUNCT
ap-3989	176	1	[	[	X
ap-3989	176	2	6	6	NUM
ap-3989	176	3	]	]	X
ap-3989	176	4	r.	r.	PROPN
ap-3989	176	5	glowinski	glowinski	PROPN
ap-3989	176	6	,	,	PUNCT
ap-3989	176	7	t.-w	t.-w	PROPN
ap-3989	176	8	.	.	PUNCT
ap-3989	177	1	pan	pan	PROPN
ap-3989	177	2	,	,	PUNCT
ap-3989	177	3	t.i	t.i	PROPN
ap-3989	177	4	.	.	PROPN
ap-3989	177	5	hesla	hesla	PROPN
ap-3989	177	6	,	,	PUNCT
ap-3989	177	7	d.d	d.d	PROPN
ap-3989	177	8	.	.	PROPN
ap-3989	177	9	joseph	joseph	PROPN
ap-3989	177	10	.	.	PUNCT
ap-3989	178	1	a	a	DET
ap-3989	178	2	distributed	distribute	VERB
ap-3989	178	3	lagrange	lagrange	NOUN
ap-3989	178	4	multiplier	multipli	ADJ
ap-3989	178	5	/	/	SYM
ap-3989	178	6	fictitious	fictitious	ADJ
ap-3989	178	7	domain	domain	NOUN
ap-3989	178	8	method	method	NOUN
ap-3989	178	9	for	for	ADP
ap-3989	178	10	particulate	particulate	NOUN
ap-3989	178	11	flows	flow	NOUN
ap-3989	178	12	.	.	PUNCT
ap-3989	179	1	international	international	ADJ
ap-3989	179	2	journal	journal	PROPN
ap-3989	179	3	of	of	ADP
ap-3989	179	4	multiphase	multiphase	PROPN
ap-3989	179	5	flow	flow	NOUN
ap-3989	179	6	.	.	PUNCT
ap-3989	180	1	1999	1999	NUM
ap-3989	180	2	,	,	PUNCT
ap-3989	180	3	vol	vol	NOUN
ap-3989	180	4	.	.	PROPN
ap-3989	181	1	25	25	NUM
ap-3989	181	2	,	,	PUNCT
ap-3989	181	3	pp	pp	ADJ
ap-3989	181	4	.	.	PUNCT
ap-3989	182	1	755	755	NUM
ap-3989	182	2	-	-	SYM
ap-3989	182	3	794	794	NUM
ap-3989	182	4	.	.	PUNCT
ap-3989	183	1	[	[	X
ap-3989	183	2	7	7	X
ap-3989	183	3	]	]	X
ap-3989	183	4	f.	f.	PROPN
ap-3989	183	5	bertrand	bertrand	PROPN
ap-3989	183	6	,	,	PUNCT
ap-3989	183	7	p.a	p.a	PROPN
ap-3989	183	8	.	.	PROPN
ap-3989	183	9	tanguy	tanguy	PROPN
ap-3989	183	10	,	,	PUNCT
ap-3989	183	11	f.	f.	PROPN
ap-3989	183	12	thibault	thibault	PROPN
ap-3989	183	13	.	.	PUNCT
ap-3989	184	1	a	a	DET
ap-3989	184	2	three	three	NUM
ap-3989	184	3	-	-	PUNCT
ap-3989	184	4	dimensional	dimensional	ADJ
ap-3989	184	5	fictitious	fictitious	ADJ
ap-3989	184	6	domain	domain	NOUN
ap-3989	184	7	method	method	NOUN
ap-3989	184	8	for	for	ADP
ap-3989	184	9	incompressible	incompressible	ADJ
ap-3989	184	10	fluid	fluid	ADJ
ap-3989	184	11	flow	flow	NOUN
ap-3989	184	12	problems	problem	NOUN
ap-3989	184	13	.	.	PUNCT
ap-3989	185	1	int	int	NOUN
ap-3989	185	2	.	.	PUNCT
ap-3989	186	1	j.	j.	PROPN
ap-3989	186	2	numer	numer	PROPN
ap-3989	186	3	.	.	PUNCT
ap-3989	187	1	meth	meth	PROPN
ap-3989	187	2	.	.	PUNCT
ap-3989	188	1	fluids	fluid	NOUN
ap-3989	188	2	.	.	PUNCT
ap-3989	189	1	1997	1997	NUM
ap-3989	189	2	,	,	PUNCT
ap-3989	189	3	vol	vol	NOUN
ap-3989	189	4	.	.	PROPN
ap-3989	189	5	25	25	NUM
ap-3989	189	6	,	,	PUNCT
ap-3989	189	7	pp	pp	ADJ
ap-3989	189	8	.	.	PUNCT
ap-3989	190	1	719	719	NUM
ap-3989	190	2	-	-	NUM
ap-3989	190	3	736	736	NUM
ap-3989	190	4	.	.	PUNCT
ap-3989	191	1	[	[	X
ap-3989	191	2	8	8	NUM
ap-3989	191	3	]	]	X
ap-3989	191	4	p.a	p.a	PROPN
ap-3989	191	5	.	.	PROPN
ap-3989	191	6	tanguy	tanguy	PROPN
ap-3989	191	7	,	,	PUNCT
ap-3989	191	8	f.	f.	PROPN
ap-3989	191	9	bertrand	bertrand	PROPN
ap-3989	191	10	,	,	PUNCT
ap-3989	191	11	r.	r.	PROPN
ap-3989	191	12	labie	labie	PROPN
ap-3989	191	13	,	,	PUNCT
ap-3989	191	14	e.	e.	PROPN
ap-3989	191	15	britode	britode	PROPN
ap-3989	191	16	la	la	PROPN
ap-3989	191	17	fuente	fuente	PROPN
ap-3989	191	18	.	.	PUNCT
ap-3989	192	1	numerical	numerical	ADJ
ap-3989	192	2	modelling	modelling	NOUN
ap-3989	192	3	of	of	ADP
ap-3989	192	4	the	the	DET
ap-3989	192	5	mixing	mixing	NOUN
ap-3989	192	6	of	of	ADP
ap-3989	192	7	viscoplastic	viscoplastic	ADJ
ap-3989	192	8	slurries	slurry	NOUN
ap-3989	192	9	in	in	ADP
ap-3989	192	10	a	a	DET
ap-3989	192	11	twin	twin	ADJ
ap-3989	192	12	-	-	PUNCT
ap-3989	192	13	blade	blade	NOUN
ap-3989	192	14	planetary	planetary	NOUN
ap-3989	192	15	mixer	mixer	NOUN
ap-3989	192	16	.	.	PUNCT
ap-3989	193	1	trans	trans	PROPN
ap-3989	193	2	.	.	PUNCT
ap-3989	194	1	icheme	icheme	PROPN
ap-3989	194	2	.	.	PUNCT
ap-3989	195	1	1996	1996	NUM
ap-3989	195	2	,	,	PUNCT
ap-3989	195	3	vol	vol	NOUN
ap-3989	195	4	.	.	PROPN
ap-3989	195	5	74	74	NUM
ap-3989	196	1	(	(	PUNCT
ap-3989	196	2	part	part	NOUN
ap-3989	196	3	a	a	X
ap-3989	196	4	)	)	PUNCT
ap-3989	196	5	,	,	PUNCT
ap-3989	196	6	pp	pp	ADJ
ap-3989	196	7	.	.	PUNCT
ap-3989	197	1	499	499	NUM
ap-3989	197	2	-	-	SYM
ap-3989	197	3	504	504	NUM
ap-3989	197	4	.	.	PUNCT
ap-3989	198	1	[	[	X
ap-3989	198	2	9	9	NUM
ap-3989	198	3	]	]	SYM
ap-3989	198	4	baaijens	baaijen	NOUN
ap-3989	198	5	,	,	PUNCT
ap-3989	198	6	f.p.t	f.p.t	NOUN
ap-3989	198	7	.	.	PUNCT
ap-3989	199	1	a	a	DET
ap-3989	199	2	fictitious	fictitious	ADJ
ap-3989	199	3	domain	domain	NOUN
ap-3989	199	4	/	/	SYM
ap-3989	199	5	mortar	mortar	NOUN
ap-3989	199	6	element	element	NOUN
ap-3989	199	7	method	method	NOUN
ap-3989	199	8	for	for	ADP
ap-3989	199	9	fluid	fluid	ADJ
ap-3989	199	10	–	–	PUNCT
ap-3989	199	11	structure	structure	NOUN
ap-3989	199	12	interaction	interaction	NOUN
ap-3989	199	13	.	.	PUNCT
ap-3989	200	1	int	int	NOUN
ap-3989	200	2	.	.	PUNCT
ap-3989	201	1	j.	j.	PROPN
ap-3989	201	2	numer	numer	PROPN
ap-3989	201	3	.	.	PUNCT
ap-3989	202	1	meth	meth	PROPN
ap-3989	202	2	.	.	PUNCT
ap-3989	203	1	fluids	fluid	NOUN
ap-3989	203	2	.	.	PUNCT
ap-3989	204	1	2001	2001	NUM
ap-3989	204	2	,	,	PUNCT
ap-3989	204	3	vol	vol	NOUN
ap-3989	204	4	.	.	PROPN
ap-3989	204	5	35	35	NUM
ap-3989	204	6	,	,	PUNCT
ap-3989	204	7	pp	pp	ADJ
ap-3989	204	8	.	.	PUNCT
ap-3989	205	1	743	743	NUM
ap-3989	205	2	-	-	SYM
ap-3989	205	3	761	761	NUM
ap-3989	205	4	.	.	PUNCT
ap-3989	206	1	[	[	X
ap-3989	206	2	10	10	NUM
ap-3989	206	3	]	]	X
ap-3989	206	4	yu	yu	PROPN
ap-3989	206	5	,	,	PUNCT
ap-3989	206	6	z.	z.	PROPN
ap-3989	206	7	a	a	DET
ap-3989	206	8	dlm	dlm	PROPN
ap-3989	206	9	/	/	SYM
ap-3989	206	10	fd	fd	PROPN
ap-3989	206	11	method	method	NOUN
ap-3989	206	12	for	for	ADP
ap-3989	206	13	fluid	fluid	ADJ
ap-3989	206	14	/	/	SYM
ap-3989	206	15	flexible	flexible	ADJ
ap-3989	206	16	-	-	PUNCT
ap-3989	206	17	body	body	NOUN
ap-3989	206	18	interactions	interaction	NOUN
ap-3989	206	19	.	.	PUNCT
ap-3989	207	1	j.	j.	PROPN
ap-3989	207	2	comput	comput	PROPN
ap-3989	207	3	.	.	PUNCT
ap-3989	208	1	phys	phy	NOUN
ap-3989	208	2	.	.	PUNCT
ap-3989	209	1	2005	2005	NUM
ap-3989	209	2	,	,	PUNCT
ap-3989	209	3	vol	vol	NOUN
ap-3989	209	4	.	.	PROPN
ap-3989	209	5	207	207	NUM
ap-3989	209	6	,	,	PUNCT
ap-3989	209	7	pp	pp	ADJ
ap-3989	209	8	.	.	PUNCT
ap-3989	210	1	1	1	NUM
ap-3989	210	2	-	-	SYM
ap-3989	210	3	27	27	NUM
ap-3989	210	4	.	.	PUNCT
ap-3989	211	1	[	[	X
ap-3989	211	2	11	11	NUM
ap-3989	211	3	]	]	X
ap-3989	211	4	glowinski	glowinski	NOUN
ap-3989	211	5	,	,	PUNCT
ap-3989	211	6	r.	r.	PROPN
ap-3989	211	7	finite	finite	PROPN
ap-3989	211	8	element	element	NOUN
ap-3989	211	9	methods	method	NOUN
ap-3989	211	10	for	for	ADP
ap-3989	211	11	incompressible	incompressible	ADJ
ap-3989	211	12	viscous	viscous	ADJ
ap-3989	211	13	flow	flow	NOUN
ap-3989	211	14	.	.	PUNCT
ap-3989	212	1	[	[	X
ap-3989	212	2	book	book	NOUN
ap-3989	212	3	auth	auth	ADV
ap-3989	212	4	.	.	PUNCT
ap-3989	212	5	]	]	PUNCT
ap-3989	213	1	j.l	j.l	PROPN
ap-3989	213	2	.	.	PROPN
ap-3989	213	3	lions	lions	PROPN
ap-3989	213	4	p.g	p.g	PROPN
ap-3989	213	5	.	.	PROPN
ap-3989	213	6	ciarlet	ciarlet	PROPN
ap-3989	213	7	.	.	PUNCT
ap-3989	214	1	handbook	handbook	NOUN
ap-3989	214	2	of	of	ADP
ap-3989	214	3	numerical	numerical	ADJ
ap-3989	214	4	analysis	analysis	NOUN
ap-3989	214	5	.	.	PUNCT
ap-3989	215	1	amsterdam	amsterdam	PROPN
ap-3989	215	2	,	,	PUNCT
ap-3989	215	3	north	north	NOUN
ap-3989	215	4	-	-	PUNCT
ap-3989	215	5	hollad	hollad	NOUN
ap-3989	215	6	,	,	PUNCT
ap-3989	215	7	2003	2003	NUM
ap-3989	215	8	,	,	PUNCT
ap-3989	215	9	vol	vol	NOUN
ap-3989	215	10	.	.	PROPN
ap-3989	215	11	9	9	NUM
ap-3989	215	12	,	,	PUNCT
ap-3989	215	13	pp	pp	ADJ
ap-3989	215	14	.	.	PUNCT
ap-3989	216	1	3	3	NUM
ap-3989	216	2	-	-	SYM
ap-3989	216	3	76	76	NUM
ap-3989	216	4	.	.	PUNCT
ap-3989	217	1	[	[	X
ap-3989	217	2	12	12	NUM
ap-3989	217	3	]	]	X
ap-3989	217	4	r.	r.	PROPN
ap-3989	217	5	glowinski	glowinski	PROPN
ap-3989	217	6	,	,	PUNCT
ap-3989	217	7	o.	o.	PROPN
ap-3989	217	8	pironneau	pironneau	PROPN
ap-3989	217	9	.	.	PUNCT
ap-3989	218	1	finite	finite	PROPN
ap-3989	218	2	element	element	NOUN
ap-3989	218	3	methods	method	NOUN
ap-3989	218	4	for	for	ADP
ap-3989	218	5	navier	navier	NOUN
ap-3989	218	6	-	-	PUNCT
ap-3989	218	7	stokes	stoke	NOUN
ap-3989	218	8	equations	equation	NOUN
ap-3989	218	9	.	.	PUNCT
ap-3989	219	1	annual	annual	ADJ
ap-3989	219	2	reviews	review	NOUN
ap-3989	219	3	fluid	fluid	NOUN
ap-3989	219	4	mech	mech	NOUN
ap-3989	219	5	.	.	PUNCT
ap-3989	219	6	1992	1992	NUM
ap-3989	219	7	,	,	PUNCT
ap-3989	219	8	vol	vol	NOUN
ap-3989	219	9	.	.	PROPN
ap-3989	219	10	24	24	NUM
ap-3989	219	11	,	,	PUNCT
ap-3989	219	12	pp	pp	ADJ
ap-3989	219	13	.	.	PUNCT
ap-3989	220	1	167	167	NUM
ap-3989	220	2	-	-	SYM
ap-3989	220	3	204	204	NUM
ap-3989	220	4	.	.	PUNCT
ap-3989	221	1	[	[	X
ap-3989	221	2	13	13	NUM
ap-3989	221	3	]	]	PUNCT
ap-3989	221	4	patzák	patzák	VERB
ap-3989	221	5	,	,	PUNCT
ap-3989	221	6	b.	b.	PROPN
ap-3989	221	7	oofeman	oofeman	PROPN
ap-3989	221	8	object	object	NOUN
ap-3989	221	9	-	-	PUNCT
ap-3989	221	10	oriented	orient	VERB
ap-3989	221	11	simulation	simulation	NOUN
ap-3989	221	12	tool	tool	NOUN
ap-3989	221	13	for	for	ADP
ap-3989	221	14	advanced	advanced	ADJ
ap-3989	221	15	modeling	modeling	NOUN
ap-3989	221	16	of	of	ADP
ap-3989	221	17	materials	material	NOUN
ap-3989	221	18	and	and	CCONJ
ap-3989	221	19	structures	structure	NOUN
ap-3989	221	20	.	.	PUNCT
ap-3989	222	1	acta	acta	PROPN
ap-3989	222	2	polytechnica	polytechnica	PROPN
ap-3989	222	3	.	.	PUNCT
ap-3989	223	1	2012	2012	NUM
ap-3989	223	2	,	,	PUNCT
ap-3989	223	3	vol	vol	NOUN
ap-3989	223	4	.	.	PROPN
ap-3989	224	1	52	52	NUM
ap-3989	224	2	,	,	PUNCT
ap-3989	224	3	6	6	NUM
ap-3989	224	4	,	,	PUNCT
ap-3989	224	5	pp	pp	ADJ
ap-3989	224	6	.	.	PUNCT
ap-3989	225	1	59	59	NUM
ap-3989	225	2	-	-	SYM
ap-3989	225	3	66	66	NUM
ap-3989	225	4	.	.	PUNCT
ap-3989	226	1	251	251	NUM
ap-3989	226	2	acta	acta	PROPN
ap-3989	226	3	polytechnica	polytechnica	PROPN
ap-3989	226	4	57(4):245–251	57(4):245–251	PROPN
ap-3989	226	5	,	,	PUNCT
ap-3989	226	6	2017	2017	NUM
ap-3989	226	7	1	1	NUM
ap-3989	226	8	introduction	introduction	NOUN
ap-3989	226	9	1.1	1.1	NUM
ap-3989	226	10	fictitious	fictitious	ADJ
ap-3989	226	11	domain	domain	NOUN
ap-3989	226	12	method	method	NOUN
ap-3989	226	13	2	2	NUM
ap-3989	226	14	problem	problem	NOUN
ap-3989	226	15	formulation	formulation	NOUN
ap-3989	226	16	2.1	2.1	NUM
ap-3989	226	17	the	the	DET
ap-3989	226	18	governing	govern	VERB
ap-3989	226	19	equation	equation	NOUN
ap-3989	226	20	of	of	ADP
ap-3989	226	21	the	the	DET
ap-3989	226	22	flow	flow	NOUN
ap-3989	226	23	2.2	2.2	NUM
ap-3989	226	24	governing	govern	VERB
ap-3989	226	25	equations	equation	NOUN
ap-3989	226	26	for	for	ADP
ap-3989	226	27	obstacles	obstacle	NOUN
ap-3989	226	28	3	3	NUM
ap-3989	226	29	weak	weak	ADJ
ap-3989	226	30	form	form	NOUN
ap-3989	226	31	3.1	3.1	NUM
ap-3989	226	32	a	a	DET
ap-3989	226	33	fictitious	fictitious	ADJ
ap-3989	226	34	domain	domain	NOUN
ap-3989	226	35	formulation	formulation	NOUN
ap-3989	226	36	3.2	3.2	NUM
ap-3989	226	37	time	time	NOUN
ap-3989	226	38	discretization	discretization	NOUN
ap-3989	226	39	by	by	ADP
ap-3989	226	40	operator	operator	NOUN
ap-3989	226	41	splitting	split	VERB
ap-3989	226	42	3.3	3.3	NUM
ap-3989	226	43	marchuk	marchuk	NOUN
ap-3989	226	44	’s	’s	PART
ap-3989	226	45	fractional	fractional	ADJ
ap-3989	226	46	-	-	PUNCT
ap-3989	226	47	step	step	NOUN
ap-3989	226	48	scheme	scheme	NOUN
ap-3989	226	49	4	4	NUM
ap-3989	226	50	sampling	sampling	NOUN
ap-3989	226	51	point	point	NOUN
ap-3989	226	52	selection	selection	NOUN
ap-3989	226	53	5	5	NUM
ap-3989	226	54	numerical	numerical	ADJ
ap-3989	226	55	tests	test	NOUN
ap-3989	226	56	5.1	5.1	NUM
ap-3989	226	57	flow	flow	NOUN
ap-3989	226	58	around	around	ADP
ap-3989	226	59	single	single	ADJ
ap-3989	226	60	obstacle	obstacle	NOUN
ap-3989	226	61	5.2	5.2	NUM
ap-3989	226	62	flow	flow	NOUN
ap-3989	226	63	around	around	ADP
ap-3989	226	64	two	two	NUM
ap-3989	226	65	obstacles	obstacle	NOUN
ap-3989	226	66	6	6	NUM
ap-3989	226	67	conclusion	conclusion	NOUN
ap-3989	226	68	acknowledgements	acknowledgement	NOUN
ap-3989	226	69	references	reference	NOUN