id	sid	tid	token	lemma	pos
cana-4886	1	1	communications	communication	NOUN
cana-4886	1	2	on	on	ADP
cana-4886	1	3	applied	apply	VERB
cana-4886	1	4	nonlinear	nonlinear	ADJ
cana-4886	1	5	analysis	analysis	NOUN
cana-4886	1	6	issn	issn	NOUN
cana-4886	1	7	:	:	PUNCT
cana-4886	1	8	1074	1074	NUM
cana-4886	1	9	-	-	PUNCT
cana-4886	1	10	133x	133x	NUM
cana-4886	1	11	vol	vol	VERB
cana-4886	1	12	32	32	NUM
cana-4886	1	13	no	no	NOUN
cana-4886	1	14	.	.	PUNCT
cana-4886	2	1	10s	10	NOUN
cana-4886	2	2	(	(	PUNCT
cana-4886	2	3	2025	2025	NUM
cana-4886	2	4	)	)	PUNCT
cana-4886	2	5	879	879	NUM
cana-4886	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4886	2	7	analytical	analytical	ADJ
cana-4886	2	8	and	and	CCONJ
cana-4886	2	9	numerical	numerical	ADJ
cana-4886	2	10	approaches	approach	NOUN
cana-4886	2	11	to	to	ADP
cana-4886	2	12	solving	solve	VERB
cana-4886	2	13	riemann	riemann	PROPN
cana-4886	2	14	problems	problem	NOUN
cana-4886	2	15	in	in	ADP
cana-4886	2	16	fluid	fluid	ADJ
cana-4886	2	17	dynamics	dynamic	NOUN
cana-4886	2	18	1dr	1dr	NOUN
cana-4886	2	19	.	.	PUNCT
cana-4886	3	1	j.	j.	PROPN
cana-4886	3	2	leo	leo	PROPN
cana-4886	3	3	amalraj	amalraj	PROPN
cana-4886	3	4	,	,	PUNCT
cana-4886	3	5	2dr	2dr	ADJ
cana-4886	3	6	.	.	PUNCT
cana-4886	4	1	p.	p.	PROPN
cana-4886	4	2	ramesh	ramesh	PROPN
cana-4886	4	3	,	,	PUNCT
cana-4886	4	4	3	3	NUM
cana-4886	4	5	ch	ch	NOUN
cana-4886	4	6	.	.	PUNCT
cana-4886	5	1	v.	v.	ADP
cana-4886	5	2	sivaram	sivaram	PROPN
cana-4886	5	3	prasad	prasad	PROPN
cana-4886	5	4	,	,	PUNCT
cana-4886	5	5	4	4	NUM
cana-4886	5	6	v.	v.	ADP
cana-4886	5	7	v.	v.	ADP
cana-4886	5	8	srimannarayana	srimannarayana	PROPN
cana-4886	5	9	,	,	PUNCT
cana-4886	5	10	1associate	1associate	NUM
cana-4886	5	11	professor	professor	NOUN
cana-4886	5	12	,	,	PUNCT
cana-4886	5	13	department	department	NOUN
cana-4886	5	14	of	of	ADP
cana-4886	5	15	mathematics	mathematics	PROPN
cana-4886	5	16	,	,	PUNCT
cana-4886	5	17	rmk	rmk	PROPN
cana-4886	5	18	college	college	PROPN
cana-4886	5	19	of	of	ADP
cana-4886	5	20	engineering	engineering	NOUN
cana-4886	5	21	and	and	CCONJ
cana-4886	5	22	technology	technology	NOUN
cana-4886	5	23	,	,	PUNCT
cana-4886	5	24	puduvoyal	puduvoyal	ADJ
cana-4886	5	25	,	,	PUNCT
cana-4886	5	26	thiruvallur	thiruvallur	NOUN
cana-4886	5	27	district	district	NOUN
cana-4886	5	28	,	,	PUNCT
cana-4886	5	29	tamil	tamil	PROPN
cana-4886	5	30	nadu	nadu	PROPN
cana-4886	5	31	,	,	PUNCT
cana-4886	5	32	india	india	PROPN
cana-4886	5	33	leoamalraj@rmkcet.ac.in	leoamalraj@rmkcet.ac.in	PROPN
cana-4886	5	34	2professor	2professor	PROPN
cana-4886	5	35	,	,	PUNCT
cana-4886	5	36	department	department	NOUN
cana-4886	5	37	of	of	ADP
cana-4886	5	38	mathematics	mathematic	NOUN
cana-4886	5	39	,	,	PUNCT
cana-4886	5	40	erode	erode	VERB
cana-4886	5	41	sengunthar	sengunthar	ADJ
cana-4886	5	42	engineering	engineering	PROPN
cana-4886	5	43	college	college	NOUN
cana-4886	5	44	,	,	PUNCT
cana-4886	5	45	perundurai	perundurai	NOUN
cana-4886	5	46	,	,	PUNCT
cana-4886	5	47	erode	erode	VERB
cana-4886	5	48	638057	638057	NUM
cana-4886	5	49	mail	mail	NOUN
cana-4886	5	50	vprkarur@gmail.com	vprkarur@gmail.com	X
cana-4886	5	51	3professor	3professor	NUM
cana-4886	5	52	,	,	PUNCT
cana-4886	5	53	department	department	NOUN
cana-4886	5	54	of	of	ADP
cana-4886	5	55	mathematics	mathematics	PROPN
cana-4886	5	56	,	,	PUNCT
cana-4886	5	57	aditya	aditya	PROPN
cana-4886	5	58	university	university	PROPN
cana-4886	5	59	,	,	PUNCT
cana-4886	5	60	surampalem	surampalem	NOUN
cana-4886	5	61	,	,	PUNCT
cana-4886	5	62	india	india	PROPN
cana-4886	5	63	,	,	PUNCT
cana-4886	5	64	chprasad.vsr@aec.edu.in	chprasad.vsr@aec.edu.in	PROPN
cana-4886	5	65	4assistant	4assistant	NUM
cana-4886	5	66	professor	professor	NOUN
cana-4886	5	67	,	,	PUNCT
cana-4886	5	68	dept	dept	NOUN
cana-4886	5	69	of	of	ADP
cana-4886	5	70	petroleum	petroleum	NOUN
cana-4886	5	71	technology	technology	NOUN
cana-4886	5	72	,	,	PUNCT
cana-4886	5	73	aditya	aditya	PROPN
cana-4886	5	74	university	university	PROPN
cana-4886	5	75	,	,	PUNCT
cana-4886	5	76	surampalem	surampalem	NOUN
cana-4886	5	77	,	,	PUNCT
cana-4886	5	78	india	india	PROPN
cana-4886	5	79	,	,	PUNCT
cana-4886	5	80	srimannarayana.vv@aec.edu.in	srimannarayana.vv@aec.edu.in	PART
cana-4886	5	81	article	article	NOUN
cana-4886	5	82	history	history	NOUN
cana-4886	5	83	:	:	PUNCT
cana-4886	5	84	received	receive	VERB
cana-4886	5	85	:	:	PUNCT
cana-4886	5	86	12	12	NUM
cana-4886	5	87	-	-	SYM
cana-4886	5	88	01	01	NUM
cana-4886	5	89	-	-	PUNCT
cana-4886	5	90	2025	2025	NUM
cana-4886	5	91	revised	revise	VERB
cana-4886	5	92	:	:	PUNCT
cana-4886	5	93	15	15	NUM
cana-4886	5	94	-	-	NUM
cana-4886	5	95	02	02	NUM
cana-4886	5	96	-	-	PUNCT
cana-4886	5	97	2025	2025	NUM
cana-4886	5	98	accepted	accept	VERB
cana-4886	5	99	:	:	PUNCT
cana-4886	5	100	01	01	NUM
cana-4886	5	101	-	-	SYM
cana-4886	5	102	03	03	NUM
cana-4886	5	103	-	-	PUNCT
cana-4886	5	104	2025	2025	NUM
cana-4886	5	105	abstract	abstract	NOUN
cana-4886	5	106	:	:	PUNCT
cana-4886	5	107	the	the	DET
cana-4886	5	108	riemann	riemann	PROPN
cana-4886	5	109	problem	problem	NOUN
cana-4886	5	110	represents	represent	VERB
cana-4886	5	111	an	an	DET
cana-4886	5	112	essential	essential	ADJ
cana-4886	5	113	problem	problem	NOUN
cana-4886	5	114	in	in	ADP
cana-4886	5	115	fluid	fluid	ADJ
cana-4886	5	116	dynamics	dynamic	NOUN
cana-4886	5	117	which	which	PRON
cana-4886	5	118	enables	enable	VERB
cana-4886	5	119	researchers	researcher	NOUN
cana-4886	5	120	to	to	PART
cana-4886	5	121	model	model	VERB
cana-4886	5	122	shock	shock	NOUN
cana-4886	5	123	waves	wave	NOUN
cana-4886	5	124	together	together	ADV
cana-4886	5	125	with	with	ADP
cana-4886	5	126	both	both	DET
cana-4886	5	127	rarefactions	rarefaction	NOUN
cana-4886	5	128	and	and	CCONJ
cana-4886	5	129	contact	contact	NOUN
cana-4886	5	130	discontinuities	discontinuity	NOUN
cana-4886	5	131	.	.	PUNCT
cana-4886	6	1	the	the	DET
cana-4886	6	2	research	research	NOUN
cana-4886	6	3	investigates	investigate	VERB
cana-4886	6	4	analytical	analytical	ADJ
cana-4886	6	5	and	and	CCONJ
cana-4886	6	6	numerical	numerical	ADJ
cana-4886	6	7	methodologies	methodology	NOUN
cana-4886	6	8	to	to	PART
cana-4886	6	9	solve	solve	VERB
cana-4886	6	10	fluid	fluid	ADJ
cana-4886	6	11	-	-	PUNCT
cana-4886	6	12	dynamic	dynamic	ADJ
cana-4886	6	13	riemann	riemann	NOUN
cana-4886	6	14	problems	problem	NOUN
cana-4886	6	15	and	and	CCONJ
cana-4886	6	16	details	detail	NOUN
cana-4886	6	17	their	their	PRON
cana-4886	6	18	functional	functional	ADJ
cana-4886	6	19	aspects	aspect	NOUN
cana-4886	6	20	as	as	ADV
cana-4886	6	21	well	well	ADV
cana-4886	6	22	as	as	ADP
cana-4886	6	23	restrictions	restriction	NOUN
cana-4886	6	24	.	.	PUNCT
cana-4886	7	1	analytical	analytical	ADJ
cana-4886	7	2	solutions	solution	NOUN
cana-4886	7	3	from	from	ADP
cana-4886	7	4	the	the	DET
cana-4886	7	5	method	method	NOUN
cana-4886	7	6	of	of	ADP
cana-4886	7	7	characteristics	characteristic	NOUN
cana-4886	7	8	along	along	ADP
cana-4886	7	9	with	with	ADP
cana-4886	7	10	exact	exact	ADJ
cana-4886	7	11	riemann	riemann	PROPN
cana-4886	7	12	solvers	solver	NOUN
cana-4886	7	13	form	form	VERB
cana-4886	7	14	the	the	DET
cana-4886	7	15	basis	basis	NOUN
cana-4886	7	16	for	for	ADP
cana-4886	7	17	the	the	DET
cana-4886	7	18	research	research	NOUN
cana-4886	7	19	while	while	SCONJ
cana-4886	7	20	numerical	numerical	ADJ
cana-4886	7	21	solutions	solution	NOUN
cana-4886	7	22	come	come	VERB
cana-4886	7	23	from	from	ADP
cana-4886	7	24	finite	finite	ADJ
cana-4886	7	25	volume	volume	NOUN
cana-4886	7	26	schemes	scheme	NOUN
cana-4886	7	27	and	and	CCONJ
cana-4886	7	28	roe	roe	NOUN
cana-4886	7	29	's	's	PART
cana-4886	7	30	and	and	CCONJ
cana-4886	7	31	hllc	hllc	ADJ
cana-4886	7	32	riemann	riemann	PROPN
cana-4886	7	33	solvers	solvers	PROPN
cana-4886	7	34	.	.	PUNCT
cana-4886	8	1	numerical	numerical	ADJ
cana-4886	8	2	methods	method	NOUN
cana-4886	8	3	show	show	VERB
cana-4886	8	4	both	both	DET
cana-4886	8	5	high	high	ADJ
cana-4886	8	6	precision	precision	NOUN
cana-4886	8	7	and	and	CCONJ
cana-4886	8	8	efficiency	efficiency	NOUN
cana-4886	8	9	in	in	ADP
cana-4886	8	10	their	their	PRON
cana-4886	8	11	ability	ability	NOUN
cana-4886	8	12	to	to	PART
cana-4886	8	13	generate	generate	VERB
cana-4886	8	14	accurate	accurate	ADJ
cana-4886	8	15	simulations	simulation	NOUN
cana-4886	8	16	of	of	ADP
cana-4886	8	17	shock	shock	NOUN
cana-4886	8	18	waves	wave	NOUN
cana-4886	8	19	and	and	CCONJ
cana-4886	8	20	rarefaction	rarefaction	NOUN
cana-4886	8	21	structures	structure	NOUN
cana-4886	8	22	according	accord	VERB
cana-4886	8	23	to	to	ADP
cana-4886	8	24	computational	computational	ADJ
cana-4886	8	25	results	result	NOUN
cana-4886	8	26	.	.	PUNCT
cana-4886	9	1	keywords	keyword	NOUN
cana-4886	9	2	:	:	PUNCT
cana-4886	9	3	riemann	riemann	PROPN
cana-4886	9	4	problem	problem	NOUN
cana-4886	9	5	,	,	PUNCT
cana-4886	9	6	fluid	fluid	ADJ
cana-4886	9	7	dynamics	dynamic	NOUN
cana-4886	9	8	,	,	PUNCT
cana-4886	9	9	shock	shock	NOUN
cana-4886	9	10	waves	wave	NOUN
cana-4886	9	11	,	,	PUNCT
cana-4886	9	12	rarefaction	rarefaction	NOUN
cana-4886	9	13	,	,	PUNCT
cana-4886	9	14	numerical	numerical	ADJ
cana-4886	9	15	methods	method	NOUN
cana-4886	9	16	,	,	PUNCT
cana-4886	9	17	analytical	analytical	ADJ
cana-4886	9	18	solutions	solution	NOUN
cana-4886	9	19	,	,	PUNCT
cana-4886	9	20	finite	finite	PROPN
cana-4886	9	21	volume	volume	NOUN
cana-4886	9	22	method	method	PROPN
cana-4886	9	23	i.	i.	PROPN
cana-4886	9	24	introduction	introduction	NOUN
cana-4886	9	25	fluid	fluid	NOUN
cana-4886	9	26	dynamics	dynamic	NOUN
cana-4886	9	27	experts	expert	NOUN
cana-4886	9	28	recognize	recognize	VERB
cana-4886	9	29	the	the	DET
cana-4886	9	30	riemann	riemann	PROPN
cana-4886	9	31	problem	problem	NOUN
cana-4886	9	32	as	as	ADP
cana-4886	9	33	the	the	DET
cana-4886	9	34	fundamental	fundamental	ADJ
cana-4886	9	35	initial	initial	ADJ
cana-4886	9	36	value	value	NOUN
cana-4886	9	37	problem	problem	NOUN
cana-4886	9	38	because	because	SCONJ
cana-4886	9	39	it	it	PRON
cana-4886	9	40	displays	display	VERB
cana-4886	9	41	shock	shock	NOUN
cana-4886	9	42	waves	wave	NOUN
cana-4886	9	43	and	and	CCONJ
cana-4886	9	44	rarefaction	rarefaction	NOUN
cana-4886	9	45	waves	wave	NOUN
cana-4886	9	46	and	and	CCONJ
cana-4886	9	47	contact	contact	NOUN
cana-4886	9	48	discontinuities	discontinuity	NOUN
cana-4886	9	49	.	.	PUNCT
cana-4886	10	1	bernhard	bernhard	PROPN
cana-4886	10	2	riemann	riemann	PROPN
cana-4886	10	3	established	establish	VERB
cana-4886	10	4	this	this	DET
cana-4886	10	5	problem	problem	NOUN
cana-4886	10	6	during	during	ADP
cana-4886	10	7	the	the	DET
cana-4886	10	8	nineteenth	nineteenth	ADJ
cana-4886	10	9	century	century	NOUN
cana-4886	10	10	to	to	PART
cana-4886	10	11	serve	serve	VERB
cana-4886	10	12	as	as	ADP
cana-4886	10	13	both	both	DET
cana-4886	10	14	computational	computational	ADJ
cana-4886	10	15	fluid	fluid	ADJ
cana-4886	10	16	dynamics	dynamic	NOUN
cana-4886	10	17	(	(	PUNCT
cana-4886	10	18	cfd	cfd	NOUN
cana-4886	10	19	)	)	PUNCT
cana-4886	10	20	and	and	CCONJ
cana-4886	10	21	numerical	numerical	ADJ
cana-4886	10	22	methods	method	NOUN
cana-4886	10	23	for	for	ADP
cana-4886	10	24	hyperbolic	hyperbolic	ADJ
cana-4886	10	25	conservation	conservation	NOUN
cana-4886	10	26	laws	law	NOUN
cana-4886	10	27	'	'	PART
cana-4886	10	28	standard	standard	ADJ
cana-4886	10	29	benchmark	benchmark	NOUN
cana-4886	10	30	evaluation	evaluation	NOUN
cana-4886	10	31	.	.	PUNCT
cana-4886	11	1	the	the	DET
cana-4886	11	2	problem	problem	NOUN
cana-4886	11	3	provides	provide	VERB
cana-4886	11	4	a	a	DET
cana-4886	11	5	straightforward	straightforward	ADJ
cana-4886	11	6	yet	yet	CCONJ
cana-4886	11	7	effective	effective	ADJ
cana-4886	11	8	mechanism	mechanism	NOUN
cana-4886	11	9	for	for	ADP
cana-4886	11	10	interpreting	interpret	VERB
cana-4886	11	11	non	non	ADJ
cana-4886	11	12	-	-	ADJ
cana-4886	11	13	linear	linear	ADJ
cana-4886	11	14	interactions	interaction	NOUN
cana-4886	11	15	between	between	ADP
cana-4886	11	16	waves	wave	NOUN
cana-4886	11	17	that	that	PRON
cana-4886	11	18	occur	occur	VERB
cana-4886	11	19	inside	inside	ADP
cana-4886	11	20	compressible	compressible	ADJ
cana-4886	11	21	fluid	fluid	NOUN
cana-4886	11	22	systems	system	NOUN
cana-4886	11	23	[	[	X
cana-4886	11	24	1	1	NUM
cana-4886	11	25	]	]	PUNCT
cana-4886	11	26	.	.	PUNCT
cana-4886	12	1	the	the	DET
cana-4886	12	2	riemann	riemann	PROPN
cana-4886	12	3	problem	problem	NOUN
cana-4886	12	4	becomes	become	VERB
cana-4886	12	5	crucial	crucial	ADJ
cana-4886	12	6	because	because	SCONJ
cana-4886	12	7	it	it	PRON
cana-4886	12	8	generates	generate	VERB
cana-4886	12	9	predictable	predictable	ADJ
cana-4886	12	10	wave	wave	NOUN
cana-4886	12	11	forms	form	NOUN
cana-4886	12	12	from	from	ADP
cana-4886	12	13	discontinuous	discontinuous	ADJ
cana-4886	12	14	fluid	fluid	NOUN
cana-4886	12	15	conditions	condition	NOUN
cana-4886	12	16	which	which	PRON
cana-4886	12	17	the	the	DET
cana-4886	12	18	euler	euler	PROPN
cana-4886	12	19	equations	equation	NOUN
cana-4886	12	20	govern	govern	VERB
cana-4886	12	21	.	.	PUNCT
cana-4886	13	1	inviscid	inviscid	ADJ
cana-4886	13	2	fluids	fluid	NOUN
cana-4886	13	3	obey	obey	VERB
cana-4886	13	4	the	the	DET
cana-4886	13	5	euler	euler	NOUN
cana-4886	13	6	equations	equation	NOUN
cana-4886	13	7	which	which	PRON
cana-4886	13	8	show	show	VERB
cana-4886	13	9	mass	mass	NOUN
cana-4886	13	10	and	and	CCONJ
cana-4886	13	11	momentum	momentum	NOUN
cana-4886	13	12	and	and	CCONJ
cana-4886	13	13	energy	energy	NOUN
cana-4886	13	14	conservation	conservation	NOUN
cana-4886	13	15	in	in	ADP
cana-4886	13	16	a	a	DET
cana-4886	13	17	hyperbolic	hyperbolic	ADJ
cana-4886	13	18	partial	partial	ADJ
cana-4886	13	19	differential	differential	NOUN
cana-4886	13	20	system	system	NOUN
cana-4886	13	21	.	.	PUNCT
cana-4886	14	1	when	when	SCONJ
cana-4886	14	2	the	the	DET
cana-4886	14	3	problem	problem	NOUN
cana-4886	14	4	exists	exist	VERB
cana-4886	14	5	solely	solely	ADV
cana-4886	14	6	in	in	ADP
cana-4886	14	7	one	one	NUM
cana-4886	14	8	dimension	dimension	NOUN
cana-4886	14	9	it	it	PRON
cana-4886	14	10	shows	show	VERB
cana-4886	14	11	two	two	NUM
cana-4886	14	12	constant	constant	ADJ
cana-4886	14	13	states	state	NOUN
cana-4886	14	14	and	and	CCONJ
cana-4886	14	15	a	a	DET
cana-4886	14	16	communications	communication	NOUN
cana-4886	14	17	on	on	ADP
cana-4886	14	18	applied	apply	VERB
cana-4886	14	19	nonlinear	nonlinear	ADJ
cana-4886	14	20	analysis	analysis	NOUN
cana-4886	14	21	issn	issn	NOUN
cana-4886	14	22	:	:	PUNCT
cana-4886	14	23	1074	1074	NUM
cana-4886	14	24	-	-	PUNCT
cana-4886	14	25	133x	133x	NUM
cana-4886	14	26	vol	vol	VERB
cana-4886	14	27	32	32	NUM
cana-4886	14	28	no	no	NOUN
cana-4886	14	29	.	.	PUNCT
cana-4886	15	1	10s	10	NOUN
cana-4886	15	2	(	(	PUNCT
cana-4886	15	3	2025	2025	NUM
cana-4886	15	4	)	)	PUNCT
cana-4886	15	5	880	880	NUM
cana-4886	15	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4886	15	7	discontinuity	discontinuity	NOUN
cana-4886	15	8	point	point	NOUN
cana-4886	15	9	that	that	PRON
cana-4886	15	10	produces	produce	VERB
cana-4886	15	11	either	either	CCONJ
cana-4886	15	12	shock	shock	NOUN
cana-4886	15	13	waves	wave	NOUN
cana-4886	15	14	or	or	CCONJ
cana-4886	15	15	rarefaction	rarefaction	NOUN
cana-4886	15	16	waves	wave	NOUN
cana-4886	15	17	and	and	CCONJ
cana-4886	15	18	contact	contact	NOUN
cana-4886	15	19	discontinuities	discontinuity	NOUN
cana-4886	15	20	upon	upon	SCONJ
cana-4886	15	21	evolution	evolution	NOUN
cana-4886	15	22	.	.	PUNCT
cana-4886	16	1	research	research	NOUN
cana-4886	16	2	groups	group	NOUN
cana-4886	16	3	can	can	AUX
cana-4886	16	4	understand	understand	VERB
cana-4886	16	5	wave	wave	NOUN
cana-4886	16	6	propagation	propagation	NOUN
cana-4886	16	7	through	through	ADP
cana-4886	16	8	analytical	analytical	ADJ
cana-4886	16	9	solutions	solution	NOUN
cana-4886	16	10	of	of	ADP
cana-4886	16	11	the	the	DET
cana-4886	16	12	riemann	riemann	PROPN
cana-4886	16	13	problem	problem	NOUN
cana-4886	16	14	only	only	ADV
cana-4886	16	15	when	when	SCONJ
cana-4886	16	16	they	they	PRON
cana-4886	16	17	can	can	AUX
cana-4886	16	18	derive	derive	VERB
cana-4886	16	19	exact	exact	ADJ
cana-4886	16	20	results	result	NOUN
cana-4886	16	21	through	through	ADP
cana-4886	16	22	characteristic	characteristic	ADJ
cana-4886	16	23	methods	method	NOUN
cana-4886	16	24	.	.	PUNCT
cana-4886	17	1	solving	solve	VERB
cana-4886	17	2	the	the	DET
cana-4886	17	3	governing	govern	VERB
cana-4886	17	4	equations	equation	NOUN
cana-4886	17	5	through	through	ADP
cana-4886	17	6	method	method	NOUN
cana-4886	17	7	of	of	ADP
cana-4886	17	8	characteristics	characteristic	NOUN
cana-4886	17	9	decomposes	decompose	VERB
cana-4886	17	10	the	the	DET
cana-4886	17	11	equations	equation	NOUN
cana-4886	17	12	into	into	ADP
cana-4886	17	13	separate	separate	ADJ
cana-4886	17	14	regions	region	NOUN
cana-4886	17	15	that	that	PRON
cana-4886	17	16	maintain	maintain	VERB
cana-4886	17	17	constant	constant	ADJ
cana-4886	17	18	solution	solution	NOUN
cana-4886	17	19	values	value	NOUN
cana-4886	17	20	.	.	PUNCT
cana-4886	18	1	the	the	DET
cana-4886	18	2	mathematical	mathematical	ADJ
cana-4886	18	3	solution	solution	NOUN
cana-4886	18	4	of	of	ADP
cana-4886	18	5	this	this	DET
cana-4886	18	6	problem	problem	NOUN
cana-4886	18	7	leads	lead	VERB
cana-4886	18	8	to	to	ADP
cana-4886	18	9	either	either	CCONJ
cana-4886	18	10	a	a	DET
cana-4886	18	11	shock	shock	NOUN
cana-4886	18	12	wave	wave	NOUN
cana-4886	18	13	or	or	CCONJ
cana-4886	18	14	a	a	DET
cana-4886	18	15	rarefaction	rarefaction	NOUN
cana-4886	18	16	wave	wave	NOUN
cana-4886	18	17	or	or	CCONJ
cana-4886	18	18	a	a	DET
cana-4886	18	19	contact	contact	NOUN
cana-4886	18	20	discontinuity	discontinuity	NOUN
cana-4886	18	21	depending	depend	VERB
cana-4886	18	22	on	on	ADP
cana-4886	18	23	the	the	DET
cana-4886	18	24	specified	specified	ADJ
cana-4886	18	25	conditions	condition	NOUN
cana-4886	18	26	during	during	ADP
cana-4886	18	27	initialization	initialization	NOUN
cana-4886	18	28	[	[	X
cana-4886	18	29	3	3	NUM
cana-4886	18	30	-	-	SYM
cana-4886	18	31	6	6	NUM
cana-4886	18	32	]	]	PUNCT
cana-4886	18	33	.	.	PUNCT
cana-4886	19	1	numerical	numerical	ADJ
cana-4886	19	2	methods	method	NOUN
cana-4886	19	3	have	have	AUX
cana-4886	19	4	been	be	AUX
cana-4886	19	5	established	establish	VERB
cana-4886	19	6	to	to	PART
cana-4886	19	7	efficiently	efficiently	ADV
cana-4886	19	8	compute	compute	VERB
cana-4886	19	9	approximate	approximate	ADJ
cana-4886	19	10	riemann	riemann	PROPN
cana-4886	19	11	problem	problem	NOUN
cana-4886	19	12	solutions	solution	NOUN
cana-4886	19	13	because	because	SCONJ
cana-4886	19	14	of	of	ADP
cana-4886	19	15	their	their	PRON
cana-4886	19	16	ability	ability	NOUN
cana-4886	19	17	to	to	PART
cana-4886	19	18	address	address	VERB
cana-4886	19	19	the	the	DET
cana-4886	19	20	original	original	ADJ
cana-4886	19	21	analysis	analysis	NOUN
cana-4886	19	22	limitations	limitation	NOUN
cana-4886	19	23	.	.	PUNCT
cana-4886	20	1	godunov	godunov	AUX
cana-4886	20	2	set	set	VERB
cana-4886	20	3	the	the	DET
cana-4886	20	4	foundation	foundation	NOUN
cana-4886	20	5	for	for	ADP
cana-4886	20	6	the	the	DET
cana-4886	20	7	first	first	ADJ
cana-4886	20	8	numerical	numerical	ADJ
cana-4886	20	9	method	method	NOUN
cana-4886	20	10	through	through	ADP
cana-4886	20	11	his	his	PRON
cana-4886	20	12	approach	approach	NOUN
cana-4886	20	13	that	that	PRON
cana-4886	20	14	involved	involve	VERB
cana-4886	20	15	solving	solve	VERB
cana-4886	20	16	riemann	riemann	PROPN
cana-4886	20	17	problems	problem	NOUN
cana-4886	20	18	at	at	ADP
cana-4886	20	19	individual	individual	ADJ
cana-4886	20	20	cell	cell	NOUN
cana-4886	20	21	interfaces	interface	NOUN
cana-4886	20	22	throughout	throughout	ADP
cana-4886	20	23	the	the	DET
cana-4886	20	24	discrete	discrete	ADJ
cana-4886	20	25	domain	domain	NOUN
cana-4886	20	26	[	[	X
cana-4886	20	27	12	12	NUM
cana-4886	20	28	]	]	PUNCT
cana-4886	20	29	.	.	PUNCT
cana-4886	21	1	numerical	numerical	ADJ
cana-4886	21	2	techniques	technique	NOUN
cana-4886	21	3	based	base	VERB
cana-4886	21	4	on	on	ADP
cana-4886	21	5	riemann	riemann	PROPN
cana-4886	21	6	solvers	solver	NOUN
cana-4886	21	7	have	have	AUX
cana-4886	21	8	allowed	allow	VERB
cana-4886	21	9	researchers	researcher	NOUN
cana-4886	21	10	to	to	PART
cana-4886	21	11	create	create	VERB
cana-4886	21	12	different	different	ADJ
cana-4886	21	13	approximate	approximate	ADJ
cana-4886	21	14	solvers	solver	NOUN
cana-4886	21	15	for	for	ADP
cana-4886	21	16	riemann	riemann	PROPN
cana-4886	21	17	problems	problem	NOUN
cana-4886	21	18	resulting	result	VERB
cana-4886	21	19	in	in	ADP
cana-4886	21	20	roe	roe	PROPN
cana-4886	21	21	’s	’s	PART
cana-4886	21	22	solver	solver	PROPN
cana-4886	21	23	and	and	CCONJ
cana-4886	21	24	the	the	DET
cana-4886	21	25	harten	harten	VERB
cana-4886	21	26	-	-	PUNCT
cana-4886	21	27	lax	lax	ADJ
cana-4886	21	28	-	-	PUNCT
cana-4886	21	29	van	van	NOUN
cana-4886	21	30	leer	leer	NOUN
cana-4886	21	31	-	-	PUNCT
cana-4886	21	32	contact	contact	NOUN
cana-4886	21	33	(	(	PUNCT
cana-4886	21	34	hllc	hllc	ADJ
cana-4886	21	35	)	)	PUNCT
cana-4886	21	36	solver	solver	ADV
cana-4886	21	37	and	and	CCONJ
cana-4886	21	38	the	the	DET
cana-4886	21	39	weighted	weight	VERB
cana-4886	21	40	essentially	essentially	ADV
cana-4886	21	41	non	non	ADJ
cana-4886	21	42	-	-	ADJ
cana-4886	21	43	oscillatory	oscillatory	ADJ
cana-4886	21	44	(	(	PUNCT
cana-4886	21	45	weno	weno	NOUN
cana-4886	21	46	)	)	PUNCT
cana-4886	21	47	and	and	CCONJ
cana-4886	21	48	discontinuous	discontinuous	ADJ
cana-4886	21	49	galerkin	galerkin	NOUN
cana-4886	21	50	(	(	PUNCT
cana-4886	21	51	dg	dg	NOUN
cana-4886	21	52	)	)	PUNCT
cana-4886	21	53	methods	method	NOUN
cana-4886	21	54	.	.	PUNCT
cana-4886	22	1	every	every	DET
cana-4886	22	2	numerical	numerical	ADJ
cana-4886	22	3	method	method	NOUN
cana-4886	22	4	provides	provide	VERB
cana-4886	22	5	particular	particular	ADJ
cana-4886	22	6	benefits	benefit	NOUN
cana-4886	22	7	together	together	ADV
cana-4886	22	8	with	with	ADP
cana-4886	22	9	specific	specific	ADJ
cana-4886	22	10	constraints	constraint	NOUN
cana-4886	22	11	.	.	PUNCT
cana-4886	23	1	roe	roe	PROPN
cana-4886	23	2	's	's	PART
cana-4886	23	3	solver	solver	NOUN
cana-4886	23	4	performs	perform	VERB
cana-4886	23	5	accurately	accurately	ADV
cana-4886	23	6	in	in	ADP
cana-4886	23	7	wave	wave	NOUN
cana-4886	23	8	structure	structure	NOUN
cana-4886	23	9	prediction	prediction	NOUN
cana-4886	23	10	however	however	ADV
cana-4886	23	11	it	it	PRON
cana-4886	23	12	experiences	experience	VERB
cana-4886	23	13	numerical	numerical	ADJ
cana-4886	23	14	problems	problem	NOUN
cana-4886	23	15	close	close	ADJ
cana-4886	23	16	to	to	ADP
cana-4886	23	17	shock	shock	NOUN
cana-4886	23	18	points	point	NOUN
cana-4886	23	19	.	.	PUNCT
cana-4886	24	1	the	the	DET
cana-4886	24	2	hllc	hllc	PROPN
cana-4886	24	3	solver	solver	NOUN
cana-4886	24	4	demonstrates	demonstrate	VERB
cana-4886	24	5	better	well	ADJ
cana-4886	24	6	robustness	robustness	NOUN
cana-4886	24	7	and	and	CCONJ
cana-4886	24	8	accuracy	accuracy	NOUN
cana-4886	24	9	when	when	SCONJ
cana-4886	24	10	dealing	deal	VERB
cana-4886	24	11	with	with	ADP
cana-4886	24	12	contact	contact	NOUN
cana-4886	24	13	discontinues	discontinue	VERB
cana-4886	24	14	due	due	ADP
cana-4886	24	15	to	to	ADP
cana-4886	24	16	its	its	PRON
cana-4886	24	17	advanced	advanced	ADJ
cana-4886	24	18	resolution	resolution	NOUN
cana-4886	24	19	capabilities	capability	NOUN
cana-4886	24	20	.	.	PUNCT
cana-4886	25	1	enhanced	enhance	VERB
cana-4886	25	2	solution	solution	NOUN
cana-4886	25	3	accuracy	accuracy	NOUN
cana-4886	25	4	results	result	NOUN
cana-4886	25	5	from	from	ADP
cana-4886	25	6	using	use	VERB
cana-4886	25	7	weno	weno	NOUN
cana-4886	25	8	high	high	ADJ
cana-4886	25	9	-	-	PUNCT
cana-4886	25	10	order	order	NOUN
cana-4886	25	11	schemes	scheme	NOUN
cana-4886	25	12	although	although	SCONJ
cana-4886	25	13	the	the	DET
cana-4886	25	14	complexity	complexity	NOUN
cana-4886	25	15	of	of	ADP
cana-4886	25	16	computations	computation	NOUN
cana-4886	25	17	increases	increase	VERB
cana-4886	25	18	substantially	substantially	ADV
cana-4886	25	19	.	.	PUNCT
cana-4886	26	1	the	the	DET
cana-4886	26	2	decision	decision	NOUN
cana-4886	26	3	regarding	regard	VERB
cana-4886	26	4	the	the	DET
cana-4886	26	5	appropriate	appropriate	ADJ
cana-4886	26	6	solver	solver	NOUN
cana-4886	26	7	depends	depend	VERB
cana-4886	26	8	on	on	ADP
cana-4886	26	9	what	what	PRON
cana-4886	26	10	fluid	fluid	ADJ
cana-4886	26	11	dynamics	dynamic	NOUN
cana-4886	26	12	issues	issue	NOUN
cana-4886	26	13	need	need	VERB
cana-4886	26	14	to	to	PART
cana-4886	26	15	be	be	AUX
cana-4886	26	16	solved	solve	VERB
cana-4886	26	17	in	in	ADP
cana-4886	26	18	a	a	DET
cana-4886	26	19	particular	particular	ADJ
cana-4886	26	20	situation	situation	NOUN
cana-4886	26	21	[	[	X
cana-4886	26	22	10	10	NUM
cana-4886	26	23	]	]	PUNCT
cana-4886	26	24	.	.	PUNCT
cana-4886	27	1	riemann	riemann	PROPN
cana-4886	27	2	solvers	solver	NOUN
cana-4886	27	3	maintain	maintain	VERB
cana-4886	27	4	a	a	DET
cana-4886	27	5	key	key	ADJ
cana-4886	27	6	position	position	NOUN
cana-4886	27	7	in	in	ADP
cana-4886	27	8	computational	computational	ADJ
cana-4886	27	9	fluid	fluid	ADJ
cana-4886	27	10	dynamics	dynamic	NOUN
cana-4886	27	11	applications	application	NOUN
cana-4886	27	12	so	so	SCONJ
cana-4886	27	13	researchers	researcher	NOUN
cana-4886	27	14	have	have	AUX
cana-4886	27	15	studied	study	VERB
cana-4886	27	16	various	various	ADJ
cana-4886	27	17	enhancements	enhancement	NOUN
cana-4886	27	18	to	to	ADP
cana-4886	27	19	their	their	PRON
cana-4886	27	20	efficiency	efficiency	NOUN
cana-4886	27	21	together	together	ADV
cana-4886	27	22	with	with	ADP
cana-4886	27	23	accuracy	accuracy	NOUN
cana-4886	27	24	and	and	CCONJ
cana-4886	27	25	stability	stability	NOUN
cana-4886	27	26	characteristics	characteristic	NOUN
cana-4886	27	27	.	.	PUNCT
cana-4886	28	1	modern	modern	ADJ
cana-4886	28	2	solvers	solver	NOUN
cana-4886	28	3	power	power	VERB
cana-4886	28	4	the	the	DET
cana-4886	28	5	operation	operation	NOUN
cana-4886	28	6	of	of	ADP
cana-4886	28	7	large	large	ADJ
cana-4886	28	8	-	-	PUNCT
cana-4886	28	9	scale	scale	NOUN
cana-4886	28	10	simulations	simulation	NOUN
cana-4886	28	11	which	which	PRON
cana-4886	28	12	perform	perform	VERB
cana-4886	28	13	simulations	simulation	NOUN
cana-4886	28	14	for	for	ADP
cana-4886	28	15	aerospace	aerospace	NOUN
cana-4886	28	16	applications	application	NOUN
cana-4886	28	17	and	and	CCONJ
cana-4886	28	18	astrophysical	astrophysical	ADJ
cana-4886	28	19	and	and	CCONJ
cana-4886	28	20	industrial	industrial	ADJ
cana-4886	28	21	fluid	fluid	NOUN
cana-4886	28	22	flow	flow	NOUN
cana-4886	28	23	issues	issue	NOUN
cana-4886	28	24	.	.	PUNCT
cana-4886	29	1	the	the	DET
cana-4886	29	2	paper	paper	NOUN
cana-4886	29	3	delves	delve	VERB
cana-4886	29	4	into	into	ADP
cana-4886	29	5	detailed	detailed	ADJ
cana-4886	29	6	information	information	NOUN
cana-4886	29	7	about	about	ADP
cana-4886	29	8	analytical	analytical	ADJ
cana-4886	29	9	and	and	CCONJ
cana-4886	29	10	numerical	numerical	ADJ
cana-4886	29	11	methods	method	NOUN
cana-4886	29	12	to	to	PART
cana-4886	29	13	solve	solve	VERB
cana-4886	29	14	riemann	riemann	PROPN
cana-4886	29	15	problems	problem	NOUN
cana-4886	29	16	by	by	ADP
cana-4886	29	17	examining	examine	VERB
cana-4886	29	18	their	their	PRON
cana-4886	29	19	fundamental	fundamental	ADJ
cana-4886	29	20	theories	theory	NOUN
cana-4886	29	21	and	and	CCONJ
cana-4886	29	22	implementation	implementation	NOUN
cana-4886	29	23	features	feature	NOUN
cana-4886	29	24	and	and	CCONJ
cana-4886	29	25	performance	performance	NOUN
cana-4886	29	26	comparisons	comparison	NOUN
cana-4886	29	27	.	.	PUNCT
cana-4886	30	1	novelty	novelty	NOUN
cana-4886	30	2	and	and	CCONJ
cana-4886	30	3	contribution	contribution	NOUN
cana-4886	30	4	the	the	DET
cana-4886	30	5	research	research	NOUN
cana-4886	30	6	approaches	approach	VERB
cana-4886	30	7	the	the	DET
cana-4886	30	8	riemann	riemann	PROPN
cana-4886	30	9	fluid	fluid	NOUN
cana-4886	30	10	dynamics	dynamic	NOUN
cana-4886	30	11	problem	problem	NOUN
cana-4886	30	12	through	through	ADP
cana-4886	30	13	a	a	DET
cana-4886	30	14	combination	combination	NOUN
cana-4886	30	15	of	of	ADP
cana-4886	30	16	modern	modern	ADJ
cana-4886	30	17	numerical	numerical	ADJ
cana-4886	30	18	methods	method	NOUN
cana-4886	30	19	with	with	ADP
cana-4886	30	20	analytical	analytical	ADJ
cana-4886	30	21	perspective	perspective	NOUN
cana-4886	30	22	solutions	solution	NOUN
cana-4886	30	23	[	[	X
cana-4886	30	24	11	11	NUM
cana-4886	30	25	]	]	PUNCT
cana-4886	30	26	.	.	PUNCT
cana-4886	31	1	previous	previous	ADJ
cana-4886	31	2	research	research	NOUN
cana-4886	31	3	mainly	mainly	ADV
cana-4886	31	4	dealt	deal	VERB
cana-4886	31	5	with	with	ADP
cana-4886	31	6	either	either	CCONJ
cana-4886	31	7	deriving	derive	VERB
cana-4886	31	8	exact	exact	ADJ
cana-4886	31	9	solutions	solution	NOUN
cana-4886	31	10	or	or	CCONJ
cana-4886	31	11	developing	develop	VERB
cana-4886	31	12	numerical	numerical	ADJ
cana-4886	31	13	approximations	approximation	NOUN
cana-4886	31	14	but	but	CCONJ
cana-4886	31	15	this	this	DET
cana-4886	31	16	paper	paper	NOUN
cana-4886	31	17	attempts	attempt	VERB
cana-4886	31	18	to	to	PART
cana-4886	31	19	unify	unify	VERB
cana-4886	31	20	these	these	DET
cana-4886	31	21	independent	independent	ADJ
cana-4886	31	22	methods	method	NOUN
cana-4886	31	23	.	.	PUNCT
cana-4886	32	1	this	this	DET
cana-4886	32	2	research	research	NOUN
cana-4886	32	3	delivers	deliver	VERB
cana-4886	32	4	three	three	NUM
cana-4886	32	5	main	main	ADJ
cana-4886	32	6	contributions	contribution	NOUN
cana-4886	32	7	which	which	PRON
cana-4886	32	8	follow	follow	VERB
cana-4886	32	9	:	:	PUNCT
cana-4886	32	10	a.	a.	NOUN
cana-4886	32	11	comprehensive	comprehensive	ADJ
cana-4886	32	12	comparative	comparative	ADJ
cana-4886	32	13	analysis	analysis	NOUN
cana-4886	32	14	•	•	ADP
cana-4886	32	15	this	this	DET
cana-4886	32	16	paper	paper	NOUN
cana-4886	32	17	provides	provide	VERB
cana-4886	32	18	an	an	DET
cana-4886	32	19	extensive	extensive	ADJ
cana-4886	32	20	comparison	comparison	NOUN
cana-4886	32	21	between	between	ADP
cana-4886	32	22	analytical	analytical	ADJ
cana-4886	32	23	and	and	CCONJ
cana-4886	32	24	numerical	numerical	ADJ
cana-4886	32	25	solutions	solution	NOUN
cana-4886	32	26	compared	compare	VERB
cana-4886	32	27	to	to	ADP
cana-4886	32	28	the	the	DET
cana-4886	32	29	traditional	traditional	ADJ
cana-4886	32	30	approach	approach	NOUN
cana-4886	32	31	when	when	SCONJ
cana-4886	32	32	researchers	researcher	NOUN
cana-4886	32	33	analyze	analyze	VERB
cana-4886	32	34	either	either	CCONJ
cana-4886	32	35	methodology	methodology	NOUN
cana-4886	32	36	independently	independently	ADV
cana-4886	32	37	.	.	PUNCT
cana-4886	33	1	the	the	DET
cana-4886	33	2	study	study	NOUN
cana-4886	33	3	explains	explain	VERB
cana-4886	33	4	both	both	DET
cana-4886	33	5	methods	method	NOUN
cana-4886	33	6	strengths	strength	NOUN
cana-4886	33	7	and	and	CCONJ
cana-4886	33	8	disadvantages	disadvantage	NOUN
cana-4886	33	9	.	.	PUNCT
cana-4886	34	1	communications	communication	NOUN
cana-4886	34	2	on	on	ADP
cana-4886	34	3	applied	apply	VERB
cana-4886	34	4	nonlinear	nonlinear	ADJ
cana-4886	34	5	analysis	analysis	NOUN
cana-4886	34	6	issn	issn	NOUN
cana-4886	34	7	:	:	PUNCT
cana-4886	34	8	1074	1074	NUM
cana-4886	34	9	-	-	PUNCT
cana-4886	34	10	133x	133x	NUM
cana-4886	34	11	vol	vol	VERB
cana-4886	34	12	32	32	NUM
cana-4886	34	13	no	no	NOUN
cana-4886	34	14	.	.	PUNCT
cana-4886	35	1	10s	10	NOUN
cana-4886	35	2	(	(	PUNCT
cana-4886	35	3	2025	2025	NUM
cana-4886	35	4	)	)	PUNCT
cana-4886	35	5	881	881	NUM
cana-4886	35	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4886	35	7	•	•	NOUN
cana-4886	35	8	this	this	DET
cana-4886	35	9	work	work	NOUN
cana-4886	35	10	offers	offer	VERB
cana-4886	35	11	theoretical	theoretical	ADJ
cana-4886	35	12	derivations	derivation	NOUN
cana-4886	35	13	for	for	ADP
cana-4886	35	14	the	the	DET
cana-4886	35	15	method	method	NOUN
cana-4886	35	16	of	of	ADP
cana-4886	35	17	characteristics	characteristic	NOUN
cana-4886	35	18	as	as	ADV
cana-4886	35	19	well	well	ADV
cana-4886	35	20	as	as	ADP
cana-4886	35	21	exact	exact	ADJ
cana-4886	35	22	riemann	riemann	PROPN
cana-4886	35	23	solvers	solver	NOUN
cana-4886	35	24	and	and	CCONJ
cana-4886	35	25	features	feature	VERB
cana-4886	35	26	implementation	implementation	NOUN
cana-4886	35	27	of	of	ADP
cana-4886	35	28	modern	modern	ADJ
cana-4886	35	29	numerical	numerical	ADJ
cana-4886	35	30	solvers	solver	NOUN
cana-4886	35	31	including	include	VERB
cana-4886	35	32	roe	roe	PROPN
cana-4886	35	33	,	,	PUNCT
cana-4886	35	34	hllc	hllc	INTJ
cana-4886	35	35	,	,	PUNCT
cana-4886	35	36	and	and	CCONJ
cana-4886	35	37	weno	weno	PROPN
cana-4886	35	38	.	.	PUNCT
cana-4886	36	1	b.	b.	PROPN
cana-4886	36	2	implementation	implementation	NOUN
cana-4886	36	3	and	and	CCONJ
cana-4886	36	4	performance	performance	NOUN
cana-4886	36	5	evaluation	evaluation	NOUN
cana-4886	36	6	of	of	ADP
cana-4886	36	7	modern	modern	ADJ
cana-4886	36	8	numerical	numerical	ADJ
cana-4886	36	9	solvers	solver	NOUN
cana-4886	36	10	•	•	ADP
cana-4886	36	11	the	the	DET
cana-4886	36	12	study	study	NOUN
cana-4886	36	13	validates	validate	VERB
cana-4886	36	14	diverse	diverse	ADJ
cana-4886	36	15	numerical	numerical	PROPN
cana-4886	36	16	riemann	riemann	PROPN
cana-4886	36	17	solvers	solver	NOUN
cana-4886	36	18	based	base	VERB
cana-4886	36	19	on	on	ADP
cana-4886	36	20	their	their	PRON
cana-4886	36	21	accuracy	accuracy	NOUN
cana-4886	36	22	levels	level	NOUN
cana-4886	36	23	together	together	ADV
cana-4886	36	24	with	with	ADP
cana-4886	36	25	their	their	PRON
cana-4886	36	26	computational	computational	ADJ
cana-4886	36	27	efficiency	efficiency	NOUN
cana-4886	36	28	and	and	CCONJ
cana-4886	36	29	robustness	robustness	NOUN
cana-4886	36	30	properties	property	NOUN
cana-4886	36	31	.	.	PUNCT
cana-4886	37	1	•	•	NUM
cana-4886	37	2	the	the	DET
cana-4886	37	3	studied	study	VERB
cana-4886	37	4	solvers	solver	NOUN
cana-4886	37	5	demonstrate	demonstrate	VERB
cana-4886	37	6	their	their	PRON
cana-4886	37	7	suitability	suitability	NOUN
cana-4886	37	8	for	for	ADP
cana-4886	37	9	particular	particular	ADJ
cana-4886	37	10	fluid	fluid	NOUN
cana-4886	37	11	flow	flow	NOUN
cana-4886	37	12	conditions	condition	NOUN
cana-4886	37	13	by	by	ADP
cana-4886	37	14	testing	test	VERB
cana-4886	37	15	them	they	PRON
cana-4886	37	16	against	against	ADP
cana-4886	37	17	standard	standard	ADJ
cana-4886	37	18	benchmark	benchmark	NOUN
cana-4886	37	19	tests	test	NOUN
cana-4886	37	20	.	.	PUNCT
cana-4886	38	1	c.	c.	NOUN
cana-4886	38	2	addressing	address	VERB
cana-4886	38	3	challenges	challenge	NOUN
cana-4886	38	4	in	in	ADP
cana-4886	38	5	numerical	numerical	ADJ
cana-4886	38	6	simulations	simulation	NOUN
cana-4886	38	7	•	•	ADP
cana-4886	38	8	the	the	DET
cana-4886	38	9	research	research	NOUN
cana-4886	38	10	focuses	focus	VERB
cana-4886	38	11	on	on	ADP
cana-4886	38	12	essential	essential	ADJ
cana-4886	38	13	problems	problem	NOUN
cana-4886	38	14	affecting	affect	VERB
cana-4886	38	15	high	high	ADJ
cana-4886	38	16	-	-	PUNCT
cana-4886	38	17	fidelity	fidelity	NOUN
cana-4886	38	18	cfd	cfd	NOUN
cana-4886	38	19	simulations	simulation	NOUN
cana-4886	38	20	consisting	consist	VERB
cana-4886	38	21	of	of	ADP
cana-4886	38	22	numerical	numerical	ADJ
cana-4886	38	23	dissipation	dissipation	NOUN
cana-4886	38	24	,	,	PUNCT
cana-4886	38	25	non	non	ADJ
cana-4886	38	26	-	-	ADJ
cana-4886	38	27	physical	physical	ADJ
cana-4886	38	28	oscillations	oscillation	NOUN
cana-4886	38	29	and	and	CCONJ
cana-4886	38	30	computational	computational	ADJ
cana-4886	38	31	efficiency	efficiency	NOUN
cana-4886	38	32	difficulties	difficulty	NOUN
cana-4886	38	33	.	.	PUNCT
cana-4886	39	1	•	•	NUM
cana-4886	39	2	the	the	DET
cana-4886	39	3	paper	paper	NOUN
cana-4886	39	4	includes	include	VERB
cana-4886	39	5	a	a	DET
cana-4886	39	6	review	review	NOUN
cana-4886	39	7	discussing	discuss	VERB
cana-4886	39	8	ways	way	NOUN
cana-4886	39	9	to	to	PART
cana-4886	39	10	enhance	enhance	VERB
cana-4886	39	11	hybrid	hybrid	ADJ
cana-4886	39	12	models	model	NOUN
cana-4886	39	13	which	which	PRON
cana-4886	39	14	merge	merge	VERB
cana-4886	39	15	analytical	analytical	ADJ
cana-4886	39	16	and	and	CCONJ
cana-4886	39	17	numerical	numerical	ADJ
cana-4886	39	18	methods	method	NOUN
cana-4886	39	19	to	to	PART
cana-4886	39	20	optimize	optimize	VERB
cana-4886	39	21	their	their	PRON
cana-4886	39	22	operational	operational	ADJ
cana-4886	39	23	effectiveness	effectiveness	NOUN
cana-4886	39	24	.	.	PUNCT
cana-4886	40	1	d.	d.	PROPN
cana-4886	40	2	potential	potential	ADJ
cana-4886	40	3	applications	application	NOUN
cana-4886	40	4	and	and	CCONJ
cana-4886	40	5	future	future	ADJ
cana-4886	40	6	directions	direction	NOUN
cana-4886	40	7	•	•	ADP
cana-4886	40	8	this	this	DET
cana-4886	40	9	research	research	NOUN
cana-4886	40	10	paper	paper	NOUN
cana-4886	40	11	provides	provide	VERB
cana-4886	40	12	solutions	solution	NOUN
cana-4886	40	13	that	that	PRON
cana-4886	40	14	benefit	benefit	VERB
cana-4886	40	15	aerospace	aerospace	NOUN
cana-4886	40	16	engineering	engineering	NOUN
cana-4886	40	17	operations	operation	NOUN
cana-4886	40	18	as	as	ADV
cana-4886	40	19	well	well	ADV
cana-4886	40	20	as	as	ADP
cana-4886	40	21	astrophysical	astrophysical	ADJ
cana-4886	40	22	simulation	simulation	NOUN
cana-4886	40	23	methods	method	NOUN
cana-4886	40	24	and	and	CCONJ
cana-4886	40	25	industrial	industrial	ADJ
cana-4886	40	26	computational	computational	ADJ
cana-4886	40	27	fluid	fluid	ADJ
cana-4886	40	28	dynamics	dynamic	NOUN
cana-4886	40	29	systems	system	NOUN
cana-4886	40	30	.	.	PUNCT
cana-4886	41	1	the	the	DET
cana-4886	41	2	conducted	conduct	VERB
cana-4886	41	3	research	research	NOUN
cana-4886	41	4	adds	add	VERB
cana-4886	41	5	to	to	ADP
cana-4886	41	6	existing	exist	VERB
cana-4886	41	7	knowledge	knowledge	NOUN
cana-4886	41	8	by	by	ADP
cana-4886	41	9	performing	perform	VERB
cana-4886	41	10	a	a	DET
cana-4886	41	11	thorough	thorough	ADJ
cana-4886	41	12	examination	examination	NOUN
cana-4886	41	13	of	of	ADP
cana-4886	41	14	riemann	riemann	PROPN
cana-4886	41	15	problem	problem	NOUN
cana-4886	41	16	solution	solution	NOUN
cana-4886	41	17	methods	method	NOUN
cana-4886	41	18	which	which	PRON
cana-4886	41	19	include	include	VERB
cana-4886	41	20	analytical	analytical	ADJ
cana-4886	41	21	and	and	CCONJ
cana-4886	41	22	numerical	numerical	ADJ
cana-4886	41	23	techniques	technique	NOUN
cana-4886	41	24	.	.	PUNCT
cana-4886	42	1	this	this	DET
cana-4886	42	2	study	study	NOUN
cana-4886	42	3	provides	provide	VERB
cana-4886	42	4	valuable	valuable	ADJ
cana-4886	42	5	direction	direction	NOUN
cana-4886	42	6	to	to	ADP
cana-4886	42	7	researchers	researcher	NOUN
cana-4886	42	8	and	and	CCONJ
cana-4886	42	9	engineers	engineer	NOUN
cana-4886	42	10	for	for	ADP
cana-4886	42	11	choosing	choose	VERB
cana-4886	42	12	efficient	efficient	ADJ
cana-4886	42	13	methods	method	NOUN
cana-4886	42	14	to	to	PART
cana-4886	42	15	solve	solve	VERB
cana-4886	42	16	practical	practical	ADJ
cana-4886	42	17	fluid	fluid	NOUN
cana-4886	42	18	dynamics	dynamic	NOUN
cana-4886	42	19	applications	application	NOUN
cana-4886	42	20	.	.	PUNCT
cana-4886	43	1	ii	ii	PROPN
cana-4886	43	2	.	.	PROPN
cana-4886	43	3	related	relate	VERB
cana-4886	43	4	works	work	NOUN
cana-4886	43	5	scientists	scientist	NOUN
cana-4886	43	6	have	have	AUX
cana-4886	43	7	thoroughly	thoroughly	ADV
cana-4886	43	8	researched	research	VERB
cana-4886	43	9	the	the	DET
cana-4886	43	10	riemann	riemann	PROPN
cana-4886	43	11	problem	problem	NOUN
cana-4886	43	12	in	in	ADP
cana-4886	43	13	fluid	fluid	ADJ
cana-4886	43	14	dynamics	dynamic	NOUN
cana-4886	43	15	because	because	SCONJ
cana-4886	43	16	it	it	PRON
cana-4886	43	17	represents	represent	VERB
cana-4886	43	18	an	an	DET
cana-4886	43	19	essential	essential	ADJ
cana-4886	43	20	mathematical	mathematical	ADJ
cana-4886	43	21	model	model	NOUN
cana-4886	43	22	for	for	ADP
cana-4886	43	23	describing	describe	VERB
cana-4886	43	24	compressible	compressible	ADJ
cana-4886	43	25	flow	flow	NOUN
cana-4886	43	26	wave	wave	NOUN
cana-4886	43	27	dynamics	dynamic	NOUN
cana-4886	43	28	.	.	PUNCT
cana-4886	44	1	scientists	scientist	NOUN
cana-4886	44	2	initially	initially	ADV
cana-4886	44	3	concentrated	concentrate	VERB
cana-4886	44	4	on	on	ADP
cana-4886	44	5	using	use	VERB
cana-4886	44	6	method	method	NOUN
cana-4886	44	7	of	of	ADP
cana-4886	44	8	characteristics	characteristic	NOUN
cana-4886	44	9	to	to	PART
cana-4886	44	10	develop	develop	VERB
cana-4886	44	11	exact	exact	ADJ
cana-4886	44	12	solutions	solution	NOUN
cana-4886	44	13	to	to	PART
cana-4886	44	14	acquire	acquire	VERB
cana-4886	44	15	foundational	foundational	ADJ
cana-4886	44	16	knowledge	knowledge	NOUN
cana-4886	44	17	about	about	ADP
cana-4886	44	18	shock	shock	NOUN
cana-4886	44	19	waves	wave	NOUN
cana-4886	44	20	together	together	ADV
cana-4886	44	21	with	with	ADP
cana-4886	44	22	rarefaction	rarefaction	NOUN
cana-4886	44	23	waves	wave	NOUN
cana-4886	44	24	and	and	CCONJ
cana-4886	44	25	contact	contact	NOUN
cana-4886	44	26	discontinuities	discontinuity	NOUN
cana-4886	44	27	.	.	PUNCT
cana-4886	45	1	the	the	DET
cana-4886	45	2	framework	framework	NOUN
cana-4886	45	3	of	of	ADP
cana-4886	45	4	characteristic	characteristic	ADJ
cana-4886	45	5	waves	wave	NOUN
cana-4886	45	6	serves	serve	VERB
cana-4886	45	7	as	as	ADP
cana-4886	45	8	the	the	DET
cana-4886	45	9	foundation	foundation	NOUN
cana-4886	45	10	for	for	ADP
cana-4886	45	11	solving	solve	VERB
cana-4886	45	12	basic	basic	ADJ
cana-4886	45	13	one	one	NUM
cana-4886	45	14	-	-	PUNCT
cana-4886	45	15	dimensional	dimensional	ADJ
cana-4886	45	16	solutions	solution	NOUN
cana-4886	45	17	of	of	ADP
cana-4886	45	18	simple	simple	ADJ
cana-4886	45	19	problems	problem	NOUN
cana-4886	45	20	.	.	PUNCT
cana-4886	46	1	the	the	DET
cana-4886	46	2	rise	rise	NOUN
cana-4886	46	3	of	of	ADP
cana-4886	46	4	complicated	complicated	ADJ
cana-4886	46	5	fluid	fluid	ADJ
cana-4886	46	6	flow	flow	NOUN
cana-4886	46	7	problems	problem	NOUN
cana-4886	46	8	surpassed	surpass	VERB
cana-4886	46	9	the	the	DET
cana-4886	46	10	analytical	analytical	ADJ
cana-4886	46	11	methods	method	NOUN
cana-4886	46	12	because	because	SCONJ
cana-4886	46	13	they	they	PRON
cana-4886	46	14	failed	fail	VERB
cana-4886	46	15	to	to	PART
cana-4886	46	16	manage	manage	VERB
cana-4886	46	17	multidimensional	multidimensional	ADJ
cana-4886	46	18	effects	effect	NOUN
cana-4886	46	19	as	as	ADV
cana-4886	46	20	well	well	ADV
cana-4886	46	21	as	as	ADP
cana-4886	46	22	viscous	viscous	ADJ
cana-4886	46	23	interactions	interaction	NOUN
cana-4886	46	24	and	and	CCONJ
cana-4886	46	25	turbulence	turbulence	NOUN
cana-4886	46	26	.	.	PUNCT
cana-4886	47	1	in	in	ADP
cana-4886	47	2	2005	2005	NUM
cana-4886	47	3	e.	e.	PROPN
cana-4886	47	4	f.	f.	PROPN
cana-4886	47	5	toro	toro	PROPN
cana-4886	47	6	et.al	et.al	PROPN
cana-4886	47	7	.	.	PUNCT
cana-4886	48	1	and	and	CCONJ
cana-4886	48	2	v.	v.	ADP
cana-4886	48	3	a.	a.	NOUN
cana-4886	48	4	titarev	titarev	PROPN
cana-4886	48	5	et.al	et.al	PROPN
cana-4886	48	6	.	.	PUNCT
cana-4886	48	7	,	,	PUNCT
cana-4886	49	1	[	[	X
cana-4886	49	2	2	2	X
cana-4886	49	3	]	]	PUNCT
cana-4886	49	4	introduce	introduce	VERB
cana-4886	49	5	the	the	DET
cana-4886	49	6	numerical	numerical	ADJ
cana-4886	49	7	approaches	approach	NOUN
cana-4886	49	8	were	be	AUX
cana-4886	49	9	developed	develop	VERB
cana-4886	49	10	as	as	ADP
cana-4886	49	11	a	a	DET
cana-4886	49	12	solution	solution	NOUN
cana-4886	49	13	to	to	PART
cana-4886	49	14	overcome	overcome	VERB
cana-4886	49	15	such	such	ADJ
cana-4886	49	16	restrictions	restriction	NOUN
cana-4886	49	17	which	which	PRON
cana-4886	49	18	resulted	result	VERB
cana-4886	49	19	in	in	ADP
cana-4886	49	20	the	the	DET
cana-4886	49	21	establishment	establishment	NOUN
cana-4886	49	22	of	of	ADP
cana-4886	49	23	different	different	ADJ
cana-4886	49	24	finite	finite	ADJ
cana-4886	49	25	volume	volume	NOUN
cana-4886	49	26	methods	method	NOUN
cana-4886	49	27	and	and	CCONJ
cana-4886	49	28	approximate	approximate	ADJ
cana-4886	49	29	riemann	riemann	PROPN
cana-4886	49	30	solvers	solver	NOUN
cana-4886	49	31	.	.	PUNCT
cana-4886	50	1	numerical	numerical	ADJ
cana-4886	50	2	methods	method	NOUN
cana-4886	50	3	achieved	achieve	VERB
cana-4886	50	4	their	their	PRON
cana-4886	50	5	first	first	ADJ
cana-4886	50	6	major	major	ADJ
cana-4886	50	7	advancement	advancement	NOUN
cana-4886	50	8	by	by	ADP
cana-4886	50	9	introducing	introduce	VERB
cana-4886	50	10	a	a	DET
cana-4886	50	11	godunov	godunov	NOUN
cana-4886	50	12	-	-	PUNCT
cana-4886	50	13	type	type	NOUN
cana-4886	50	14	scheme	scheme	NOUN
cana-4886	50	15	that	that	PRON
cana-4886	50	16	solves	solve	VERB
cana-4886	50	17	riemann	riemann	PROPN
cana-4886	50	18	problems	problem	NOUN
cana-4886	50	19	at	at	ADP
cana-4886	50	20	cell	cell	NOUN
cana-4886	50	21	interfaces	interface	NOUN
cana-4886	50	22	to	to	PART
cana-4886	50	23	calculate	calculate	VERB
cana-4886	50	24	approximate	approximate	ADJ
cana-4886	50	25	solutions	solution	NOUN
cana-4886	50	26	.	.	PUNCT
cana-4886	51	1	numerical	numerical	PROPN
cana-4886	51	2	solver	solver	PROPN
cana-4886	51	3	developers	developer	NOUN
cana-4886	51	4	made	make	VERB
cana-4886	51	5	multiple	multiple	ADJ
cana-4886	51	6	enhancements	enhancement	NOUN
cana-4886	51	7	throughout	throughout	ADP
cana-4886	51	8	years	year	NOUN
cana-4886	51	9	which	which	PRON
cana-4886	51	10	improved	improve	VERB
cana-4886	51	11	both	both	DET
cana-4886	51	12	precision	precision	NOUN
cana-4886	51	13	and	and	CCONJ
cana-4886	51	14	conservation	conservation	NOUN
cana-4886	51	15	of	of	ADP
cana-4886	51	16	solutions	solution	NOUN
cana-4886	51	17	while	while	SCONJ
cana-4886	51	18	decreasing	decrease	VERB
cana-4886	51	19	computational	computational	ADJ
cana-4886	51	20	time	time	NOUN
cana-4886	51	21	demands	demand	NOUN
cana-4886	51	22	.	.	PUNCT
cana-4886	52	1	riemann	riemann	PROPN
cana-4886	52	2	solving	solving	NOUN
cana-4886	52	3	techniques	technique	NOUN
cana-4886	52	4	were	be	AUX
cana-4886	52	5	created	create	VERB
cana-4886	52	6	to	to	PART
cana-4886	52	7	replace	replace	VERB
cana-4886	52	8	pricey	pricey	ADJ
cana-4886	52	9	exact	exact	ADJ
cana-4886	52	10	solvers	solver	NOUN
cana-4886	52	11	yet	yet	ADV
cana-4886	52	12	delivered	deliver	VERB
cana-4886	52	13	both	both	CCONJ
cana-4886	52	14	speed	speed	NOUN
cana-4886	52	15	and	and	CCONJ
cana-4886	52	16	precision	precision	NOUN
cana-4886	52	17	for	for	ADP
cana-4886	52	18	their	their	PRON
cana-4886	52	19	computations	computation	NOUN
cana-4886	52	20	.	.	PUNCT
cana-4886	53	1	the	the	DET
cana-4886	53	2	use	use	NOUN
cana-4886	53	3	of	of	ADP
cana-4886	53	4	roe	roe	PROPN
cana-4886	53	5	’s	’s	PART
cana-4886	53	6	solver	solver	PROPN
cana-4886	53	7	spread	spread	VERB
cana-4886	53	8	widely	widely	ADV
cana-4886	53	9	because	because	SCONJ
cana-4886	53	10	it	it	PRON
cana-4886	53	11	generated	generate	VERB
cana-4886	53	12	efficient	efficient	ADJ
cana-4886	53	13	linearized	linearize	VERB
cana-4886	53	14	communications	communication	NOUN
cana-4886	53	15	on	on	ADP
cana-4886	53	16	applied	apply	VERB
cana-4886	53	17	nonlinear	nonlinear	ADJ
cana-4886	53	18	analysis	analysis	NOUN
cana-4886	53	19	issn	issn	NOUN
cana-4886	53	20	:	:	PUNCT
cana-4886	53	21	1074	1074	NUM
cana-4886	53	22	-	-	PUNCT
cana-4886	53	23	133x	133x	NUM
cana-4886	53	24	vol	vol	VERB
cana-4886	53	25	32	32	NUM
cana-4886	53	26	no	no	NOUN
cana-4886	53	27	.	.	PUNCT
cana-4886	54	1	10s	10	NOUN
cana-4886	54	2	(	(	PUNCT
cana-4886	54	3	2025	2025	NUM
cana-4886	54	4	)	)	PUNCT
cana-4886	54	5	882	882	NUM
cana-4886	54	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4886	54	7	wave	wave	NOUN
cana-4886	54	8	structure	structure	NOUN
cana-4886	54	9	approximations	approximation	NOUN
cana-4886	54	10	.	.	PUNCT
cana-4886	55	1	roe	roe	PROPN
cana-4886	55	2	's	's	PART
cana-4886	55	3	method	method	NOUN
cana-4886	55	4	produces	produce	VERB
cana-4886	55	5	non	non	ADJ
cana-4886	55	6	-	-	ADJ
cana-4886	55	7	physical	physical	ADJ
cana-4886	55	8	oscillations	oscillation	NOUN
cana-4886	55	9	in	in	ADP
cana-4886	55	10	the	the	DET
cana-4886	55	11	vicinity	vicinity	NOUN
cana-4886	55	12	of	of	ADP
cana-4886	55	13	intense	intense	ADJ
cana-4886	55	14	shock	shock	NOUN
cana-4886	55	15	zones	zone	NOUN
cana-4886	55	16	which	which	PRON
cana-4886	55	17	necessitates	necessitate	VERB
cana-4886	55	18	entropy	entropy	NOUN
cana-4886	55	19	fixes	fix	NOUN
cana-4886	55	20	for	for	ADP
cana-4886	55	21	achieving	achieve	VERB
cana-4886	55	22	better	well	ADJ
cana-4886	55	23	robustness	robustness	NOUN
cana-4886	55	24	.	.	PUNCT
cana-4886	56	1	in	in	ADP
cana-4886	56	2	2021	2021	NUM
cana-4886	56	3	d.	d.	PROPN
cana-4886	56	4	baigereyev	baigereyev	PROPN
cana-4886	56	5	et.al	et.al	PROPN
cana-4886	56	6	.	.	PUNCT
cana-4886	56	7	,	,	PUNCT
cana-4886	56	8	n.	n.	PROPN
cana-4886	56	9	alimbekova	alimbekova	PROPN
cana-4886	56	10	et.al	et.al	PROPN
cana-4886	56	11	.	.	PROPN
cana-4886	56	12	,	,	PUNCT
cana-4886	56	13	a.	a.	PROPN
cana-4886	56	14	berdyshev	berdyshev	PROPN
cana-4886	56	15	et.al	et.al	PROPN
cana-4886	56	16	.	.	PROPN
cana-4886	56	17	,	,	PUNCT
cana-4886	56	18	and	and	CCONJ
cana-4886	56	19	m.	m.	PROPN
cana-4886	56	20	madiyarov	madiyarov	PROPN
cana-4886	56	21	et.al	et.al	PROPN
cana-4886	56	22	.	.	PUNCT
cana-4886	57	1	[	[	X
cana-4886	57	2	14	14	NUM
cana-4886	57	3	]	]	PUNCT
cana-4886	57	4	introduce	introduce	VERB
cana-4886	57	5	the	the	DET
cana-4886	57	6	extension	extension	NOUN
cana-4886	57	7	of	of	ADP
cana-4886	57	8	harten	harten	VERB
cana-4886	57	9	-	-	PUNCT
cana-4886	57	10	lax	lax	ADJ
cana-4886	57	11	-	-	PUNCT
cana-4886	57	12	van	van	NOUN
cana-4886	57	13	leer	leer	NOUN
cana-4886	57	14	solvers	solver	NOUN
cana-4886	57	15	managed	manage	VERB
cana-4886	57	16	to	to	PART
cana-4886	57	17	overcome	overcome	VERB
cana-4886	57	18	a	a	DET
cana-4886	57	19	number	number	NOUN
cana-4886	57	20	of	of	ADP
cana-4886	57	21	limitations	limitation	NOUN
cana-4886	57	22	that	that	PRON
cana-4886	57	23	existed	exist	VERB
cana-4886	57	24	within	within	ADP
cana-4886	57	25	roe	roe	PROPN
cana-4886	57	26	's	's	PART
cana-4886	57	27	method	method	NOUN
cana-4886	57	28	.	.	PUNCT
cana-4886	58	1	the	the	DET
cana-4886	58	2	hllc	hllc	PROPN
cana-4886	58	3	solver	solver	PROPN
cana-4886	58	4	maintains	maintain	VERB
cana-4886	58	5	computational	computational	ADJ
cana-4886	58	6	efficiency	efficiency	NOUN
cana-4886	58	7	for	for	ADP
cana-4886	58	8	solving	solve	VERB
cana-4886	58	9	contact	contact	NOUN
cana-4886	58	10	discontinuities	discontinuity	NOUN
cana-4886	58	11	and	and	CCONJ
cana-4886	58	12	provides	provide	VERB
cana-4886	58	13	better	well	ADJ
cana-4886	58	14	accuracy	accuracy	NOUN
cana-4886	58	15	in	in	ADP
cana-4886	58	16	resolving	resolve	VERB
cana-4886	58	17	anomalies	anomaly	NOUN
cana-4886	58	18	than	than	ADP
cana-4886	58	19	other	other	ADJ
cana-4886	58	20	approaches	approach	NOUN
cana-4886	58	21	.	.	PUNCT
cana-4886	59	1	the	the	DET
cana-4886	59	2	solver	solver	NOUN
cana-4886	59	3	finds	find	VERB
cana-4886	59	4	extensive	extensive	ADJ
cana-4886	59	5	use	use	NOUN
cana-4886	59	6	in	in	ADP
cana-4886	59	7	cfd	cfd	NOUN
cana-4886	59	8	applications	application	NOUN
cana-4886	59	9	because	because	SCONJ
cana-4886	59	10	aerospace	aerospace	NOUN
cana-4886	59	11	and	and	CCONJ
cana-4886	59	12	astrophysical	astrophysical	ADJ
cana-4886	59	13	simulations	simulation	NOUN
cana-4886	59	14	require	require	VERB
cana-4886	59	15	high	high	ADJ
cana-4886	59	16	precision	precision	NOUN
cana-4886	59	17	shock	shock	NOUN
cana-4886	59	18	structure	structure	NOUN
cana-4886	59	19	capture	capture	NOUN
cana-4886	59	20	.	.	PUNCT
cana-4886	60	1	numerical	numerical	ADJ
cana-4886	60	2	methods	method	NOUN
cana-4886	60	3	of	of	ADP
cana-4886	60	4	higher	high	ADJ
cana-4886	60	5	-	-	PUNCT
cana-4886	60	6	order	order	NOUN
cana-4886	60	7	have	have	AUX
cana-4886	60	8	emerged	emerge	VERB
cana-4886	60	9	at	at	ADP
cana-4886	60	10	the	the	DET
cana-4886	60	11	same	same	ADJ
cana-4886	60	12	time	time	NOUN
cana-4886	60	13	to	to	PART
cana-4886	60	14	reduce	reduce	VERB
cana-4886	60	15	dissipation	dissipation	NOUN
cana-4886	60	16	levels	level	NOUN
cana-4886	60	17	while	while	SCONJ
cana-4886	60	18	delivering	deliver	VERB
cana-4886	60	19	advanced	advanced	ADJ
cana-4886	60	20	discontinuity	discontinuity	NOUN
cana-4886	60	21	resolution	resolution	NOUN
cana-4886	60	22	capabilities	capability	NOUN
cana-4886	60	23	.	.	PUNCT
cana-4886	61	1	weighted	weight	VERB
cana-4886	61	2	essentially	essentially	ADV
cana-4886	61	3	non	non	ADJ
cana-4886	61	4	-	-	ADJ
cana-4886	61	5	oscillatory	oscillatory	ADJ
cana-4886	61	6	(	(	PUNCT
cana-4886	61	7	weno	weno	ADJ
cana-4886	61	8	)	)	PUNCT
cana-4886	61	9	schemes	scheme	NOUN
cana-4886	61	10	together	together	ADV
cana-4886	61	11	with	with	ADP
cana-4886	61	12	discontinuous	discontinuous	ADJ
cana-4886	61	13	galerkin	galerkin	NOUN
cana-4886	61	14	(	(	PUNCT
cana-4886	61	15	dg	dg	NOUN
cana-4886	61	16	)	)	PUNCT
cana-4886	61	17	methods	method	NOUN
cana-4886	61	18	stand	stand	VERB
cana-4886	61	19	as	as	ADP
cana-4886	61	20	the	the	DET
cana-4886	61	21	top	top	ADJ
cana-4886	61	22	methods	method	NOUN
cana-4886	61	23	for	for	ADP
cana-4886	61	24	solving	solve	VERB
cana-4886	61	25	hyperbolic	hyperbolic	ADJ
cana-4886	61	26	conservation	conservation	NOUN
cana-4886	61	27	laws	law	NOUN
cana-4886	61	28	because	because	SCONJ
cana-4886	61	29	of	of	ADP
cana-4886	61	30	their	their	PRON
cana-4886	61	31	elite	elite	ADJ
cana-4886	61	32	performance	performance	NOUN
cana-4886	61	33	outcomes	outcome	NOUN
cana-4886	61	34	.	.	PUNCT
cana-4886	62	1	such	such	ADJ
cana-4886	62	2	approaches	approach	NOUN
cana-4886	62	3	present	present	VERB
cana-4886	62	4	practical	practical	ADJ
cana-4886	62	5	problems	problem	NOUN
cana-4886	62	6	with	with	ADP
cana-4886	62	7	respect	respect	NOUN
cana-4886	62	8	to	to	ADP
cana-4886	62	9	computational	computational	ADJ
cana-4886	62	10	complexity	complexity	NOUN
cana-4886	62	11	when	when	SCONJ
cana-4886	62	12	applied	apply	VERB
cana-4886	62	13	to	to	ADP
cana-4886	62	14	extensive	extensive	ADJ
cana-4886	62	15	simulations	simulation	NOUN
cana-4886	62	16	.	.	PUNCT
cana-4886	63	1	technological	technological	ADJ
cana-4886	63	2	research	research	NOUN
cana-4886	63	3	of	of	ADP
cana-4886	63	4	the	the	DET
cana-4886	63	5	riemann	riemann	PROPN
cana-4886	63	6	problem	problem	NOUN
cana-4886	63	7	in	in	ADP
cana-4886	63	8	fluid	fluid	ADJ
cana-4886	63	9	dynamics	dynamic	NOUN
cana-4886	63	10	remains	remain	VERB
cana-4886	63	11	comprehensive	comprehensive	ADJ
cana-4886	63	12	because	because	SCONJ
cana-4886	63	13	it	it	PRON
cana-4886	63	14	offers	offer	VERB
cana-4886	63	15	vital	vital	ADJ
cana-4886	63	16	mathematical	mathematical	ADJ
cana-4886	63	17	descriptions	description	NOUN
cana-4886	63	18	for	for	ADP
cana-4886	63	19	compressible	compressible	ADJ
cana-4886	63	20	flow	flow	NOUN
cana-4886	63	21	wave	wave	NOUN
cana-4886	63	22	dynamics	dynamic	NOUN
cana-4886	63	23	.	.	PUNCT
cana-4886	64	1	scientists	scientist	NOUN
cana-4886	64	2	employed	employ	VERB
cana-4886	64	3	the	the	DET
cana-4886	64	4	method	method	NOUN
cana-4886	64	5	of	of	ADP
cana-4886	64	6	characteristics	characteristic	NOUN
cana-4886	64	7	to	to	PART
cana-4886	64	8	generate	generate	VERB
cana-4886	64	9	exact	exact	ADJ
cana-4886	64	10	solutions	solution	NOUN
cana-4886	64	11	for	for	ADP
cana-4886	64	12	obtaining	obtain	VERB
cana-4886	64	13	basic	basic	ADJ
cana-4886	64	14	shock	shock	NOUN
cana-4886	64	15	wave	wave	NOUN
cana-4886	64	16	comprehension	comprehension	NOUN
cana-4886	64	17	as	as	ADV
cana-4886	64	18	well	well	ADV
cana-4886	64	19	as	as	ADP
cana-4886	64	20	rarefaction	rarefaction	NOUN
cana-4886	64	21	wave	wave	NOUN
cana-4886	64	22	knowledge	knowledge	NOUN
cana-4886	64	23	and	and	CCONJ
cana-4886	64	24	contact	contact	NOUN
cana-4886	64	25	discontinuity	discontinuity	NOUN
cana-4886	64	26	information	information	NOUN
cana-4886	64	27	.	.	PUNCT
cana-4886	65	1	basic	basic	ADJ
cana-4886	65	2	one	one	NUM
cana-4886	65	3	-	-	PUNCT
cana-4886	65	4	dimensional	dimensional	ADJ
cana-4886	65	5	solutions	solution	NOUN
cana-4886	65	6	of	of	ADP
cana-4886	65	7	simple	simple	ADJ
cana-4886	65	8	problems	problem	NOUN
cana-4886	65	9	find	find	VERB
cana-4886	65	10	their	their	PRON
cana-4886	65	11	foundation	foundation	NOUN
cana-4886	65	12	within	within	ADP
cana-4886	65	13	the	the	DET
cana-4886	65	14	characteristic	characteristic	ADJ
cana-4886	65	15	wave	wave	NOUN
cana-4886	65	16	framework	framework	NOUN
cana-4886	65	17	.	.	PUNCT
cana-4886	66	1	the	the	DET
cana-4886	66	2	analytical	analytical	ADJ
cana-4886	66	3	methods	method	NOUN
cana-4886	66	4	fell	fall	VERB
cana-4886	66	5	short	short	ADV
cana-4886	66	6	of	of	ADP
cana-4886	66	7	solving	solve	VERB
cana-4886	66	8	complex	complex	ADJ
cana-4886	66	9	fluid	fluid	ADJ
cana-4886	66	10	flow	flow	NOUN
cana-4886	66	11	problems	problem	NOUN
cana-4886	66	12	since	since	SCONJ
cana-4886	66	13	they	they	PRON
cana-4886	66	14	lacked	lack	VERB
cana-4886	66	15	capability	capability	NOUN
cana-4886	66	16	to	to	PART
cana-4886	66	17	control	control	VERB
cana-4886	66	18	multidimensional	multidimensional	ADJ
cana-4886	66	19	effects	effect	NOUN
cana-4886	66	20	alongside	alongside	ADP
cana-4886	66	21	viscous	viscous	ADJ
cana-4886	66	22	interactions	interaction	NOUN
cana-4886	66	23	and	and	CCONJ
cana-4886	66	24	turbulence	turbulence	NOUN
cana-4886	66	25	.	.	PUNCT
cana-4886	67	1	product	product	NOUN
cana-4886	67	2	development	development	NOUN
cana-4886	67	3	through	through	ADP
cana-4886	67	4	numerical	numerical	ADJ
cana-4886	67	5	methods	method	NOUN
cana-4886	67	6	solved	solve	VERB
cana-4886	67	7	these	these	DET
cana-4886	67	8	limitations	limitation	NOUN
cana-4886	67	9	and	and	CCONJ
cana-4886	67	10	led	lead	VERB
cana-4886	67	11	to	to	ADP
cana-4886	67	12	the	the	DET
cana-4886	67	13	creation	creation	NOUN
cana-4886	67	14	of	of	ADP
cana-4886	67	15	different	different	ADJ
cana-4886	67	16	finite	finite	ADJ
cana-4886	67	17	volume	volume	NOUN
cana-4886	67	18	methods	method	NOUN
cana-4886	67	19	and	and	CCONJ
cana-4886	67	20	approximate	approximate	ADJ
cana-4886	67	21	riemann	riemann	PROPN
cana-4886	67	22	solvers	solver	NOUN
cana-4886	67	23	.	.	PUNCT
cana-4886	68	1	the	the	DET
cana-4886	68	2	first	first	ADJ
cana-4886	68	3	major	major	ADJ
cana-4886	68	4	advancement	advancement	NOUN
cana-4886	68	5	in	in	ADP
cana-4886	68	6	numerical	numerical	ADJ
cana-4886	68	7	methods	method	NOUN
cana-4886	68	8	brought	bring	VERB
cana-4886	68	9	forward	forward	ADV
cana-4886	68	10	godunov	godunov	NOUN
cana-4886	68	11	-	-	PUNCT
cana-4886	68	12	type	type	NOUN
cana-4886	68	13	schemes	scheme	NOUN
cana-4886	68	14	that	that	PRON
cana-4886	68	15	resolve	resolve	VERB
cana-4886	68	16	cell	cell	NOUN
cana-4886	68	17	interface	interface	NOUN
cana-4886	68	18	riemann	riemann	PROPN
cana-4886	68	19	problems	problem	NOUN
cana-4886	68	20	to	to	PART
cana-4886	68	21	obtain	obtain	VERB
cana-4886	68	22	approximate	approximate	ADJ
cana-4886	68	23	solutions	solution	NOUN
cana-4886	68	24	.	.	PUNCT
cana-4886	69	1	the	the	DET
cana-4886	69	2	origins	origin	NOUN
cana-4886	69	3	of	of	ADP
cana-4886	69	4	contemporary	contemporary	PROPN
cana-4886	69	5	cfd	cfd	PROPN
cana-4886	69	6	solver	solver	PROPN
cana-4886	69	7	technology	technology	NOUN
cana-4886	69	8	developed	develop	VERB
cana-4886	69	9	from	from	ADP
cana-4886	69	10	this	this	DET
cana-4886	69	11	methodology	methodology	NOUN
cana-4886	69	12	providing	provide	VERB
cana-4886	69	13	the	the	DET
cana-4886	69	14	capability	capability	NOUN
cana-4886	69	15	to	to	PART
cana-4886	69	16	simulate	simulate	VERB
cana-4886	69	17	fast	fast	ADJ
cana-4886	69	18	aerodynamic	aerodynamic	ADJ
cana-4886	69	19	flows	flow	NOUN
cana-4886	69	20	together	together	ADV
cana-4886	69	21	with	with	ADP
cana-4886	69	22	astrophysical	astrophysical	ADJ
cana-4886	69	23	systems	system	NOUN
cana-4886	69	24	as	as	ADV
cana-4886	69	25	well	well	ADV
cana-4886	69	26	as	as	ADP
cana-4886	69	27	industrial	industrial	ADJ
cana-4886	69	28	fluid	fluid	NOUN
cana-4886	69	29	operations	operation	NOUN
cana-4886	69	30	.	.	PUNCT
cana-4886	70	1	numerical	numerical	PROPN
cana-4886	70	2	solver	solver	PROPN
cana-4886	70	3	developers	developer	NOUN
cana-4886	70	4	made	make	VERB
cana-4886	70	5	years	year	NOUN
cana-4886	70	6	of	of	ADP
cana-4886	70	7	continuous	continuous	ADJ
cana-4886	70	8	work	work	NOUN
cana-4886	70	9	to	to	PART
cana-4886	70	10	enhance	enhance	VERB
cana-4886	70	11	both	both	DET
cana-4886	70	12	solution	solution	NOUN
cana-4886	70	13	precision	precision	NOUN
cana-4886	70	14	and	and	CCONJ
cana-4886	70	15	accuracy	accuracy	NOUN
cana-4886	70	16	and	and	CCONJ
cana-4886	70	17	reduce	reduce	VERB
cana-4886	70	18	computational	computational	ADJ
cana-4886	70	19	time	time	NOUN
cana-4886	70	20	requirements	requirement	NOUN
cana-4886	70	21	.	.	PUNCT
cana-4886	71	1	riemann	riemann	PROPN
cana-4886	71	2	-	-	PUNCT
cana-4886	71	3	based	base	VERB
cana-4886	71	4	methods	method	NOUN
cana-4886	71	5	emerged	emerge	VERB
cana-4886	71	6	as	as	ADP
cana-4886	71	7	less	less	ADV
cana-4886	71	8	expensive	expensive	ADJ
cana-4886	71	9	solutions	solution	NOUN
cana-4886	71	10	to	to	PART
cana-4886	71	11	replace	replace	VERB
cana-4886	71	12	traditional	traditional	ADJ
cana-4886	71	13	exact	exact	ADJ
cana-4886	71	14	methods	method	NOUN
cana-4886	71	15	while	while	SCONJ
cana-4886	71	16	performing	perform	VERB
cana-4886	71	17	accurate	accurate	ADJ
cana-4886	71	18	and	and	CCONJ
cana-4886	71	19	speedy	speedy	ADJ
cana-4886	71	20	calculations	calculation	NOUN
cana-4886	71	21	on	on	ADP
cana-4886	71	22	each	each	DET
cana-4886	71	23	step	step	NOUN
cana-4886	71	24	of	of	ADP
cana-4886	71	25	computation	computation	NOUN
cana-4886	71	26	.	.	PUNCT
cana-4886	72	1	roe	roe	PROPN
cana-4886	72	2	’s	’s	PART
cana-4886	72	3	solver	solver	PROPN
cana-4886	72	4	became	become	VERB
cana-4886	72	5	massively	massively	ADV
cana-4886	72	6	popular	popular	ADJ
cana-4886	72	7	because	because	SCONJ
cana-4886	72	8	it	it	PRON
cana-4886	72	9	created	create	VERB
cana-4886	72	10	efficient	efficient	ADJ
cana-4886	72	11	wave	wave	NOUN
cana-4886	72	12	structure	structure	NOUN
cana-4886	72	13	linearizations	linearization	NOUN
cana-4886	72	14	.	.	PUNCT
cana-4886	73	1	the	the	DET
cana-4886	73	2	non	non	ADJ
cana-4886	73	3	-	-	ADJ
cana-4886	73	4	physical	physical	ADJ
cana-4886	73	5	oscillations	oscillation	NOUN
cana-4886	73	6	created	create	VERB
cana-4886	73	7	by	by	ADP
cana-4886	73	8	roe	roe	PROPN
cana-4886	73	9	's	's	PART
cana-4886	73	10	method	method	NOUN
cana-4886	73	11	near	near	ADP
cana-4886	73	12	shock	shock	NOUN
cana-4886	73	13	areas	area	NOUN
cana-4886	73	14	demand	demand	VERB
cana-4886	73	15	entropy	entropy	NOUN
cana-4886	73	16	treatments	treatment	NOUN
cana-4886	73	17	to	to	PART
cana-4886	73	18	reach	reach	VERB
cana-4886	73	19	robust	robust	ADJ
cana-4886	73	20	solutions	solution	NOUN
cana-4886	73	21	.	.	PUNCT
cana-4886	74	1	in	in	ADP
cana-4886	74	2	2023	2023	NUM
cana-4886	74	3	n.	n.	NOUN
cana-4886	74	4	kamran	kamran	PROPN
cana-4886	74	5	et.al	et.al	PROPN
cana-4886	74	6	.	.	PROPN
cana-4886	74	7	,	,	PUNCT
cana-4886	74	8	m.	m.	NOUN
cana-4886	74	9	asif	asif	PROPN
cana-4886	74	10	et.al	et.al	PROPN
cana-4886	74	11	.	.	PROPN
cana-4886	74	12	,	,	PUNCT
cana-4886	74	13	k.	k.	PROPN
cana-4886	74	14	shah	shah	PROPN
cana-4886	74	15	et.al	et.al	PROPN
cana-4886	74	16	.	.	PROPN
cana-4886	74	17	,	,	PUNCT
cana-4886	74	18	b.	b.	PROPN
cana-4886	74	19	abdalla	abdalla	PROPN
cana-4886	74	20	et.al	et.al	PROPN
cana-4886	74	21	.	.	PROPN
cana-4886	74	22	,	,	PUNCT
cana-4886	74	23	and	and	CCONJ
cana-4886	74	24	t.	t.	PROPN
cana-4886	74	25	abdeljawad	abdeljawad	PROPN
cana-4886	74	26	et.al	et.al	PROPN
cana-4886	74	27	.	.	PUNCT
cana-4886	75	1	[	[	X
cana-4886	75	2	13	13	NUM
cana-4886	75	3	]	]	PUNCT
cana-4886	75	4	introduce	introduce	VERB
cana-4886	75	5	the	the	DET
cana-4886	75	6	extended	extended	ADJ
cana-4886	75	7	version	version	NOUN
cana-4886	75	8	of	of	ADP
cana-4886	75	9	harten	harten	VERB
cana-4886	75	10	-	-	PUNCT
cana-4886	75	11	lax	lax	ADJ
cana-4886	75	12	-	-	PUNCT
cana-4886	75	13	van	van	NOUN
cana-4886	75	14	leer	leer	NOUN
cana-4886	75	15	solvers	solver	NOUN
cana-4886	75	16	solved	solve	VERB
cana-4886	75	17	multiple	multiple	ADJ
cana-4886	75	18	problems	problem	NOUN
cana-4886	75	19	that	that	PRON
cana-4886	75	20	roe	roe	PROPN
cana-4886	75	21	's	's	PART
cana-4886	75	22	method	method	NOUN
cana-4886	75	23	previously	previously	ADV
cana-4886	75	24	contained	contain	VERB
cana-4886	75	25	.	.	PUNCT
cana-4886	76	1	by	by	ADP
cana-4886	76	2	employing	employ	VERB
cana-4886	76	3	hllc	hllc	ADJ
cana-4886	76	4	solver	solver	NOUN
cana-4886	76	5	calculations	calculation	NOUN
cana-4886	76	6	remain	remain	VERB
cana-4886	76	7	efficient	efficient	ADJ
cana-4886	76	8	for	for	ADP
cana-4886	76	9	dealing	deal	VERB
cana-4886	76	10	with	with	ADP
cana-4886	76	11	contact	contact	NOUN
cana-4886	76	12	discontinuities	discontinuity	NOUN
cana-4886	76	13	and	and	CCONJ
cana-4886	76	14	achieve	achieve	VERB
cana-4886	76	15	superior	superior	ADJ
cana-4886	76	16	anomaly	anomaly	NOUN
cana-4886	76	17	detection	detection	NOUN
cana-4886	76	18	precision	precision	NOUN
cana-4886	76	19	in	in	ADP
cana-4886	76	20	comparison	comparison	NOUN
cana-4886	76	21	to	to	ADP
cana-4886	76	22	alternative	alternative	ADJ
cana-4886	76	23	methods	method	NOUN
cana-4886	76	24	.	.	PUNCT
cana-4886	77	1	the	the	DET
cana-4886	77	2	solver	solver	VERB
cana-4886	77	3	addresses	address	NOUN
cana-4886	77	4	cfd	cfd	NOUN
cana-4886	77	5	applications	application	NOUN
cana-4886	77	6	specifically	specifically	ADV
cana-4886	77	7	due	due	ADJ
cana-4886	77	8	to	to	ADP
cana-4886	77	9	aerospace	aerospace	NOUN
cana-4886	77	10	and	and	CCONJ
cana-4886	77	11	astrophysical	astrophysical	ADJ
cana-4886	77	12	simulation	simulation	NOUN
cana-4886	77	13	requirements	requirement	NOUN
cana-4886	77	14	which	which	PRON
cana-4886	77	15	demand	demand	VERB
cana-4886	77	16	highly	highly	ADV
cana-4886	77	17	precise	precise	ADJ
cana-4886	77	18	shock	shock	NOUN
cana-4886	77	19	structure	structure	NOUN
cana-4886	77	20	detection	detection	NOUN
cana-4886	77	21	.	.	PUNCT
cana-4886	78	1	communications	communication	NOUN
cana-4886	78	2	on	on	ADP
cana-4886	78	3	applied	apply	VERB
cana-4886	78	4	nonlinear	nonlinear	ADJ
cana-4886	78	5	analysis	analysis	NOUN
cana-4886	78	6	issn	issn	NOUN
cana-4886	78	7	:	:	PUNCT
cana-4886	78	8	1074	1074	NUM
cana-4886	78	9	-	-	PUNCT
cana-4886	78	10	133x	133x	NUM
cana-4886	78	11	vol	vol	VERB
cana-4886	78	12	32	32	NUM
cana-4886	78	13	no	no	NOUN
cana-4886	78	14	.	.	PUNCT
cana-4886	79	1	10s	10	NOUN
cana-4886	79	2	(	(	PUNCT
cana-4886	79	3	2025	2025	NUM
cana-4886	79	4	)	)	PUNCT
cana-4886	79	5	883	883	NUM
cana-4886	79	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4886	79	7	different	different	ADJ
cana-4886	79	8	higher	high	ADJ
cana-4886	79	9	-	-	PUNCT
cana-4886	79	10	order	order	NOUN
cana-4886	79	11	calculation	calculation	NOUN
cana-4886	79	12	methods	method	NOUN
cana-4886	79	13	emerged	emerge	VERB
cana-4886	79	14	at	at	ADP
cana-4886	79	15	the	the	DET
cana-4886	79	16	same	same	ADJ
cana-4886	79	17	time	time	NOUN
cana-4886	79	18	to	to	PART
cana-4886	79	19	reduce	reduce	VERB
cana-4886	79	20	numerical	numerical	ADJ
cana-4886	79	21	losses	loss	NOUN
cana-4886	79	22	while	while	SCONJ
cana-4886	79	23	improving	improve	VERB
cana-4886	79	24	discontinuity	discontinuity	NOUN
cana-4886	79	25	resolution	resolution	NOUN
cana-4886	79	26	capabilities	capability	NOUN
cana-4886	79	27	.	.	PUNCT
cana-4886	80	1	weno	weno	PROPN
cana-4886	80	2	schemes	scheme	NOUN
cana-4886	80	3	together	together	ADV
cana-4886	80	4	with	with	ADP
cana-4886	80	5	dg	dg	PROPN
cana-4886	80	6	methods	method	NOUN
cana-4886	80	7	represent	represent	VERB
cana-4886	80	8	the	the	DET
cana-4886	80	9	current	current	ADJ
cana-4886	80	10	best	good	ADJ
cana-4886	80	11	practices	practice	NOUN
cana-4886	80	12	for	for	ADP
cana-4886	80	13	accurate	accurate	ADJ
cana-4886	80	14	solutions	solution	NOUN
cana-4886	80	15	of	of	ADP
cana-4886	80	16	hyperbolic	hyperbolic	ADJ
cana-4886	80	17	conservation	conservation	NOUN
cana-4886	80	18	laws	law	NOUN
cana-4886	80	19	since	since	SCONJ
cana-4886	80	20	their	their	PRON
cana-4886	80	21	performance	performance	NOUN
cana-4886	80	22	quality	quality	NOUN
cana-4886	80	23	outstrips	outstrip	VERB
cana-4886	80	24	other	other	ADJ
cana-4886	80	25	alternatives	alternative	NOUN
cana-4886	80	26	.	.	PUNCT
cana-4886	81	1	modern	modern	ADJ
cana-4886	81	2	reconstruction	reconstruction	NOUN
cana-4886	81	3	techniques	technique	NOUN
cana-4886	81	4	assist	assist	VERB
cana-4886	81	5	these	these	DET
cana-4886	81	6	methods	method	NOUN
cana-4886	81	7	to	to	PART
cana-4886	81	8	keep	keep	VERB
cana-4886	81	9	accuracy	accuracy	NOUN
cana-4886	81	10	by	by	ADP
cana-4886	81	11	minimizing	minimize	VERB
cana-4886	81	12	numerical	numerical	ADJ
cana-4886	81	13	artifacts	artifact	NOUN
cana-4886	81	14	.	.	PUNCT
cana-4886	82	1	extended	extend	VERB
cana-4886	82	2	simulations	simulation	NOUN
cana-4886	82	3	face	face	VERB
cana-4886	82	4	practical	practical	ADJ
cana-4886	82	5	issues	issue	NOUN
cana-4886	82	6	regarding	regard	VERB
cana-4886	82	7	computational	computational	ADJ
cana-4886	82	8	complexity	complexity	NOUN
cana-4886	82	9	because	because	SCONJ
cana-4886	82	10	of	of	ADP
cana-4886	82	11	these	these	DET
cana-4886	82	12	applied	apply	VERB
cana-4886	82	13	methods	method	NOUN
cana-4886	82	14	.	.	PUNCT
cana-4886	83	1	iii	iii	X
cana-4886	83	2	.	.	PROPN
cana-4886	83	3	proposed	propose	VERB
cana-4886	83	4	methodology	methodology	NOUN
cana-4886	83	5	the	the	DET
cana-4886	83	6	methodology	methodology	NOUN
cana-4886	83	7	for	for	ADP
cana-4886	83	8	solving	solve	VERB
cana-4886	83	9	the	the	DET
cana-4886	83	10	riemann	riemann	PROPN
cana-4886	83	11	problem	problem	NOUN
cana-4886	83	12	in	in	ADP
cana-4886	83	13	fluid	fluid	ADJ
cana-4886	83	14	dynamics	dynamic	NOUN
cana-4886	83	15	involves	involve	VERB
cana-4886	83	16	two	two	NUM
cana-4886	83	17	primary	primary	ADJ
cana-4886	83	18	approaches	approach	NOUN
cana-4886	83	19	:	:	PUNCT
cana-4886	83	20	an	an	DET
cana-4886	83	21	analytical	analytical	ADJ
cana-4886	83	22	approach	approach	NOUN
cana-4886	83	23	based	base	VERB
cana-4886	83	24	on	on	ADP
cana-4886	83	25	exact	exact	ADJ
cana-4886	83	26	solutions	solution	NOUN
cana-4886	83	27	using	use	VERB
cana-4886	83	28	the	the	DET
cana-4886	83	29	method	method	NOUN
cana-4886	83	30	of	of	ADP
cana-4886	83	31	characteristics	characteristic	NOUN
cana-4886	83	32	and	and	CCONJ
cana-4886	83	33	a	a	DET
cana-4886	83	34	numerical	numerical	ADJ
cana-4886	83	35	approach	approach	NOUN
cana-4886	83	36	employing	employ	VERB
cana-4886	83	37	finite	finite	ADJ
cana-4886	83	38	volume	volume	NOUN
cana-4886	83	39	methods	method	NOUN
cana-4886	83	40	and	and	CCONJ
cana-4886	83	41	approximate	approximate	ADJ
cana-4886	83	42	riemann	riemann	PROPN
cana-4886	83	43	solvers	solver	NOUN
cana-4886	83	44	.	.	PUNCT
cana-4886	84	1	this	this	DET
cana-4886	84	2	section	section	NOUN
cana-4886	84	3	details	detail	VERB
cana-4886	84	4	the	the	DET
cana-4886	84	5	governing	govern	VERB
cana-4886	84	6	equations	equation	NOUN
cana-4886	84	7	,	,	PUNCT
cana-4886	84	8	solution	solution	NOUN
cana-4886	84	9	techniques	technique	NOUN
cana-4886	84	10	,	,	PUNCT
cana-4886	84	11	numerical	numerical	ADJ
cana-4886	84	12	discretization	discretization	NOUN
cana-4886	84	13	,	,	PUNCT
cana-4886	84	14	and	and	CCONJ
cana-4886	84	15	computational	computational	ADJ
cana-4886	84	16	implementation	implementation	NOUN
cana-4886	84	17	[	[	X
cana-4886	84	18	7	7	NUM
cana-4886	84	19	]	]	PUNCT
cana-4886	84	20	.	.	PUNCT
cana-4886	85	1	a.	a.	NOUN
cana-4886	85	2	governing	govern	VERB
cana-4886	85	3	equations	equation	NOUN
cana-4886	85	4	of	of	ADP
cana-4886	85	5	fluid	fluid	ADJ
cana-4886	85	6	dynamics	dynamic	NOUN
cana-4886	85	7	an	an	DET
cana-4886	85	8	inviscid	inviscid	ADJ
cana-4886	85	9	compressible	compressible	ADJ
cana-4886	85	10	flow	flow	NOUN
cana-4886	85	11	consisting	consist	VERB
cana-4886	85	12	of	of	ADP
cana-4886	85	13	the	the	DET
cana-4886	85	14	conservation	conservation	NOUN
cana-4886	85	15	laws	law	NOUN
cana-4886	85	16	requires	require	VERB
cana-4886	85	17	the	the	DET
cana-4886	85	18	euler	euler	PROPN
cana-4886	85	19	equations	equation	NOUN
cana-4886	85	20	to	to	PART
cana-4886	85	21	govern	govern	VERB
cana-4886	85	22	the	the	DET
cana-4886	85	23	riemann	riemann	PROPN
cana-4886	85	24	problem	problem	NOUN
cana-4886	85	25	.	.	PUNCT
cana-4886	86	1	the	the	DET
cana-4886	86	2	one	one	NUM
cana-4886	86	3	-	-	PUNCT
cana-4886	86	4	dimensional	dimensional	ADJ
cana-4886	86	5	euler	euler	NOUN
cana-4886	86	6	equations	equation	NOUN
cana-4886	86	7	in	in	ADP
cana-4886	86	8	conservative	conservative	ADJ
cana-4886	86	9	form	form	NOUN
cana-4886	86	10	present	present	VERB
cana-4886	86	11	the	the	DET
cana-4886	86	12	mathematical	mathematical	ADJ
cana-4886	86	13	system	system	NOUN
cana-4886	86	14	below	below	ADV
cana-4886	86	15	:	:	PUNCT
cana-4886	87	1	𝜕𝐔	𝜕𝐔	PROPN
cana-4886	87	2	𝜕𝑡	𝜕𝑡	NOUN
cana-4886	87	3	+	+	CCONJ
cana-4886	87	4	𝜕𝐅(u	𝜕𝐅(u	ADJ
cana-4886	87	5	)	)	PUNCT
cana-4886	87	6	𝜕𝑥	𝜕𝑥	NOUN
cana-4886	88	1	=	=	SYM
cana-4886	88	2	0	0	NUM
cana-4886	88	3	where	where	SCONJ
cana-4886	88	4	𝐔	𝐔	NOUN
cana-4886	88	5	=	=	NOUN
cana-4886	88	6	[	[	PUNCT
cana-4886	88	7	𝜌	𝜌	X
cana-4886	88	8	𝜌𝑢	𝜌𝑢	NOUN
cana-4886	88	9	𝐸	𝐸	PROPN
cana-4886	88	10	]	]	PUNCT
cana-4886	88	11	,	,	PUNCT
cana-4886	88	12	𝐅(𝐔	𝐅(𝐔	NUM
cana-4886	88	13	)	)	PUNCT
cana-4886	88	14	=	=	NOUN
cana-4886	89	1	[	[	PUNCT
cana-4886	89	2	𝜌𝑢	𝜌𝑢	NOUN
cana-4886	89	3	𝜌𝑢2	𝜌𝑢2	NOUN
cana-4886	89	4	+	+	SYM
cana-4886	89	5	𝑝	𝑝	PROPN
cana-4886	89	6	(	(	PUNCT
cana-4886	89	7	𝐸	𝐸	PROPN
cana-4886	89	8	+	+	NUM
cana-4886	89	9	𝑝)𝑢	𝑝)𝑢	NOUN
cana-4886	89	10	]	]	PUNCT
cana-4886	89	11	here	here	ADV
cana-4886	89	12	,	,	PUNCT
cana-4886	89	13	𝜌	𝜌	X
cana-4886	89	14	is	be	AUX
cana-4886	89	15	the	the	DET
cana-4886	89	16	fluid	fluid	ADJ
cana-4886	89	17	density	density	NOUN
cana-4886	89	18	,	,	PUNCT
cana-4886	89	19	𝑢	𝑢	PROPN
cana-4886	89	20	is	be	AUX
cana-4886	89	21	the	the	DET
cana-4886	89	22	velocity	velocity	NOUN
cana-4886	89	23	,	,	PUNCT
cana-4886	89	24	𝑝	𝑝	PROPN
cana-4886	89	25	is	be	AUX
cana-4886	89	26	the	the	DET
cana-4886	89	27	pressure	pressure	NOUN
cana-4886	89	28	,	,	PUNCT
cana-4886	89	29	and	and	CCONJ
cana-4886	89	30	𝐸	𝐸	PROPN
cana-4886	89	31	is	be	AUX
cana-4886	89	32	the	the	DET
cana-4886	89	33	total	total	ADJ
cana-4886	89	34	energy	energy	NOUN
cana-4886	89	35	per	per	ADP
cana-4886	89	36	unit	unit	NOUN
cana-4886	89	37	volume	volume	NOUN
cana-4886	89	38	,	,	PUNCT
cana-4886	89	39	defined	define	VERB
cana-4886	89	40	as	as	ADP
cana-4886	89	41	:	:	PUNCT
cana-4886	89	42	𝐸	𝐸	PROPN
cana-4886	89	43	=	=	SYM
cana-4886	89	44	𝑝	𝑝	PROPN
cana-4886	90	1	𝛾	𝛾	ADP
cana-4886	90	2	−	−	NUM
cana-4886	90	3	1	1	NUM
cana-4886	90	4	+	+	CCONJ
cana-4886	90	5	1	1	NUM
cana-4886	90	6	2	2	NUM
cana-4886	90	7	𝜌𝑢2	𝜌𝑢2	NOUN
cana-4886	90	8	where	where	SCONJ
cana-4886	90	9	𝛾	𝛾	NOUN
cana-4886	90	10	is	be	AUX
cana-4886	90	11	the	the	DET
cana-4886	90	12	heat	heat	NOUN
cana-4886	90	13	capacity	capacity	NOUN
cana-4886	90	14	ratio	ratio	NOUN
cana-4886	90	15	(	(	PUNCT
cana-4886	90	16	typically	typically	ADV
cana-4886	90	17	𝛾	𝛾	ADP
cana-4886	90	18	=	=	SYM
cana-4886	90	19	1.4	1.4	NUM
cana-4886	90	20	for	for	ADP
cana-4886	90	21	air	air	NOUN
cana-4886	90	22	)	)	PUNCT
cana-4886	90	23	.	.	PUNCT
cana-4886	91	1	b.	b.	PROPN
cana-4886	91	2	analytical	analytical	ADJ
cana-4886	91	3	approach	approach	NOUN
cana-4886	91	4	:	:	PUNCT
cana-4886	91	5	exact	exact	PROPN
cana-4886	91	6	riemann	riemann	PROPN
cana-4886	91	7	solver	solver	VERB
cana-4886	91	8	the	the	DET
cana-4886	91	9	exact	exact	ADJ
cana-4886	91	10	solution	solution	NOUN
cana-4886	91	11	of	of	ADP
cana-4886	91	12	the	the	DET
cana-4886	91	13	riemann	riemann	PROPN
cana-4886	91	14	problem	problem	NOUN
cana-4886	91	15	involves	involve	VERB
cana-4886	91	16	solving	solve	VERB
cana-4886	91	17	the	the	DET
cana-4886	91	18	non	non	ADJ
cana-4886	91	19	-	-	ADJ
cana-4886	91	20	linear	linear	ADJ
cana-4886	91	21	system	system	NOUN
cana-4886	91	22	formed	form	VERB
cana-4886	91	23	by	by	ADP
cana-4886	91	24	the	the	DET
cana-4886	91	25	rankine	rankine	PROPN
cana-4886	91	26	-	-	PUNCT
cana-4886	91	27	hugoniot	hugoniot	NOUN
cana-4886	91	28	jump	jump	NOUN
cana-4886	91	29	conditions	condition	NOUN
cana-4886	91	30	and	and	CCONJ
cana-4886	91	31	the	the	DET
cana-4886	91	32	rarefaction	rarefaction	NOUN
cana-4886	91	33	wave	wave	NOUN
cana-4886	91	34	solution	solution	NOUN
cana-4886	91	35	.	.	PUNCT
cana-4886	92	1	the	the	DET
cana-4886	92	2	wave	wave	NOUN
cana-4886	92	3	structures	structure	NOUN
cana-4886	92	4	are	be	AUX
cana-4886	92	5	determined	determine	VERB
cana-4886	92	6	by	by	ADP
cana-4886	92	7	:	:	PUNCT
cana-4886	92	8	•	•	NOUN
cana-4886	92	9	shock	shock	NOUN
cana-4886	92	10	waves	wave	NOUN
cana-4886	92	11	:	:	PUNCT
cana-4886	92	12	satisfy	satisfy	VERB
cana-4886	92	13	the	the	DET
cana-4886	92	14	rankine	rankine	PROPN
cana-4886	92	15	-	-	PUNCT
cana-4886	92	16	hugoniot	hugoniot	NOUN
cana-4886	92	17	conditions	condition	NOUN
cana-4886	92	18	:	:	PUNCT
cana-4886	92	19	𝑠	𝑠	X
cana-4886	92	20	=	=	PUNCT
cana-4886	92	21	𝜌𝑅𝑢𝑅	𝜌𝑅𝑢𝑅	NOUN
cana-4886	92	22	−	−	NOUN
cana-4886	92	23	𝜌𝐿𝑢𝐿	𝜌𝐿𝑢𝐿	NOUN
cana-4886	92	24	𝜌𝑅	𝜌𝑅	ADJ
cana-4886	92	25	−	−	VERB
cana-4886	92	26	𝜌𝐿	𝜌𝐿	NOUN
cana-4886	92	27	where	where	SCONJ
cana-4886	92	28	𝑠	𝑠	PROPN
cana-4886	92	29	is	be	AUX
cana-4886	92	30	the	the	DET
cana-4886	92	31	shock	shock	NOUN
cana-4886	92	32	speed	speed	NOUN
cana-4886	92	33	,	,	PUNCT
cana-4886	92	34	and	and	CCONJ
cana-4886	92	35	subscripts	subscript	VERB
cana-4886	92	36	𝐿	𝐿	PROPN
cana-4886	92	37	and	and	CCONJ
cana-4886	92	38	𝑅	𝑅	PROPN
cana-4886	92	39	denote	denote	NOUN
cana-4886	92	40	left	leave	VERB
cana-4886	92	41	and	and	CCONJ
cana-4886	92	42	right	right	ADJ
cana-4886	92	43	states	state	NOUN
cana-4886	92	44	.	.	PUNCT
cana-4886	93	1	•	•	NUM
cana-4886	93	2	rarefaction	rarefaction	NOUN
cana-4886	93	3	waves	wave	NOUN
cana-4886	93	4	:	:	PUNCT
cana-4886	93	5	satisfy	satisfy	VERB
cana-4886	93	6	the	the	DET
cana-4886	93	7	self	self	NOUN
cana-4886	93	8	-	-	PUNCT
cana-4886	93	9	similar	similar	ADJ
cana-4886	93	10	solution	solution	NOUN
cana-4886	93	11	using	use	VERB
cana-4886	93	12	the	the	DET
cana-4886	93	13	method	method	NOUN
cana-4886	93	14	of	of	ADP
cana-4886	93	15	characteristics	characteristic	NOUN
cana-4886	93	16	:	:	PUNCT
cana-4886	93	17	communications	communication	NOUN
cana-4886	93	18	on	on	ADP
cana-4886	93	19	applied	apply	VERB
cana-4886	93	20	nonlinear	nonlinear	ADJ
cana-4886	93	21	analysis	analysis	NOUN
cana-4886	93	22	issn	issn	NOUN
cana-4886	93	23	:	:	PUNCT
cana-4886	93	24	1074	1074	NUM
cana-4886	93	25	-	-	PUNCT
cana-4886	93	26	133x	133x	NUM
cana-4886	93	27	vol	vol	VERB
cana-4886	93	28	32	32	NUM
cana-4886	93	29	no	no	NOUN
cana-4886	93	30	.	.	PUNCT
cana-4886	94	1	10s	10	NOUN
cana-4886	94	2	(	(	PUNCT
cana-4886	94	3	2025	2025	NUM
cana-4886	94	4	)	)	PUNCT
cana-4886	94	5	884	884	NUM
cana-4886	94	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4886	94	7	𝑑𝑥	𝑑𝑥	VERB
cana-4886	94	8	𝑑𝑡	𝑑𝑡	ADP
cana-4886	94	9	=	=	PUNCT
cana-4886	94	10	𝑢	𝑢	PRON
cana-4886	94	11	±	±	NUM
cana-4886	94	12	𝑎	𝑎	NOUN
cana-4886	94	13	𝛾	𝛾	NOUN
cana-4886	94	14	where	where	SCONJ
cana-4886	94	15	𝑎	𝑎	NOUN
cana-4886	94	16	=	=	NOUN
cana-4886	94	17	√𝛾𝑝/𝜌	√𝛾𝑝/𝜌	NOUN
cana-4886	94	18	is	be	AUX
cana-4886	94	19	the	the	DET
cana-4886	94	20	speed	speed	NOUN
cana-4886	94	21	of	of	ADP
cana-4886	94	22	sound	sound	NOUN
cana-4886	94	23	.	.	PUNCT
cana-4886	95	1	the	the	DET
cana-4886	95	2	solution	solution	NOUN
cana-4886	95	3	is	be	AUX
cana-4886	95	4	computed	compute	VERB
cana-4886	95	5	iteratively	iteratively	ADV
cana-4886	95	6	using	use	VERB
cana-4886	95	7	newton	newton	PROPN
cana-4886	95	8	-	-	PUNCT
cana-4886	95	9	raphson	raphson	NOUN
cana-4886	95	10	methods	method	NOUN
cana-4886	95	11	to	to	PART
cana-4886	95	12	determine	determine	VERB
cana-4886	95	13	intermediate	intermediate	ADJ
cana-4886	95	14	states	state	NOUN
cana-4886	95	15	.	.	PUNCT
cana-4886	96	1	c.	c.	PROPN
cana-4886	96	2	numerical	numerical	PROPN
cana-4886	96	3	approach	approach	PROPN
cana-4886	96	4	:	:	PUNCT
cana-4886	96	5	finite	finite	PROPN
cana-4886	96	6	volume	volume	NOUN
cana-4886	96	7	discretization	discretization	NOUN
cana-4886	96	8	for	for	ADP
cana-4886	96	9	practical	practical	ADJ
cana-4886	96	10	fluid	fluid	ADJ
cana-4886	96	11	dynamics	dynamic	NOUN
cana-4886	96	12	problems	problem	NOUN
cana-4886	96	13	,	,	PUNCT
cana-4886	96	14	numerical	numerical	ADJ
cana-4886	96	15	methods	method	NOUN
cana-4886	96	16	are	be	AUX
cana-4886	96	17	employed	employ	VERB
cana-4886	96	18	.	.	PUNCT
cana-4886	97	1	the	the	DET
cana-4886	97	2	finite	finite	PROPN
cana-4886	97	3	volume	volume	NOUN
cana-4886	97	4	method	method	NOUN
cana-4886	97	5	(	(	PUNCT
cana-4886	97	6	fvm	fvm	ADV
cana-4886	97	7	)	)	PUNCT
cana-4886	97	8	is	be	AUX
cana-4886	97	9	used	use	VERB
cana-4886	97	10	to	to	PART
cana-4886	97	11	discretize	discretize	VERB
cana-4886	97	12	the	the	DET
cana-4886	97	13	euler	euler	PROPN
cana-4886	97	14	equations	equation	NOUN
cana-4886	97	15	over	over	ADP
cana-4886	97	16	control	control	NOUN
cana-4886	97	17	volumes	volume	NOUN
cana-4886	97	18	.	.	PUNCT
cana-4886	98	1	applying	apply	VERB
cana-4886	98	2	fvm	fvm	ADJ
cana-4886	98	3	to	to	ADP
cana-4886	98	4	the	the	DET
cana-4886	98	5	governing	govern	VERB
cana-4886	98	6	equation	equation	NOUN
cana-4886	98	7	,	,	PUNCT
cana-4886	98	8	we	we	PRON
cana-4886	98	9	obtain	obtain	VERB
cana-4886	98	10	:	:	PUNCT
cana-4886	98	11	𝜕	𝜕	PROPN
cana-4886	98	12	𝜕𝑡	𝜕𝑡	NOUN
cana-4886	98	13	∫	∫	PROPN
cana-4886	98	14	  	  	SPACE
cana-4886	99	1	𝑉𝑖	𝑉𝑖	PROPN
cana-4886	99	2	𝐔𝑑𝑉	𝐔𝑑𝑉	NOUN
cana-4886	100	1	+	+	NOUN
cana-4886	100	2	∫	∫	PROPN
cana-4886	100	3	  	  	SPACE
cana-4886	100	4	𝜕𝑉	𝜕𝑉	PROPN
cana-4886	100	5	𝐅(𝐔	𝐅(𝐔	NOUN
cana-4886	100	6	)	)	PUNCT
cana-4886	100	7	⋅	⋅	ADJ
cana-4886	100	8	𝐧𝑑𝐴	𝐧𝑑𝐴	NOUN
cana-4886	100	9	=	=	SYM
cana-4886	100	10	0	0	NUM
cana-4886	100	11	using	use	VERB
cana-4886	100	12	numerical	numerical	ADJ
cana-4886	100	13	integration	integration	NOUN
cana-4886	100	14	over	over	ADP
cana-4886	100	15	each	each	DET
cana-4886	100	16	control	control	NOUN
cana-4886	100	17	volume	volume	NOUN
cana-4886	100	18	,	,	PUNCT
cana-4886	100	19	the	the	DET
cana-4886	100	20	semi	semi	ADJ
cana-4886	100	21	-	-	ADJ
cana-4886	100	22	discrete	discrete	ADJ
cana-4886	100	23	form	form	NOUN
cana-4886	100	24	is	be	AUX
cana-4886	100	25	written	write	VERB
cana-4886	100	26	as	as	ADP
cana-4886	100	27	:	:	PUNCT
cana-4886	100	28	𝑑𝐔𝑖	𝑑𝐔𝑖	NOUN
cana-4886	100	29	𝑑𝑡	𝑑𝑡	ADP
cana-4886	100	30	=	=	SYM
cana-4886	100	31	−	−	PROPN
cana-4886	100	32	1	1	NUM
cana-4886	100	33	δ𝑥	δ𝑥	CCONJ
cana-4886	100	34	(	(	PUNCT
cana-4886	100	35	𝐅𝑖+1/2	𝐅𝑖+1/2	PROPN
cana-4886	100	36	−	−	PROPN
cana-4886	100	37	𝐅𝑖−1/2	𝐅𝑖−1/2	PROPN
cana-4886	100	38	)	)	PUNCT
cana-4886	100	39	where	where	SCONJ
cana-4886	100	40	𝐅𝑖+1/2	𝐅𝑖+1/2	NOUN
cana-4886	100	41	represents	represent	VERB
cana-4886	100	42	the	the	DET
cana-4886	100	43	numerical	numerical	ADJ
cana-4886	100	44	flux	flux	PROPN
cana-4886	100	45	computed	compute	VERB
cana-4886	100	46	using	use	VERB
cana-4886	100	47	riemann	riemann	PROPN
cana-4886	100	48	solvers	solver	NOUN
cana-4886	100	49	.	.	PUNCT
cana-4886	101	1	d.	d.	PROPN
cana-4886	101	2	approximate	approximate	PROPN
cana-4886	101	3	riemann	riemann	PROPN
cana-4886	101	4	solvers	solver	NOUN
cana-4886	101	5	to	to	PART
cana-4886	101	6	efficiently	efficiently	ADV
cana-4886	101	7	compute	compute	VERB
cana-4886	101	8	the	the	DET
cana-4886	101	9	fluxes	flux	NOUN
cana-4886	101	10	,	,	PUNCT
cana-4886	101	11	approximate	approximate	ADJ
cana-4886	101	12	solvers	solver	NOUN
cana-4886	101	13	such	such	ADJ
cana-4886	101	14	as	as	ADP
cana-4886	101	15	roe	roe	PROPN
cana-4886	101	16	's	's	PART
cana-4886	101	17	solver	solver	NOUN
cana-4886	101	18	and	and	CCONJ
cana-4886	101	19	the	the	DET
cana-4886	101	20	hllc	hllc	ADJ
cana-4886	101	21	solver	solver	NOUN
cana-4886	101	22	are	be	AUX
cana-4886	101	23	used	use	VERB
cana-4886	101	24	.	.	PUNCT
cana-4886	102	1	•	•	NUM
cana-4886	102	2	roe	roe	PROPN
cana-4886	102	3	's	's	PART
cana-4886	102	4	solver	solver	PRON
cana-4886	102	5	:	:	PUNCT
cana-4886	102	6	linearizes	linearize	VERB
cana-4886	102	7	the	the	DET
cana-4886	102	8	euler	euler	PROPN
cana-4886	102	9	equations	equation	NOUN
cana-4886	102	10	by	by	ADP
cana-4886	102	11	approximating	approximate	VERB
cana-4886	102	12	the	the	DET
cana-4886	102	13	jacobian	jacobian	ADJ
cana-4886	102	14	matrix	matrix	NOUN
cana-4886	102	15	:	:	PUNCT
cana-4886	102	16	𝐀	𝐀	PROPN
cana-4886	102	17	=	=	SYM
cana-4886	102	18	𝜕𝐅	𝜕𝐅	PROPN
cana-4886	102	19	𝜕𝐔	𝜕𝐔	NUM
cana-4886	102	20	the	the	DET
cana-4886	102	21	eigenvalues	eigenvalue	NOUN
cana-4886	102	22	of	of	ADP
cana-4886	102	23	𝐀	𝐀	PROPN
cana-4886	102	24	determine	determine	VERB
cana-4886	102	25	wave	wave	NOUN
cana-4886	102	26	speeds	speed	NOUN
cana-4886	102	27	,	,	PUNCT
cana-4886	102	28	and	and	CCONJ
cana-4886	102	29	the	the	DET
cana-4886	102	30	flux	flux	NOUN
cana-4886	102	31	is	be	AUX
cana-4886	102	32	computed	compute	VERB
cana-4886	102	33	as	as	ADP
cana-4886	102	34	:	:	PUNCT
cana-4886	102	35	𝐅𝑖+1/2	𝐅𝑖+1/2	NOUN
cana-4886	102	36	=	=	NOUN
cana-4886	102	37	1	1	NUM
cana-4886	102	38	2	2	NUM
cana-4886	102	39	[	[	X
cana-4886	102	40	𝐅(𝐔𝐋	𝐅(𝐔𝐋	NOUN
cana-4886	102	41	)	)	PUNCT
cana-4886	102	42	+	+	X
cana-4886	103	1	𝐅(𝐔𝐑	𝐅(𝐔𝐑	NOUN
cana-4886	103	2	)	)	PUNCT
cana-4886	103	3	]	]	PUNCT
cana-4886	104	1	−	−	PROPN
cana-4886	104	2	1	1	NUM
cana-4886	104	3	2	2	NUM
cana-4886	104	4	∑	∑	NOUN
cana-4886	104	5	  	  	SPACE
cana-4886	104	6	𝑘	𝑘	PRON
cana-4886	104	7	|𝜆𝑘|𝐫𝐤δ𝐔	|𝜆𝑘|𝐫𝐤δ𝐔	X
cana-4886	104	8	•	•	NOUN
cana-4886	104	9	hllc	hllc	ADV
cana-4886	104	10	solver	solver	ADV
cana-4886	104	11	:	:	PUNCT
cana-4886	104	12	improves	improve	VERB
cana-4886	104	13	upon	upon	SCONJ
cana-4886	104	14	the	the	DET
cana-4886	104	15	hll	hll	NOUN
cana-4886	104	16	method	method	NOUN
cana-4886	104	17	by	by	ADP
cana-4886	104	18	resolving	resolve	VERB
cana-4886	104	19	contact	contact	NOUN
cana-4886	104	20	waves	wave	NOUN
cana-4886	104	21	.	.	PUNCT
cana-4886	105	1	it	it	PRON
cana-4886	105	2	computes	compute	VERB
cana-4886	105	3	fluxes	flux	NOUN
cana-4886	105	4	as	as	ADP
cana-4886	105	5	:	:	PUNCT
cana-4886	105	6	𝐅𝐻𝐿𝐿𝐶	𝐅𝐻𝐿𝐿𝐶	PROPN
cana-4886	105	7	=	=	PUNCT
cana-4886	105	8	{	{	PUNCT
cana-4886	105	9	𝐅𝐿	𝐅𝐿	PROPN
cana-4886	105	10	,	,	PUNCT
cana-4886	105	11	if	if	SCONJ
cana-4886	105	12	𝑠𝐿	𝑠𝐿	PROPN
cana-4886	105	13	>	>	X
cana-4886	105	14	0	0	NUM
cana-4886	105	15	𝐅∗	𝐅∗	NUM
cana-4886	105	16	,	,	PUNCT
cana-4886	105	17	if	if	SCONJ
cana-4886	105	18	𝑠𝐿	𝑠𝐿	PROPN
cana-4886	105	19	≤	≤	NOUN
cana-4886	105	20	0	0	NUM
cana-4886	105	21	≤	≤	NOUN
cana-4886	105	22	𝑠𝑅	𝑠𝑅	X
cana-4886	105	23	𝐅𝑅	𝐅𝑅	PROPN
cana-4886	105	24	,	,	PUNCT
cana-4886	105	25	if	if	SCONJ
cana-4886	105	26	𝑠𝑅	𝑠𝑅	PROPN
cana-4886	105	27	<	<	X
cana-4886	105	28	0	0	PUNCT
cana-4886	105	29	where	where	SCONJ
cana-4886	105	30	𝑠𝐿	𝑠𝐿	PROPN
cana-4886	105	31	and	and	CCONJ
cana-4886	105	32	𝑠𝑅	𝑠𝑅	NOUN
cana-4886	105	33	are	be	AUX
cana-4886	105	34	the	the	DET
cana-4886	105	35	wave	wave	NOUN
cana-4886	105	36	speeds	speed	NOUN
cana-4886	105	37	.	.	PUNCT
cana-4886	106	1	e.	e.	PROPN
cana-4886	106	2	computational	computational	ADJ
cana-4886	106	3	implementation	implementation	NOUN
cana-4886	106	4	the	the	DET
cana-4886	106	5	numerical	numerical	ADJ
cana-4886	106	6	scheme	scheme	NOUN
cana-4886	106	7	follows	follow	VERB
cana-4886	106	8	these	these	DET
cana-4886	106	9	steps	step	NOUN
cana-4886	106	10	:	:	PUNCT
cana-4886	106	11	1	1	X
cana-4886	106	12	.	.	X
cana-4886	106	13	initialization	initialization	NOUN
cana-4886	106	14	:	:	PUNCT
cana-4886	106	15	define	define	VERB
cana-4886	106	16	initial	initial	ADJ
cana-4886	106	17	left	leave	VERB
cana-4886	106	18	and	and	CCONJ
cana-4886	106	19	right	right	ADJ
cana-4886	106	20	states	state	NOUN
cana-4886	106	21	(	(	PUNCT
cana-4886	106	22	𝜌𝐿	𝜌𝐿	PROPN
cana-4886	106	23	,	,	PUNCT
cana-4886	106	24	𝑢𝐿	𝑢𝐿	PROPN
cana-4886	106	25	,	,	PUNCT
cana-4886	106	26	𝑝𝐿	𝑝𝐿	NOUN
cana-4886	106	27	)	)	PUNCT
cana-4886	106	28	and	and	CCONJ
cana-4886	106	29	(	(	PUNCT
cana-4886	106	30	𝜌𝑅	𝜌𝑅	ADJ
cana-4886	106	31	,	,	PUNCT
cana-4886	106	32	𝑢𝑅	𝑢𝑅	PROPN
cana-4886	106	33	,	,	PUNCT
cana-4886	106	34	𝑝𝑅	𝑝𝑅	NUM
cana-4886	106	35	)	)	PUNCT
cana-4886	106	36	.	.	PUNCT
cana-4886	107	1	2	2	X
cana-4886	107	2	.	.	X
cana-4886	107	3	flux	flux	PROPN
cana-4886	107	4	computation	computation	PROPN
cana-4886	107	5	:	:	PUNCT
cana-4886	107	6	compute	compute	PROPN
cana-4886	107	7	numerical	numerical	ADJ
cana-4886	107	8	fluxes	flux	NOUN
cana-4886	107	9	using	use	VERB
cana-4886	107	10	roe	roe	NOUN
cana-4886	107	11	or	or	CCONJ
cana-4886	107	12	hllc	hllc	ADJ
cana-4886	107	13	solvers	solver	NOUN
cana-4886	107	14	.	.	PUNCT
cana-4886	108	1	communications	communication	NOUN
cana-4886	108	2	on	on	ADP
cana-4886	108	3	applied	apply	VERB
cana-4886	108	4	nonlinear	nonlinear	ADJ
cana-4886	108	5	analysis	analysis	NOUN
cana-4886	108	6	issn	issn	NOUN
cana-4886	108	7	:	:	PUNCT
cana-4886	108	8	1074	1074	NUM
cana-4886	108	9	-	-	PUNCT
cana-4886	108	10	133x	133x	NUM
cana-4886	108	11	vol	vol	VERB
cana-4886	108	12	32	32	NUM
cana-4886	108	13	no	no	NOUN
cana-4886	108	14	.	.	PUNCT
cana-4886	109	1	10s	10	NOUN
cana-4886	109	2	(	(	PUNCT
cana-4886	109	3	2025	2025	NUM
cana-4886	109	4	)	)	PUNCT
cana-4886	109	5	885	885	NUM
cana-4886	109	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4886	109	7	3	3	NUM
cana-4886	109	8	.	.	NOUN
cana-4886	109	9	time	time	NOUN
cana-4886	109	10	integration	integration	NOUN
cana-4886	109	11	:	:	PUNCT
cana-4886	109	12	advance	advance	VERB
cana-4886	109	13	the	the	DET
cana-4886	109	14	solution	solution	NOUN
cana-4886	109	15	using	use	VERB
cana-4886	109	16	explicit	explicit	ADJ
cana-4886	109	17	time	time	NOUN
cana-4886	109	18	-	-	PUNCT
cana-4886	109	19	stepping	step	VERB
cana-4886	109	20	methods	method	NOUN
cana-4886	109	21	such	such	ADJ
cana-4886	109	22	as	as	ADP
cana-4886	109	23	the	the	DET
cana-4886	109	24	rungekutta	rungekutta	NOUN
cana-4886	109	25	method	method	NOUN
cana-4886	109	26	:	:	PUNCT
cana-4886	109	27	𝐔𝑛+1	𝐔𝑛+1	NOUN
cana-4886	110	1	=	=	PUNCT
cana-4886	110	2	𝐔𝑛	𝐔𝑛	PROPN
cana-4886	110	3	+	+	CCONJ
cana-4886	110	4	δ𝑡	δ𝑡	X
cana-4886	110	5	⋅	⋅	PROPN
cana-4886	110	6	𝑑𝐔	𝑑𝐔	PROPN
cana-4886	110	7	𝑑𝑡	𝑑𝑡	ADP
cana-4886	110	8	4	4	NUM
cana-4886	110	9	.	.	PUNCT
cana-4886	110	10	boundary	boundary	ADJ
cana-4886	110	11	conditions	condition	NOUN
cana-4886	110	12	:	:	PUNCT
cana-4886	110	13	apply	apply	VERB
cana-4886	110	14	transmissive	transmissive	ADJ
cana-4886	110	15	or	or	CCONJ
cana-4886	110	16	reflective	reflective	ADJ
cana-4886	110	17	boundary	boundary	ADJ
cana-4886	110	18	conditions	condition	NOUN
cana-4886	110	19	.	.	PUNCT
cana-4886	111	1	5	5	X
cana-4886	111	2	.	.	X
cana-4886	111	3	iteration	iteration	NOUN
cana-4886	111	4	:	:	PUNCT
cana-4886	111	5	repeat	repeat	VERB
cana-4886	111	6	until	until	SCONJ
cana-4886	111	7	the	the	DET
cana-4886	111	8	solution	solution	NOUN
cana-4886	111	9	reaches	reach	VERB
cana-4886	111	10	steady	steady	ADJ
cana-4886	111	11	-	-	PUNCT
cana-4886	111	12	state	state	NOUN
cana-4886	111	13	or	or	CCONJ
cana-4886	111	14	final	final	ADJ
cana-4886	111	15	simulation	simulation	NOUN
cana-4886	111	16	time	time	NOUN
cana-4886	111	17	.	.	PUNCT
cana-4886	112	1	flowchart	flowchart	NOUN
cana-4886	112	2	of	of	ADP
cana-4886	112	3	the	the	DET
cana-4886	112	4	proposed	propose	VERB
cana-4886	112	5	method	method	NOUN
cana-4886	112	6	figure	figure	NOUN
cana-4886	112	7	1	1	NUM
cana-4886	112	8	:	:	PUNCT
cana-4886	112	9	solution	solution	NOUN
cana-4886	112	10	framework	framework	NOUN
cana-4886	112	11	for	for	ADP
cana-4886	112	12	analytical	analytical	ADJ
cana-4886	112	13	and	and	CCONJ
cana-4886	112	14	numerical	numerical	ADJ
cana-4886	112	15	approaches	approach	NOUN
cana-4886	112	16	to	to	ADP
cana-4886	112	17	the	the	DET
cana-4886	112	18	riemann	riemann	PROPN
cana-4886	112	19	problem	problem	NOUN
cana-4886	112	20	in	in	ADP
cana-4886	112	21	fluid	fluid	ADJ
cana-4886	112	22	dynamics	dynamic	NOUN
cana-4886	112	23	communications	communication	NOUN
cana-4886	112	24	on	on	ADP
cana-4886	112	25	applied	apply	VERB
cana-4886	112	26	nonlinear	nonlinear	ADJ
cana-4886	112	27	analysis	analysis	NOUN
cana-4886	112	28	issn	issn	NOUN
cana-4886	112	29	:	:	PUNCT
cana-4886	112	30	1074	1074	NUM
cana-4886	112	31	-	-	PUNCT
cana-4886	112	32	133x	133x	NUM
cana-4886	112	33	vol	vol	VERB
cana-4886	112	34	32	32	NUM
cana-4886	112	35	no	no	NOUN
cana-4886	112	36	.	.	PUNCT
cana-4886	113	1	10s	10	NOUN
cana-4886	113	2	(	(	PUNCT
cana-4886	113	3	2025	2025	NUM
cana-4886	113	4	)	)	PUNCT
cana-4886	113	5	886	886	NUM
cana-4886	113	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4886	113	7	f.	f.	PROPN
cana-4886	113	8	validation	validation	PROPN
cana-4886	113	9	and	and	CCONJ
cana-4886	113	10	performance	performance	NOUN
cana-4886	113	11	analysis	analysis	NOUN
cana-4886	113	12	to	to	PART
cana-4886	113	13	validate	validate	VERB
cana-4886	113	14	the	the	DET
cana-4886	113	15	methodology	methodology	NOUN
cana-4886	113	16	,	,	PUNCT
cana-4886	113	17	the	the	DET
cana-4886	113	18	numerical	numerical	ADJ
cana-4886	113	19	solutions	solution	NOUN
cana-4886	113	20	are	be	AUX
cana-4886	113	21	compared	compare	VERB
cana-4886	113	22	against	against	ADP
cana-4886	113	23	analytical	analytical	ADJ
cana-4886	113	24	solutions	solution	NOUN
cana-4886	113	25	and	and	CCONJ
cana-4886	113	26	benchmark	benchmark	NOUN
cana-4886	113	27	test	test	NOUN
cana-4886	113	28	cases	case	NOUN
cana-4886	113	29	.	.	PUNCT
cana-4886	114	1	the	the	DET
cana-4886	114	2	accuracy	accuracy	NOUN
cana-4886	114	3	is	be	AUX
cana-4886	114	4	evaluated	evaluate	VERB
cana-4886	114	5	using	use	VERB
cana-4886	114	6	l2	l2	NOUN
cana-4886	114	7	-	-	PUNCT
cana-4886	114	8	norm	norm	NOUN
cana-4886	114	9	error	error	NOUN
cana-4886	114	10	analysis	analysis	NOUN
cana-4886	114	11	:	:	PUNCT
cana-4886	114	12	computational	computational	ADJ
cana-4886	114	13	efficiency	efficiency	NOUN
cana-4886	114	14	is	be	AUX
cana-4886	114	15	measured	measure	VERB
cana-4886	114	16	using	use	VERB
cana-4886	114	17	execution	execution	NOUN
cana-4886	114	18	time	time	NOUN
cana-4886	114	19	and	and	CCONJ
cana-4886	114	20	iterations	iteration	NOUN
cana-4886	114	21	to	to	PART
cana-4886	114	22	convergence	convergence	VERB
cana-4886	114	23	.	.	PUNCT
cana-4886	115	1	the	the	DET
cana-4886	115	2	best	well	ADV
cana-4886	115	3	performing	performing	NOUN
cana-4886	115	4	solver	solver	NOUN
cana-4886	115	5	is	be	AUX
cana-4886	115	6	determined	determine	VERB
cana-4886	115	7	based	base	VERB
cana-4886	115	8	on	on	ADP
cana-4886	115	9	accuracy	accuracy	NOUN
cana-4886	115	10	and	and	CCONJ
cana-4886	115	11	efficiency	efficiency	NOUN
cana-4886	115	12	trade	trade	NOUN
cana-4886	115	13	-	-	PUNCT
cana-4886	115	14	offs	off	NOUN
cana-4886	115	15	[	[	X
cana-4886	115	16	8	8	NUM
cana-4886	115	17	]	]	PUNCT
cana-4886	115	18	.	.	PUNCT
cana-4886	116	1	iv	iv	X
cana-4886	116	2	.	.	PROPN
cana-4886	116	3	result	result	PROPN
cana-4886	116	4	&	&	CCONJ
cana-4886	116	5	discussions	discussion	NOUN
cana-4886	116	6	a	a	DET
cana-4886	116	7	thorough	thorough	ADJ
cana-4886	116	8	evaluation	evaluation	NOUN
cana-4886	116	9	of	of	ADP
cana-4886	116	10	the	the	DET
cana-4886	116	11	riemann	riemann	PROPN
cana-4886	116	12	problem	problem	NOUN
cana-4886	116	13	solution	solution	NOUN
cana-4886	116	14	capabilities	capability	NOUN
cana-4886	116	15	of	of	ADP
cana-4886	116	16	analytical	analytical	ADJ
cana-4886	116	17	methods	method	NOUN
cana-4886	116	18	and	and	CCONJ
cana-4886	116	19	numerical	numerical	ADJ
cana-4886	116	20	methods	method	NOUN
cana-4886	116	21	is	be	AUX
cana-4886	116	22	conducted	conduct	VERB
cana-4886	116	23	through	through	ADP
cana-4886	116	24	various	various	ADJ
cana-4886	116	25	test	test	NOUN
cana-4886	116	26	cases	case	NOUN
cana-4886	116	27	.	.	PUNCT
cana-4886	117	1	the	the	DET
cana-4886	117	2	assessment	assessment	NOUN
cana-4886	117	3	of	of	ADP
cana-4886	117	4	solutions	solution	NOUN
cana-4886	117	5	focuses	focus	VERB
cana-4886	117	6	on	on	ADP
cana-4886	117	7	accuracy	accuracy	NOUN
cana-4886	117	8	of	of	ADP
cana-4886	117	9	solutions	solution	NOUN
cana-4886	117	10	together	together	ADV
cana-4886	117	11	with	with	ADP
cana-4886	117	12	computational	computational	ADJ
cana-4886	117	13	efficiency	efficiency	NOUN
cana-4886	117	14	and	and	CCONJ
cana-4886	117	15	how	how	SCONJ
cana-4886	117	16	properly	properly	ADV
cana-4886	117	17	waves	wave	VERB
cana-4886	117	18	self	self	NOUN
cana-4886	117	19	-	-	PUNCT
cana-4886	117	20	organize	organize	NOUN
cana-4886	117	21	within	within	ADP
cana-4886	117	22	numerical	numerical	ADJ
cana-4886	117	23	computations	computation	NOUN
cana-4886	117	24	.	.	PUNCT
cana-4886	118	1	the	the	DET
cana-4886	118	2	comparison	comparison	NOUN
cana-4886	118	3	between	between	ADP
cana-4886	118	4	numerical	numerical	ADJ
cana-4886	118	5	solvers	solver	NOUN
cana-4886	118	6	particularly	particularly	ADV
cana-4886	118	7	between	between	ADP
cana-4886	118	8	roe	roe	PROPN
cana-4886	118	9	’s	’s	PART
cana-4886	118	10	solver	solver	PROPN
cana-4886	118	11	and	and	CCONJ
cana-4886	118	12	the	the	DET
cana-4886	118	13	hllc	hllc	ADJ
cana-4886	118	14	solver	solver	NOUN
cana-4886	118	15	demonstrates	demonstrate	VERB
cana-4886	118	16	their	their	PRON
cana-4886	118	17	benefits	benefit	NOUN
cana-4886	118	18	as	as	ADV
cana-4886	118	19	well	well	ADV
cana-4886	118	20	as	as	ADP
cana-4886	118	21	their	their	PRON
cana-4886	118	22	corresponding	corresponding	ADJ
cana-4886	118	23	constraints	constraint	NOUN
cana-4886	118	24	.	.	PUNCT
cana-4886	119	1	a	a	DET
cana-4886	119	2	comparison	comparison	NOUN
cana-4886	119	3	exists	exist	VERB
cana-4886	119	4	between	between	ADP
cana-4886	119	5	numerical	numerical	ADJ
cana-4886	119	6	outcomes	outcome	NOUN
cana-4886	119	7	obtained	obtain	VERB
cana-4886	119	8	from	from	ADP
cana-4886	119	9	the	the	DET
cana-4886	119	10	method	method	NOUN
cana-4886	119	11	of	of	ADP
cana-4886	119	12	characteristics	characteristic	NOUN
cana-4886	119	13	and	and	CCONJ
cana-4886	119	14	exact	exact	ADJ
cana-4886	119	15	solutions	solution	NOUN
cana-4886	119	16	[	[	X
cana-4886	119	17	9	9	NUM
cana-4886	119	18	]	]	PUNCT
cana-4886	119	19	.	.	PUNCT
cana-4886	120	1	the	the	DET
cana-4886	120	2	shock	shock	NOUN
cana-4886	120	3	tube	tube	NOUN
cana-4886	120	4	problem	problem	NOUN
cana-4886	120	5	serves	serve	VERB
cana-4886	120	6	as	as	ADP
cana-4886	120	7	the	the	DET
cana-4886	120	8	initial	initial	ADJ
cana-4886	120	9	evaluation	evaluation	NOUN
cana-4886	120	10	subject	subject	NOUN
cana-4886	120	11	since	since	SCONJ
cana-4886	120	12	it	it	PRON
cana-4886	120	13	presents	present	VERB
cana-4886	120	14	a	a	DET
cana-4886	120	15	classical	classical	ADJ
cana-4886	120	16	riemann	riemann	PROPN
cana-4886	120	17	problem	problem	NOUN
cana-4886	120	18	that	that	PRON
cana-4886	120	19	contains	contain	VERB
cana-4886	120	20	two	two	NUM
cana-4886	120	21	pressure	pressure	NOUN
cana-4886	120	22	and	and	CCONJ
cana-4886	120	23	density	density	NOUN
cana-4886	120	24	zones	zone	NOUN
cana-4886	120	25	separated	separate	VERB
cana-4886	120	26	by	by	ADP
cana-4886	120	27	an	an	DET
cana-4886	120	28	initial	initial	ADJ
cana-4886	120	29	discontinuity	discontinuity	NOUN
cana-4886	120	30	.	.	PUNCT
cana-4886	121	1	the	the	DET
cana-4886	121	2	computational	computational	ADJ
cana-4886	121	3	process	process	NOUN
cana-4886	121	4	generates	generate	VERB
cana-4886	121	5	three	three	NUM
cana-4886	121	6	characteristic	characteristic	ADJ
cana-4886	121	7	features	feature	NOUN
cana-4886	121	8	:	:	PUNCT
cana-4886	121	9	shock	shock	NOUN
cana-4886	121	10	wave	wave	NOUN
cana-4886	121	11	,	,	PUNCT
cana-4886	121	12	contact	contact	NOUN
cana-4886	121	13	discontinuity	discontinuity	NOUN
cana-4886	121	14	and	and	CCONJ
cana-4886	121	15	rarefaction	rarefaction	NOUN
cana-4886	121	16	wave	wave	NOUN
cana-4886	121	17	.	.	PUNCT
cana-4886	122	1	the	the	DET
cana-4886	122	2	exact	exact	ADJ
cana-4886	122	3	solution	solution	NOUN
cana-4886	122	4	for	for	ADP
cana-4886	122	5	a	a	DET
cana-4886	122	6	shock	shock	NOUN
cana-4886	122	7	tube	tube	NOUN
cana-4886	122	8	case	case	NOUN
cana-4886	122	9	brings	bring	VERB
cana-4886	122	10	forth	forth	ADV
cana-4886	122	11	density	density	NOUN
cana-4886	122	12	,	,	PUNCT
cana-4886	122	13	velocity	velocity	NOUN
cana-4886	122	14	,	,	PUNCT
cana-4886	122	15	and	and	CCONJ
cana-4886	122	16	pressure	pressure	NOUN
cana-4886	122	17	profiles	profile	NOUN
cana-4886	122	18	through	through	ADP
cana-4886	122	19	figure	figure	NOUN
cana-4886	122	20	2	2	NUM
cana-4886	122	21	at	at	ADP
cana-4886	122	22	t=0.2	t=0.2	NOUN
cana-4886	122	23	seconds	second	NOUN
cana-4886	122	24	.	.	PUNCT
cana-4886	123	1	the	the	DET
cana-4886	123	2	analytic	analytic	ADJ
cana-4886	123	3	solution	solution	NOUN
cana-4886	123	4	reproduces	reproduce	VERB
cana-4886	123	5	fluid	fluid	ADJ
cana-4886	123	6	variable	variable	ADJ
cana-4886	123	7	behavior	behavior	NOUN
cana-4886	123	8	by	by	ADP
cana-4886	123	9	correctly	correctly	ADV
cana-4886	123	10	representing	represent	VERB
cana-4886	123	11	the	the	DET
cana-4886	123	12	wave	wave	NOUN
cana-4886	123	13	patterns	pattern	NOUN
cana-4886	123	14	which	which	PRON
cana-4886	123	15	result	result	VERB
cana-4886	123	16	from	from	ADP
cana-4886	123	17	initial	initial	ADJ
cana-4886	123	18	conditions	condition	NOUN
cana-4886	123	19	that	that	PRON
cana-4886	123	20	change	change	VERB
cana-4886	123	21	suddenly	suddenly	ADV
cana-4886	123	22	.	.	PUNCT
cana-4886	124	1	figure	figure	VERB
cana-4886	124	2	2	2	NUM
cana-4886	124	3	:	:	PUNCT
cana-4886	124	4	exact	exact	ADJ
cana-4886	124	5	solution	solution	NOUN
cana-4886	124	6	data	datum	NOUN
cana-4886	124	7	for	for	ADP
cana-4886	124	8	shock	shock	NOUN
cana-4886	124	9	tube	tube	NOUN
cana-4886	124	10	test	test	NOUN
cana-4886	124	11	case	case	NOUN
cana-4886	124	12	communications	communication	NOUN
cana-4886	124	13	on	on	ADP
cana-4886	124	14	applied	apply	VERB
cana-4886	124	15	nonlinear	nonlinear	ADJ
cana-4886	124	16	analysis	analysis	NOUN
cana-4886	124	17	issn	issn	NOUN
cana-4886	124	18	:	:	PUNCT
cana-4886	124	19	1074	1074	NUM
cana-4886	124	20	-	-	PUNCT
cana-4886	124	21	133x	133x	NUM
cana-4886	124	22	vol	vol	VERB
cana-4886	124	23	32	32	NUM
cana-4886	124	24	no	no	NOUN
cana-4886	124	25	.	.	PUNCT
cana-4886	125	1	10s	10	NOUN
cana-4886	125	2	(	(	PUNCT
cana-4886	125	3	2025	2025	NUM
cana-4886	125	4	)	)	PUNCT
cana-4886	125	5	887	887	NUM
cana-4886	125	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4886	125	7	the	the	DET
cana-4886	125	8	evaluation	evaluation	NOUN
cana-4886	125	9	of	of	ADP
cana-4886	125	10	numerical	numerical	ADJ
cana-4886	125	11	solutions	solution	NOUN
cana-4886	125	12	against	against	ADP
cana-4886	125	13	the	the	DET
cana-4886	125	14	exact	exact	ADJ
cana-4886	125	15	solution	solution	NOUN
cana-4886	125	16	uses	use	VERB
cana-4886	125	17	roe	roe	PROPN
cana-4886	125	18	’s	’s	PART
cana-4886	125	19	solver	solver	ADV
cana-4886	125	20	coupled	couple	VERB
cana-4886	125	21	with	with	ADP
cana-4886	125	22	the	the	DET
cana-4886	125	23	hllc	hllc	PROPN
cana-4886	125	24	solver	solver	NOUN
cana-4886	125	25	for	for	ADP
cana-4886	125	26	wave	wave	NOUN
cana-4886	125	27	structure	structure	NOUN
cana-4886	125	28	approximation	approximation	NOUN
cana-4886	125	29	.	.	PUNCT
cana-4886	126	1	both	both	DET
cana-4886	126	2	calculation	calculation	NOUN
cana-4886	126	3	approaches	approach	NOUN
cana-4886	126	4	generated	generate	VERB
cana-4886	126	5	the	the	DET
cana-4886	126	6	density	density	NOUN
cana-4886	126	7	profile	profile	NOUN
cana-4886	126	8	results	result	NOUN
cana-4886	126	9	which	which	PRON
cana-4886	126	10	are	be	AUX
cana-4886	126	11	presented	present	VERB
cana-4886	126	12	in	in	ADP
cana-4886	126	13	figure	figure	NOUN
cana-4886	126	14	3	3	NUM
cana-4886	126	15	.	.	PUNCT
cana-4886	127	1	roe	roe	PROPN
cana-4886	127	2	's	's	PART
cana-4886	127	3	solver	solver	NOUN
cana-4886	127	4	displays	display	VERB
cana-4886	127	5	minor	minor	ADJ
cana-4886	127	6	oscillations	oscillation	NOUN
cana-4886	127	7	close	close	ADJ
cana-4886	127	8	to	to	ADP
cana-4886	127	9	the	the	DET
cana-4886	127	10	contact	contact	NOUN
cana-4886	127	11	discontinuity	discontinuity	NOUN
cana-4886	127	12	that	that	PRON
cana-4886	127	13	the	the	DET
cana-4886	127	14	hllc	hllc	ADJ
cana-4886	127	15	solver	solver	NOUN
cana-4886	127	16	does	do	AUX
cana-4886	127	17	not	not	PART
cana-4886	127	18	produce	produce	VERB
cana-4886	127	19	although	although	SCONJ
cana-4886	127	20	both	both	DET
cana-4886	127	21	methods	method	NOUN
cana-4886	127	22	provide	provide	VERB
cana-4886	127	23	correct	correct	ADJ
cana-4886	127	24	representations	representation	NOUN
cana-4886	127	25	of	of	ADP
cana-4886	127	26	shock	shock	NOUN
cana-4886	127	27	and	and	CCONJ
cana-4886	127	28	rarefaction	rarefaction	NOUN
cana-4886	127	29	waves	wave	NOUN
cana-4886	127	30	.	.	PUNCT
cana-4886	128	1	the	the	DET
cana-4886	128	2	hllc	hllc	PROPN
cana-4886	128	3	solver	solver	PROPN
cana-4886	128	4	succeeds	succeed	VERB
cana-4886	128	5	at	at	ADP
cana-4886	128	6	resolving	resolve	VERB
cana-4886	128	7	the	the	DET
cana-4886	128	8	contact	contact	NOUN
cana-4886	128	9	wave	wave	NOUN
cana-4886	128	10	thus	thus	ADV
cana-4886	128	11	proving	prove	VERB
cana-4886	128	12	its	its	PRON
cana-4886	128	13	ability	ability	NOUN
cana-4886	128	14	to	to	PART
cana-4886	128	15	maintain	maintain	VERB
cana-4886	128	16	stable	stable	ADJ
cana-4886	128	17	resolution	resolution	NOUN
cana-4886	128	18	of	of	ADP
cana-4886	128	19	discontinuous	discontinuous	ADJ
cana-4886	128	20	solutions	solution	NOUN
cana-4886	128	21	.	.	PUNCT
cana-4886	129	1	figure	figure	VERB
cana-4886	129	2	3	3	NUM
cana-4886	129	3	:	:	PUNCT
cana-4886	129	4	density	density	NOUN
cana-4886	129	5	profiles	profile	NOUN
cana-4886	129	6	using	use	VERB
cana-4886	129	7	roe	roe	NOUN
cana-4886	129	8	’s	’s	NOUN
cana-4886	129	9	and	and	CCONJ
cana-4886	129	10	hllc	hllc	ADJ
cana-4886	129	11	solvers	solver	NOUN
cana-4886	129	12	a	a	DET
cana-4886	129	13	quantitative	quantitative	ADJ
cana-4886	129	14	analysis	analysis	NOUN
cana-4886	129	15	of	of	ADP
cana-4886	129	16	solution	solution	NOUN
cana-4886	129	17	errors	error	NOUN
cana-4886	129	18	occurs	occur	VERB
cana-4886	129	19	in	in	ADP
cana-4886	129	20	table	table	NOUN
cana-4886	129	21	1	1	NUM
cana-4886	129	22	for	for	ADP
cana-4886	129	23	numerical	numerical	ADJ
cana-4886	129	24	against	against	ADP
cana-4886	129	25	exact	exact	ADJ
cana-4886	129	26	results	result	NOUN
cana-4886	129	27	.	.	PUNCT
cana-4886	130	1	the	the	DET
cana-4886	130	2	numerical	numerical	ADJ
cana-4886	130	3	dissipation	dissipation	NOUN
cana-4886	130	4	performance	performance	NOUN
cana-4886	130	5	of	of	ADP
cana-4886	130	6	the	the	DET
cana-4886	130	7	hllc	hllc	PROPN
cana-4886	130	8	solver	solver	PROPN
cana-4886	130	9	shows	show	VERB
cana-4886	130	10	better	well	ADJ
cana-4886	130	11	accuracy	accuracy	NOUN
cana-4886	130	12	based	base	VERB
cana-4886	130	13	on	on	ADP
cana-4886	130	14	l2	l2	NOUN
cana-4886	130	15	-	-	PUNCT
cana-4886	130	16	norm	norm	NOUN
cana-4886	130	17	error	error	NOUN
cana-4886	130	18	values	value	NOUN
cana-4886	130	19	.	.	PUNCT
cana-4886	131	1	although	although	SCONJ
cana-4886	131	2	roe	roe	PROPN
cana-4886	131	3	’s	’s	PART
cana-4886	131	4	solver	solver	PROPN
cana-4886	131	5	maintains	maintain	VERB
cana-4886	131	6	high	high	ADJ
cana-4886	131	7	efficiency	efficiency	NOUN
cana-4886	131	8	it	it	PRON
cana-4886	131	9	remains	remain	VERB
cana-4886	131	10	suitable	suitable	ADJ
cana-4886	131	11	for	for	ADP
cana-4886	131	12	use	use	NOUN
cana-4886	131	13	in	in	ADP
cana-4886	131	14	demanding	demand	VERB
cana-4886	131	15	largescale	largescale	ADJ
cana-4886	131	16	simulations	simulation	NOUN
cana-4886	131	17	that	that	PRON
cana-4886	131	18	require	require	VERB
cana-4886	131	19	superior	superior	ADJ
cana-4886	131	20	performance	performance	NOUN
cana-4886	131	21	levels	level	NOUN
cana-4886	131	22	.	.	PUNCT
cana-4886	132	1	table	table	NOUN
cana-4886	132	2	1	1	NUM
cana-4886	132	3	:	:	PUNCT
cana-4886	132	4	l2	l2	NOUN
cana-4886	132	5	-	-	PUNCT
cana-4886	132	6	norm	norm	NOUN
cana-4886	132	7	error	error	NOUN
cana-4886	132	8	comparison	comparison	NOUN
cana-4886	132	9	between	between	ADP
cana-4886	132	10	roe	roe	PROPN
cana-4886	132	11	’s	’s	PART
cana-4886	132	12	and	and	CCONJ
cana-4886	132	13	hllc	hllc	ADJ
cana-4886	132	14	solvers	solver	NOUN
cana-4886	132	15	solver	solver	VERB
cana-4886	132	16	density	density	NOUN
cana-4886	132	17	error	error	NOUN
cana-4886	132	18	(	(	PUNCT
cana-4886	132	19	l2norm	l2norm	NOUN
cana-4886	132	20	)	)	PUNCT
cana-4886	132	21	velocity	velocity	NOUN
cana-4886	132	22	error	error	NOUN
cana-4886	132	23	(	(	PUNCT
cana-4886	132	24	l2	l2	NOUN
cana-4886	132	25	-	-	PUNCT
cana-4886	132	26	norm	norm	NOUN
cana-4886	132	27	)	)	PUNCT
cana-4886	132	28	pressure	pressure	NOUN
cana-4886	132	29	error	error	NOUN
cana-4886	132	30	(	(	PUNCT
cana-4886	132	31	l2norm	l2norm	NOUN
cana-4886	132	32	)	)	PUNCT
cana-4886	132	33	roe	roe	PROPN
cana-4886	132	34	’s	’s	PART
cana-4886	132	35	solver	solver	VERB
cana-4886	132	36	0.0123	0.0123	NUM
cana-4886	132	37	0.0089	0.0089	NUM
cana-4886	132	38	0.0154	0.0154	NUM
cana-4886	132	39	hllc	hllc	AUX
cana-4886	132	40	solver	solver	VERB
cana-4886	132	41	0.0091	0.0091	NUM
cana-4886	132	42	0.0073	0.0073	NUM
cana-4886	132	43	0.0112	0.0112	NUM
cana-4886	132	44	the	the	DET
cana-4886	132	45	second	second	ADJ
cana-4886	132	46	performance	performance	NOUN
cana-4886	132	47	assessment	assessment	NOUN
cana-4886	132	48	includes	include	VERB
cana-4886	132	49	computing	computing	NOUN
cana-4886	132	50	time	time	NOUN
cana-4886	132	51	tests	test	NOUN
cana-4886	132	52	with	with	ADP
cana-4886	132	53	various	various	ADJ
cana-4886	132	54	grid	grid	NOUN
cana-4886	132	55	resolutions	resolution	NOUN
cana-4886	132	56	to	to	PART
cana-4886	132	57	determine	determine	VERB
cana-4886	132	58	operational	operational	ADJ
cana-4886	132	59	durations	duration	NOUN
cana-4886	132	60	of	of	ADP
cana-4886	132	61	both	both	DET
cana-4886	132	62	numerical	numerical	ADJ
cana-4886	132	63	methods	method	NOUN
cana-4886	132	64	.	.	PUNCT
cana-4886	133	1	figure	figure	NOUN
cana-4886	133	2	4	4	NUM
cana-4886	133	3	shows	show	VERB
cana-4886	133	4	roe	roe	PROPN
cana-4886	133	5	’s	’s	PART
cana-4886	133	6	solver	solver	PROPN
cana-4886	133	7	outpaces	outpace	NOUN
cana-4886	133	8	hllc	hllc	ADV
cana-4886	133	9	in	in	ADP
cana-4886	133	10	execution	execution	NOUN
cana-4886	133	11	speed	speed	NOUN
cana-4886	133	12	especially	especially	ADV
cana-4886	133	13	when	when	SCONJ
cana-4886	133	14	the	the	DET
cana-4886	133	15	grid	grid	NOUN
cana-4886	133	16	resolution	resolution	NOUN
cana-4886	133	17	is	be	AUX
cana-4886	133	18	high	high	ADJ
cana-4886	133	19	.	.	PUNCT
cana-4886	134	1	the	the	DET
cana-4886	134	2	hllc	hllc	ADJ
cana-4886	134	3	computational	computational	ADJ
cana-4886	134	4	process	process	NOUN
cana-4886	134	5	required	require	VERB
cana-4886	134	6	extra	extra	ADJ
cana-4886	134	7	wave	wave	NOUN
cana-4886	134	8	structure	structure	NOUN
cana-4886	134	9	resolution	resolution	NOUN
cana-4886	134	10	steps	step	NOUN
cana-4886	134	11	that	that	PRON
cana-4886	134	12	lead	lead	VERB
cana-4886	134	13	to	to	ADP
cana-4886	134	14	more	more	ADV
cana-4886	134	15	accurate	accurate	ADJ
cana-4886	134	16	results	result	NOUN
cana-4886	134	17	at	at	ADP
cana-4886	134	18	the	the	DET
cana-4886	134	19	cost	cost	NOUN
cana-4886	134	20	of	of	ADP
cana-4886	134	21	increased	increase	VERB
cana-4886	134	22	computational	computational	ADJ
cana-4886	134	23	workload	workload	NOUN
cana-4886	134	24	.	.	PUNCT
cana-4886	135	1	0.127	0.127	NUM
cana-4886	135	2	0.271	0.271	NUM
cana-4886	135	3	0.807	0.807	NUM
cana-4886	135	4	0.125	0.125	NUM
cana-4886	135	5	0.265	0.265	NUM
cana-4886	135	6	0.812	0.812	NUM
cana-4886	135	7	0.125	0.125	NUM
cana-4886	135	8	0.265	0.265	NUM
cana-4886	135	9	0.812	0.812	NUM
cana-4886	135	10	0	0	NUM
cana-4886	135	11	0.1	0.1	NUM
cana-4886	135	12	0.2	0.2	NUM
cana-4886	135	13	0.3	0.3	NUM
cana-4886	135	14	0.4	0.4	NUM
cana-4886	135	15	0.5	0.5	NUM
cana-4886	135	16	0.6	0.6	NUM
cana-4886	135	17	0.7	0.7	NUM
cana-4886	135	18	0.8	0.8	NUM
cana-4886	135	19	0.9	0.9	NUM
cana-4886	135	20	0.2	0.2	NUM
cana-4886	135	21	0.4	0.4	NUM
cana-4886	135	22	0.6	0.6	NUM
cana-4886	135	23	density	density	NOUN
cana-4886	135	24	profiles	profile	NOUN
cana-4886	135	25	using	use	VERB
cana-4886	135	26	roe	roe	NOUN
cana-4886	135	27	’s	’s	NOUN
cana-4886	135	28	and	and	CCONJ
cana-4886	135	29	hllc	hllc	ADJ
cana-4886	135	30	solvers	solver	NOUN
cana-4886	135	31	roe	roe	PROPN
cana-4886	135	32	solver	solver	PROPN
cana-4886	135	33	density	density	NOUN
cana-4886	135	34	(	(	PUNCT
cana-4886	135	35	ρ	ρ	NOUN
cana-4886	135	36	)	)	PUNCT
cana-4886	135	37	hllc	hllc	ADJ
cana-4886	135	38	solver	solver	NOUN
cana-4886	135	39	density	density	NOUN
cana-4886	135	40	(	(	PUNCT
cana-4886	135	41	ρ	ρ	NOUN
cana-4886	135	42	)	)	PUNCT
cana-4886	135	43	exact	exact	ADJ
cana-4886	135	44	density	density	NOUN
cana-4886	135	45	(	(	PUNCT
cana-4886	135	46	ρ	ρ	NOUN
cana-4886	135	47	)	)	PUNCT
cana-4886	135	48	communications	communication	NOUN
cana-4886	135	49	on	on	ADP
cana-4886	135	50	applied	apply	VERB
cana-4886	135	51	nonlinear	nonlinear	ADJ
cana-4886	135	52	analysis	analysis	NOUN
cana-4886	135	53	issn	issn	NOUN
cana-4886	135	54	:	:	PUNCT
cana-4886	135	55	1074	1074	NUM
cana-4886	135	56	-	-	PUNCT
cana-4886	135	57	133x	133x	NUM
cana-4886	135	58	vol	vol	VERB
cana-4886	135	59	32	32	NUM
cana-4886	135	60	no	no	NOUN
cana-4886	135	61	.	.	PUNCT
cana-4886	136	1	10s	10	NOUN
cana-4886	136	2	(	(	PUNCT
cana-4886	136	3	2025	2025	NUM
cana-4886	136	4	)	)	PUNCT
cana-4886	136	5	888	888	NUM
cana-4886	136	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4886	136	7	figure	figure	NOUN
cana-4886	136	8	4	4	NUM
cana-4886	136	9	:	:	PUNCT
cana-4886	136	10	execution	execution	NOUN
cana-4886	136	11	time	time	NOUN
cana-4886	136	12	for	for	ADP
cana-4886	136	13	roe	roe	PROPN
cana-4886	136	14	’s	’s	PART
cana-4886	136	15	and	and	CCONJ
cana-4886	136	16	hllc	hllc	ADJ
cana-4886	136	17	solvers	solver	NOUN
cana-4886	136	18	the	the	DET
cana-4886	136	19	ability	ability	NOUN
cana-4886	136	20	of	of	ADP
cana-4886	136	21	solver	solver	VERB
cana-4886	136	22	methods	method	NOUN
cana-4886	136	23	to	to	PART
cana-4886	136	24	detect	detect	VERB
cana-4886	136	25	distinct	distinct	ADJ
cana-4886	136	26	wave	wave	NOUN
cana-4886	136	27	types	type	NOUN
cana-4886	136	28	is	be	AUX
cana-4886	136	29	analyzed	analyze	VERB
cana-4886	136	30	through	through	ADP
cana-4886	136	31	the	the	DET
cana-4886	136	32	results	result	NOUN
cana-4886	136	33	presented	present	VERB
cana-4886	136	34	in	in	ADP
cana-4886	136	35	table	table	NOUN
cana-4886	136	36	2	2	NUM
cana-4886	136	37	.	.	PUNCT
cana-4886	137	1	the	the	DET
cana-4886	137	2	performance	performance	NOUN
cana-4886	137	3	analysis	analysis	NOUN
cana-4886	137	4	of	of	ADP
cana-4886	137	5	shock	shock	NOUN
cana-4886	137	6	wave	wave	NOUN
cana-4886	137	7	,	,	PUNCT
cana-4886	137	8	rarefaction	rarefaction	NOUN
cana-4886	137	9	wave	wave	NOUN
cana-4886	137	10	and	and	CCONJ
cana-4886	137	11	contact	contact	NOUN
cana-4886	137	12	discontinuity	discontinuity	NOUN
cana-4886	137	13	capture	capture	NOUN
cana-4886	137	14	capability	capability	NOUN
cana-4886	137	15	of	of	ADP
cana-4886	137	16	each	each	DET
cana-4886	137	17	solver	solver	NOUN
cana-4886	137	18	examines	examine	VERB
cana-4886	137	19	their	their	PRON
cana-4886	137	20	deviations	deviation	NOUN
cana-4886	137	21	from	from	ADP
cana-4886	137	22	the	the	DET
cana-4886	137	23	analytical	analytical	ADJ
cana-4886	137	24	solution	solution	NOUN
cana-4886	137	25	.	.	PUNCT
cana-4886	138	1	the	the	DET
cana-4886	138	2	experimental	experimental	ADJ
cana-4886	138	3	evidence	evidence	NOUN
cana-4886	138	4	verifies	verifie	NOUN
cana-4886	138	5	that	that	PRON
cana-4886	138	6	hllc	hllc	ADV
cana-4886	138	7	delivers	deliver	VERB
cana-4886	138	8	improved	improved	ADJ
cana-4886	138	9	contact	contact	NOUN
cana-4886	138	10	discontinuity	discontinuity	NOUN
cana-4886	138	11	tracking	tracking	NOUN
cana-4886	138	12	as	as	ADP
cana-4886	138	13	roe	roe	PROPN
cana-4886	138	14	's	's	PART
cana-4886	138	15	solver	solver	NOUN
cana-4886	138	16	maintains	maintain	VERB
cana-4886	138	17	excellence	excellence	NOUN
cana-4886	138	18	for	for	ADP
cana-4886	138	19	shock	shock	NOUN
cana-4886	138	20	wave	wave	NOUN
cana-4886	138	21	prediction	prediction	NOUN
cana-4886	138	22	.	.	PUNCT
cana-4886	139	1	table	table	NOUN
cana-4886	139	2	2	2	NUM
cana-4886	139	3	:	:	PUNCT
cana-4886	140	1	accuracy	accuracy	NOUN
cana-4886	140	2	assessment	assessment	NOUN
cana-4886	140	3	of	of	ADP
cana-4886	140	4	numerical	numerical	ADJ
cana-4886	140	5	solvers	solver	NOUN
cana-4886	140	6	for	for	ADP
cana-4886	140	7	wave	wave	NOUN
cana-4886	140	8	structures	structure	NOUN
cana-4886	140	9	solver	solver	VERB
cana-4886	140	10	shock	shock	NOUN
cana-4886	140	11	wave	wave	NOUN
cana-4886	140	12	accuracy	accuracy	NOUN
cana-4886	140	13	rarefaction	rarefaction	NOUN
cana-4886	140	14	wave	wave	NOUN
cana-4886	140	15	accuracy	accuracy	NOUN
cana-4886	140	16	contact	contact	NOUN
cana-4886	140	17	discontinuity	discontinuity	NOUN
cana-4886	140	18	accuracy	accuracy	NOUN
cana-4886	140	19	roe	roe	PROPN
cana-4886	140	20	’s	’s	PART
cana-4886	140	21	solver	solver	VERB
cana-4886	140	22	high	high	ADJ
cana-4886	140	23	moderate	moderate	ADJ
cana-4886	140	24	moderate	moderate	ADJ
cana-4886	140	25	hllc	hllc	PROPN
cana-4886	140	26	solver	solver	VERB
cana-4886	140	27	high	high	ADJ
cana-4886	140	28	high	high	ADV
cana-4886	140	29	high	high	ADV
cana-4886	140	30	the	the	DET
cana-4886	140	31	research	research	NOUN
cana-4886	140	32	demonstrates	demonstrate	VERB
cana-4886	140	33	that	that	SCONJ
cana-4886	140	34	numerical	numerical	ADJ
cana-4886	140	35	solvers	solver	NOUN
cana-4886	140	36	effectively	effectively	ADV
cana-4886	140	37	solve	solve	VERB
cana-4886	140	38	riemann	riemann	PROPN
cana-4886	140	39	problems	problem	NOUN
cana-4886	140	40	but	but	CCONJ
cana-4886	140	41	users	user	NOUN
cana-4886	140	42	need	need	VERB
cana-4886	140	43	to	to	PART
cana-4886	140	44	balance	balance	VERB
cana-4886	140	45	between	between	ADP
cana-4886	140	46	precision	precision	NOUN
cana-4886	140	47	and	and	CCONJ
cana-4886	140	48	simulation	simulation	NOUN
cana-4886	140	49	speed	speed	NOUN
cana-4886	140	50	.	.	PUNCT
cana-4886	141	1	the	the	DET
cana-4886	141	2	roe	roe	PROPN
cana-4886	141	3	’s	’s	PART
cana-4886	141	4	solver	solver	PROPN
cana-4886	141	5	retains	retain	VERB
cana-4886	141	6	its	its	PRON
cana-4886	141	7	position	position	NOUN
cana-4886	141	8	as	as	ADP
cana-4886	141	9	the	the	DET
cana-4886	141	10	top	top	ADJ
cana-4886	141	11	solution	solution	NOUN
cana-4886	141	12	for	for	ADP
cana-4886	141	13	speedy	speedy	ADJ
cana-4886	141	14	simulations	simulation	NOUN
cana-4886	141	15	yet	yet	CCONJ
cana-4886	141	16	the	the	DET
cana-4886	141	17	hllc	hllc	PROPN
cana-4886	141	18	solver	solver	PROPN
cana-4886	141	19	stands	stand	VERB
cana-4886	141	20	out	out	ADP
cana-4886	141	21	most	most	ADV
cana-4886	141	22	effectively	effectively	ADV
cana-4886	141	23	when	when	SCONJ
cana-4886	141	24	contact	contact	NOUN
cana-4886	141	25	discontinuity	discontinuity	NOUN
cana-4886	141	26	precision	precision	NOUN
cana-4886	141	27	is	be	AUX
cana-4886	141	28	the	the	DET
cana-4886	141	29	main	main	ADJ
cana-4886	141	30	goal	goal	NOUN
cana-4886	141	31	.	.	PUNCT
cana-4886	142	1	v.	v.	ADP
cana-4886	142	2	conclusion	conclusion	NOUN
cana-4886	142	3	the	the	DET
cana-4886	142	4	research	research	NOUN
cana-4886	142	5	elaborates	elaborate	VERB
cana-4886	142	6	on	on	ADP
cana-4886	142	7	the	the	DET
cana-4886	142	8	advantages	advantage	NOUN
cana-4886	142	9	and	and	CCONJ
cana-4886	142	10	boundaries	boundary	NOUN
cana-4886	142	11	of	of	ADP
cana-4886	142	12	analytical	analytical	ADJ
cana-4886	142	13	and	and	CCONJ
cana-4886	142	14	numerical	numerical	ADJ
cana-4886	142	15	methods	method	NOUN
cana-4886	142	16	in	in	ADP
cana-4886	142	17	riemann	riemann	PROPN
cana-4886	142	18	problem	problem	NOUN
cana-4886	142	19	solution	solution	NOUN
cana-4886	142	20	for	for	ADP
cana-4886	142	21	fluid	fluid	ADJ
cana-4886	142	22	dynamics	dynamic	NOUN
cana-4886	142	23	applications	application	NOUN
cana-4886	142	24	.	.	PUNCT
cana-4886	143	1	the	the	DET
cana-4886	143	2	precise	precise	ADJ
cana-4886	143	3	understanding	understanding	NOUN
cana-4886	143	4	of	of	ADP
cana-4886	143	5	wave	wave	NOUN
cana-4886	143	6	interactions	interaction	NOUN
cana-4886	143	7	comes	come	VERB
cana-4886	143	8	from	from	ADP
cana-4886	143	9	analytical	analytical	ADJ
cana-4886	143	10	solutions	solution	NOUN
cana-4886	143	11	but	but	CCONJ
cana-4886	143	12	such	such	ADJ
cana-4886	143	13	methods	method	NOUN
cana-4886	143	14	prove	prove	VERB
cana-4886	143	15	unpractical	unpractical	ADJ
cana-4886	143	16	when	when	SCONJ
cana-4886	143	17	dealing	deal	VERB
cana-4886	143	18	with	with	ADP
cana-4886	143	19	complex	complex	ADJ
cana-4886	143	20	systems	system	NOUN
cana-4886	143	21	.	.	PUNCT
cana-4886	144	1	future	future	ADJ
cana-4886	144	2	investigations	investigation	NOUN
cana-4886	144	3	need	need	VERB
cana-4886	144	4	to	to	PART
cana-4886	144	5	establish	establish	VERB
cana-4886	144	6	combined	combined	ADJ
cana-4886	144	7	analytical	analytical	ADJ
cana-4886	144	8	-	-	PUNCT
cana-4886	144	9	numerical	numerical	ADJ
cana-4886	144	10	integration	integration	NOUN
cana-4886	144	11	techniques	technique	NOUN
cana-4886	144	12	because	because	SCONJ
cana-4886	144	13	they	they	PRON
cana-4886	144	14	will	will	AUX
cana-4886	144	15	enhance	enhance	VERB
cana-4886	144	16	both	both	DET
cana-4886	144	17	precision	precision	NOUN
cana-4886	144	18	and	and	CCONJ
cana-4886	144	19	performance	performance	NOUN
cana-4886	144	20	within	within	ADP
cana-4886	144	21	computational	computational	ADJ
cana-4886	144	22	fluid	fluid	ADJ
cana-4886	144	23	dynamics	dynamic	NOUN
cana-4886	144	24	models	model	NOUN
cana-4886	144	25	.	.	PUNCT
cana-4886	145	1	0.0032	0.0032	NUM
cana-4886	145	2	0.0154	0.0154	NUM
cana-4886	145	3	0.0347	0.0347	NUM
cana-4886	145	4	0.0048	0.0048	NUM
cana-4886	145	5	0.0213	0.0213	NUM
cana-4886	146	1	0.0526	0.0526	NUM
cana-4886	146	2	0	0	NUM
cana-4886	147	1	0.01	0.01	NUM
cana-4886	147	2	0.02	0.02	NUM
cana-4886	147	3	0.03	0.03	NUM
cana-4886	147	4	0.04	0.04	NUM
cana-4886	147	5	0.05	0.05	NUM
cana-4886	147	6	0.06	0.06	NUM
cana-4886	147	7	100	100	NUM
cana-4886	147	8	cells	cell	NOUN
cana-4886	147	9	500	500	NUM
cana-4886	147	10	cells	cell	NOUN
cana-4886	147	11	1000	1000	NUM
cana-4886	147	12	cells	cell	NOUN
cana-4886	147	13	execution	execution	NOUN
cana-4886	147	14	time	time	NOUN
cana-4886	147	15	for	for	ADP
cana-4886	147	16	roe	roe	PROPN
cana-4886	147	17	’s	’s	PART
cana-4886	147	18	and	and	CCONJ
cana-4886	147	19	hllc	hllc	ADJ
cana-4886	147	20	solvers	solver	NOUN
cana-4886	147	21	roe	roe	PROPN
cana-4886	147	22	solver	solver	PROPN
cana-4886	147	23	execution	execution	NOUN
cana-4886	147	24	time	time	NOUN
cana-4886	147	25	(	(	PUNCT
cana-4886	147	26	s	s	X
cana-4886	147	27	)	)	PUNCT
cana-4886	147	28	hllc	hllc	ADJ
cana-4886	147	29	solver	solver	NOUN
cana-4886	147	30	execution	execution	NOUN
cana-4886	147	31	time	time	NOUN
cana-4886	147	32	(	(	PUNCT
cana-4886	147	33	s	s	NOUN
cana-4886	147	34	)	)	PUNCT
cana-4886	147	35	communications	communication	NOUN
cana-4886	147	36	on	on	ADP
cana-4886	147	37	applied	apply	VERB
cana-4886	147	38	nonlinear	nonlinear	ADJ
cana-4886	147	39	analysis	analysis	NOUN
cana-4886	147	40	issn	issn	NOUN
cana-4886	147	41	:	:	PUNCT
cana-4886	147	42	1074	1074	NUM
cana-4886	147	43	-	-	PUNCT
cana-4886	147	44	133x	133x	NUM
cana-4886	147	45	vol	vol	VERB
cana-4886	147	46	32	32	NUM
cana-4886	147	47	no	no	NOUN
cana-4886	147	48	.	.	PUNCT
cana-4886	148	1	10s	10	NOUN
cana-4886	148	2	(	(	PUNCT
cana-4886	148	3	2025	2025	NUM
cana-4886	148	4	)	)	PUNCT
cana-4886	148	5	889	889	NUM
cana-4886	148	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4886	148	7	references	reference	NOUN
cana-4886	148	8	[	[	X
cana-4886	148	9	1	1	NUM
cana-4886	148	10	]	]	PUNCT
cana-4886	148	11	m.	m.	NOUN
cana-4886	148	12	ruggeri	ruggeri	PROPN
cana-4886	148	13	,	,	PUNCT
cana-4886	148	14	i.	i.	PROPN
cana-4886	148	15	roy	roy	PROPN
cana-4886	148	16	,	,	PUNCT
cana-4886	148	17	m.	m.	PROPN
cana-4886	148	18	j.	j.	PROPN
cana-4886	148	19	mueterthies	mueterthies	PROPN
cana-4886	148	20	,	,	PUNCT
cana-4886	148	21	t.	t.	NOUN
cana-4886	148	22	gruenwald	gruenwald	NOUN
cana-4886	148	23	,	,	PUNCT
cana-4886	148	24	and	and	CCONJ
cana-4886	148	25	c.	c.	PROPN
cana-4886	148	26	scalo	scalo	PROPN
cana-4886	148	27	,	,	PUNCT
cana-4886	148	28	“	"	PUNCT
cana-4886	148	29	neural	neural	ADJ
cana-4886	148	30	-	-	PUNCT
cana-4886	148	31	network	network	NOUN
cana-4886	148	32	-	-	PUNCT
cana-4886	148	33	based	base	VERB
cana-4886	148	34	riemann	riemann	PROPN
cana-4886	148	35	solver	solver	VERB
cana-4886	148	36	for	for	ADP
cana-4886	148	37	real	real	ADJ
cana-4886	148	38	fluids	fluid	NOUN
cana-4886	148	39	and	and	CCONJ
cana-4886	148	40	high	high	ADJ
cana-4886	148	41	explosives	explosive	NOUN
cana-4886	148	42	;	;	PUNCT
cana-4886	148	43	application	application	NOUN
cana-4886	148	44	to	to	ADP
cana-4886	148	45	computational	computational	ADJ
cana-4886	148	46	fluid	fluid	ADJ
cana-4886	148	47	dynamics	dynamic	NOUN
cana-4886	148	48	,	,	PUNCT
cana-4886	148	49	”	"	PUNCT
cana-4886	148	50	physics	physics	NOUN
cana-4886	148	51	of	of	ADP
cana-4886	148	52	fluids	fluid	NOUN
cana-4886	148	53	,	,	PUNCT
cana-4886	148	54	vol	vol	NOUN
cana-4886	148	55	.	.	PROPN
cana-4886	149	1	34	34	NUM
cana-4886	149	2	,	,	PUNCT
cana-4886	149	3	no	no	INTJ
cana-4886	149	4	.	.	NOUN
cana-4886	149	5	11	11	NUM
cana-4886	149	6	,	,	PUNCT
cana-4886	149	7	oct	oct	PROPN
cana-4886	149	8	.	.	PROPN
cana-4886	149	9	2022	2022	NUM
cana-4886	149	10	,	,	PUNCT
cana-4886	149	11	doi	doi	NOUN
cana-4886	149	12	:	:	PUNCT
cana-4886	149	13	10.1063/5.0123466	10.1063/5.0123466	NUM
cana-4886	149	14	.	.	PUNCT
cana-4886	150	1	[	[	X
cana-4886	150	2	2	2	X
cana-4886	150	3	]	]	PUNCT
cana-4886	150	4	e.	e.	PROPN
cana-4886	150	5	f.	f.	PROPN
cana-4886	150	6	toro	toro	PROPN
cana-4886	150	7	and	and	CCONJ
cana-4886	150	8	v.	v.	ADP
cana-4886	150	9	a.	a.	PROPN
cana-4886	150	10	titarev	titarev	PROPN
cana-4886	150	11	,	,	PUNCT
cana-4886	150	12	“	"	PUNCT
cana-4886	150	13	derivative	derivative	ADJ
cana-4886	150	14	riemann	riemann	PROPN
cana-4886	150	15	solvers	solver	NOUN
cana-4886	150	16	for	for	ADP
cana-4886	150	17	systems	system	NOUN
cana-4886	150	18	of	of	ADP
cana-4886	150	19	conservation	conservation	NOUN
cana-4886	150	20	laws	law	NOUN
cana-4886	150	21	and	and	CCONJ
cana-4886	150	22	ader	ader	PROPN
cana-4886	150	23	methods	method	NOUN
cana-4886	150	24	,	,	PUNCT
cana-4886	150	25	”	"	PUNCT
cana-4886	150	26	journal	journal	NOUN
cana-4886	150	27	of	of	ADP
cana-4886	150	28	computational	computational	ADJ
cana-4886	150	29	physics	physics	NOUN
cana-4886	150	30	,	,	PUNCT
cana-4886	150	31	vol	vol	NOUN
cana-4886	150	32	.	.	PROPN
cana-4886	150	33	212	212	NUM
cana-4886	150	34	,	,	PUNCT
cana-4886	150	35	no	no	INTJ
cana-4886	150	36	.	.	NOUN
cana-4886	150	37	1	1	NUM
cana-4886	150	38	,	,	PUNCT
cana-4886	150	39	pp	pp	ADJ
cana-4886	150	40	.	.	PUNCT
cana-4886	151	1	150–165	150–165	NUM
cana-4886	151	2	,	,	PUNCT
cana-4886	151	3	aug	aug	PROPN
cana-4886	151	4	.	.	PROPN
cana-4886	151	5	2005	2005	NUM
cana-4886	151	6	,	,	PUNCT
cana-4886	151	7	doi	doi	NOUN
cana-4886	151	8	:	:	PUNCT
cana-4886	151	9	10.1016	10.1016	NUM
cana-4886	151	10	/	/	SYM
cana-4886	151	11	j.jcp.2005.06.018	j.jcp.2005.06.018	PROPN
cana-4886	151	12	.	.	PUNCT
cana-4886	152	1	[	[	X
cana-4886	152	2	3	3	NUM
cana-4886	152	3	]	]	PUNCT
cana-4886	152	4	bouras	boura	NOUN
cana-4886	152	5	et	et	PROPN
cana-4886	152	6	al	al	PROPN
cana-4886	152	7	.	.	PROPN
cana-4886	152	8	,	,	PUNCT
cana-4886	152	9	“	"	PUNCT
cana-4886	152	10	investigation	investigation	NOUN
cana-4886	152	11	of	of	ADP
cana-4886	152	12	shock	shock	NOUN
cana-4886	152	13	waves	wave	NOUN
cana-4886	152	14	in	in	ADP
cana-4886	152	15	the	the	DET
cana-4886	152	16	relativistic	relativistic	ADJ
cana-4886	152	17	riemann	riemann	PROPN
cana-4886	152	18	problem	problem	NOUN
cana-4886	152	19	:	:	PUNCT
cana-4886	152	20	a	a	DET
cana-4886	152	21	comparison	comparison	NOUN
cana-4886	152	22	of	of	ADP
cana-4886	152	23	viscous	viscous	ADJ
cana-4886	152	24	fluid	fluid	NOUN
cana-4886	152	25	dynamics	dynamic	NOUN
cana-4886	152	26	to	to	ADP
cana-4886	152	27	kinetic	kinetic	ADJ
cana-4886	152	28	theory	theory	NOUN
cana-4886	152	29	,	,	PUNCT
cana-4886	152	30	”	"	PUNCT
cana-4886	152	31	physical	physical	ADJ
cana-4886	152	32	review	review	NOUN
cana-4886	152	33	c	c	NOUN
cana-4886	152	34	,	,	PUNCT
cana-4886	152	35	vol	vol	NOUN
cana-4886	152	36	.	.	PROPN
cana-4886	152	37	82	82	NUM
cana-4886	152	38	,	,	PUNCT
cana-4886	152	39	no	no	INTJ
cana-4886	152	40	.	.	NOUN
cana-4886	152	41	2	2	NUM
cana-4886	152	42	,	,	PUNCT
cana-4886	152	43	aug	aug	PROPN
cana-4886	152	44	.	.	PROPN
cana-4886	152	45	2010	2010	NUM
cana-4886	152	46	,	,	PUNCT
cana-4886	152	47	doi	doi	NOUN
cana-4886	152	48	:	:	PUNCT
cana-4886	152	49	10.1103	10.1103	NUM
cana-4886	152	50	/	/	SYM
cana-4886	152	51	physrevc.82.024910	physrevc.82.024910	NOUN
cana-4886	152	52	.	.	PUNCT
cana-4886	153	1	[	[	X
cana-4886	153	2	4	4	X
cana-4886	153	3	]	]	X
cana-4886	153	4	f.	f.	NOUN
cana-4886	153	5	alauzet	alauzet	PROPN
cana-4886	153	6	and	and	CCONJ
cana-4886	153	7	a.	a.	NOUN
cana-4886	153	8	loseille	loseille	NOUN
cana-4886	153	9	,	,	PUNCT
cana-4886	153	10	“	"	PUNCT
cana-4886	153	11	a	a	DET
cana-4886	153	12	decade	decade	NOUN
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cana-4886	153	14	progress	progress	NOUN
cana-4886	153	15	on	on	ADP
cana-4886	153	16	anisotropic	anisotropic	NOUN
cana-4886	153	17	mesh	mesh	NOUN
cana-4886	153	18	adaptation	adaptation	NOUN
cana-4886	153	19	for	for	ADP
cana-4886	153	20	computational	computational	ADJ
cana-4886	153	21	fluid	fluid	ADJ
cana-4886	153	22	dynamics	dynamic	NOUN
cana-4886	153	23	,	,	PUNCT
cana-4886	153	24	”	"	PUNCT
cana-4886	153	25	computer	computer	NOUN
cana-4886	153	26	-	-	PUNCT
cana-4886	153	27	aided	aid	VERB
cana-4886	153	28	design	design	NOUN
cana-4886	153	29	,	,	PUNCT
cana-4886	153	30	vol	vol	NOUN
cana-4886	153	31	.	.	PROPN
cana-4886	153	32	72	72	NUM
cana-4886	153	33	,	,	PUNCT
cana-4886	153	34	pp	pp	ADJ
cana-4886	153	35	.	.	PUNCT
cana-4886	154	1	13–39	13–39	NUM
cana-4886	154	2	,	,	PUNCT
cana-4886	154	3	oct	oct	PROPN
cana-4886	154	4	.	.	PROPN
cana-4886	154	5	2015	2015	NUM
cana-4886	154	6	,	,	PUNCT
cana-4886	154	7	doi	doi	NOUN
cana-4886	154	8	:	:	PUNCT
cana-4886	154	9	10.1016	10.1016	NUM
cana-4886	154	10	/	/	SYM
cana-4886	154	11	j.cad.2015.09.005	j.cad.2015.09.005	PROPN
cana-4886	154	12	.	.	PUNCT
cana-4886	155	1	[	[	X
cana-4886	155	2	5	5	X
cana-4886	155	3	]	]	PUNCT
cana-4886	155	4	d.	d.	PROPN
cana-4886	155	5	zeidan	zeidan	PROPN
cana-4886	155	6	,	,	PUNCT
cana-4886	155	7	“	"	PUNCT
cana-4886	155	8	the	the	DET
cana-4886	155	9	riemann	riemann	PROPN
cana-4886	155	10	problem	problem	NOUN
cana-4886	155	11	for	for	ADP
cana-4886	155	12	a	a	DET
cana-4886	155	13	hyperbolic	hyperbolic	ADJ
cana-4886	155	14	model	model	NOUN
cana-4886	155	15	of	of	ADP
cana-4886	155	16	two	two	NUM
cana-4886	155	17	-	-	PUNCT
cana-4886	155	18	phase	phase	NOUN
cana-4886	155	19	flow	flow	NOUN
cana-4886	155	20	in	in	ADP
cana-4886	155	21	conservative	conservative	ADJ
cana-4886	155	22	form	form	NOUN
cana-4886	155	23	,	,	PUNCT
cana-4886	155	24	”	"	PUNCT
cana-4886	155	25	international	international	ADJ
cana-4886	155	26	journal	journal	NOUN
cana-4886	155	27	of	of	ADP
cana-4886	155	28	computational	computational	ADJ
cana-4886	155	29	fluid	fluid	ADJ
cana-4886	155	30	dynamics	dynamic	NOUN
cana-4886	155	31	,	,	PUNCT
cana-4886	155	32	vol	vol	NOUN
cana-4886	155	33	.	.	PROPN
cana-4886	155	34	25	25	NUM
cana-4886	155	35	,	,	PUNCT
cana-4886	155	36	no	no	INTJ
cana-4886	155	37	.	.	NOUN
cana-4886	155	38	6	6	NUM
cana-4886	155	39	,	,	PUNCT
cana-4886	155	40	pp	pp	ADJ
cana-4886	155	41	.	.	PUNCT
cana-4886	156	1	299–318	299–318	NUM
cana-4886	156	2	,	,	PUNCT
cana-4886	156	3	jul	jul	PROPN
cana-4886	156	4	.	.	PROPN
cana-4886	156	5	2011	2011	NUM
cana-4886	156	6	,	,	PUNCT
cana-4886	156	7	doi	doi	NOUN
cana-4886	156	8	:	:	PUNCT
cana-4886	156	9	10.1080/10618562.2011.590800	10.1080/10618562.2011.590800	NUM
cana-4886	156	10	.	.	PUNCT
cana-4886	157	1	[	[	X
cana-4886	157	2	6	6	NUM
cana-4886	157	3	]	]	PUNCT
cana-4886	157	4	s.	s.	PROPN
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cana-4886	157	7	o.	o.	PROPN
cana-4886	157	8	san	san	PROPN
cana-4886	157	9	,	,	PUNCT
cana-4886	157	10	“	"	PUNCT
cana-4886	157	11	cfd	cfd	NOUN
cana-4886	157	12	julia	julia	PROPN
cana-4886	157	13	:	:	PUNCT
cana-4886	157	14	a	a	DET
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cana-4886	157	16	module	module	NOUN
cana-4886	157	17	structuring	structure	VERB
cana-4886	157	18	an	an	DET
cana-4886	157	19	introductory	introductory	ADJ
cana-4886	157	20	course	course	NOUN
cana-4886	157	21	on	on	ADP
cana-4886	157	22	computational	computational	ADJ
cana-4886	157	23	fluid	fluid	ADJ
cana-4886	157	24	dynamics	dynamic	NOUN
cana-4886	157	25	,	,	PUNCT
cana-4886	157	26	”	"	PUNCT
cana-4886	157	27	fluids	fluid	NOUN
cana-4886	157	28	,	,	PUNCT
cana-4886	157	29	vol	vol	NOUN
cana-4886	157	30	.	.	PROPN
cana-4886	157	31	4	4	NUM
cana-4886	157	32	,	,	PUNCT
cana-4886	157	33	no	no	INTJ
cana-4886	157	34	.	.	NOUN
cana-4886	157	35	3	3	NUM
cana-4886	157	36	,	,	PUNCT
cana-4886	157	37	p.	p.	NOUN
cana-4886	157	38	159	159	NUM
cana-4886	157	39	,	,	PUNCT
cana-4886	157	40	aug	aug	PROPN
cana-4886	157	41	.	.	PROPN
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cana-4886	157	43	,	,	PUNCT
cana-4886	157	44	doi	doi	NOUN
cana-4886	157	45	:	:	PUNCT
cana-4886	157	46	10.3390	10.3390	NUM
cana-4886	157	47	/	/	SYM
cana-4886	157	48	fluids4030159	fluids4030159	PROPN
cana-4886	157	49	.	.	PUNCT
cana-4886	158	1	[	[	X
cana-4886	158	2	7	7	X
cana-4886	158	3	]	]	X
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cana-4886	158	5	i.	i.	PROPN
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cana-4886	158	8	“	"	PUNCT
cana-4886	158	9	astrophysical	astrophysical	ADJ
cana-4886	158	10	fluid	fluid	NOUN
cana-4886	158	11	dynamics	dynamic	NOUN
cana-4886	158	12	,	,	PUNCT
cana-4886	158	13	”	"	PUNCT
cana-4886	158	14	journal	journal	NOUN
cana-4886	158	15	of	of	ADP
cana-4886	158	16	plasma	plasma	NOUN
cana-4886	158	17	physics	physics	PROPN
cana-4886	158	18	,	,	PUNCT
cana-4886	158	19	vol	vol	NOUN
cana-4886	158	20	.	.	PROPN
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cana-4886	158	22	,	,	PUNCT
cana-4886	158	23	no	no	INTJ
cana-4886	158	24	.	.	NOUN
cana-4886	158	25	3	3	NUM
cana-4886	158	26	,	,	PUNCT
cana-4886	158	27	may	may	AUX
cana-4886	158	28	2016	2016	NUM
cana-4886	158	29	,	,	PUNCT
cana-4886	158	30	doi	doi	NOUN
cana-4886	158	31	:	:	PUNCT
cana-4886	158	32	10.1017	10.1017	NUM
cana-4886	158	33	/	/	SYM
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cana-4886	158	35	.	.	PUNCT
cana-4886	159	1	[	[	X
cana-4886	159	2	8	8	NUM
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cana-4886	159	4	s.	s.	PROPN
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cana-4886	159	7	z.	z.	PROPN
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cana-4886	159	10	“	"	PUNCT
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cana-4886	159	12	approach	approach	NOUN
cana-4886	159	13	to	to	ADP
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cana-4886	159	15	fractional	fractional	ADJ
cana-4886	159	16	partial	partial	ADJ
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cana-4886	159	23	,	,	PUNCT
cana-4886	159	24	”	"	PUNCT
cana-4886	159	25	physics	physics	NOUN
cana-4886	159	26	letters	letter	NOUN
cana-4886	159	27	a	a	PRON
cana-4886	159	28	,	,	PUNCT
cana-4886	159	29	vol	vol	NOUN
cana-4886	159	30	.	.	PROPN
cana-4886	159	31	355	355	NUM
cana-4886	159	32	,	,	PUNCT
cana-4886	159	33	no	no	INTJ
cana-4886	159	34	.	.	PUNCT
cana-4886	160	1	4–5	4–5	NUM
cana-4886	160	2	,	,	PUNCT
cana-4886	160	3	pp	pp	ADJ
cana-4886	160	4	.	.	PUNCT
cana-4886	161	1	271–279	271–279	NUM
cana-4886	161	2	,	,	PUNCT
cana-4886	161	3	mar	mar	PROPN
cana-4886	161	4	.	.	PROPN
cana-4886	161	5	2006	2006	NUM
cana-4886	161	6	,	,	PUNCT
cana-4886	161	7	doi	doi	NOUN
cana-4886	161	8	:	:	PUNCT
cana-4886	161	9	10.1016	10.1016	NUM
cana-4886	161	10	/	/	SYM
cana-4886	161	11	j.physleta.2006.02.048	j.physleta.2006.02.048	PROPN
cana-4886	161	12	.	.	PUNCT
cana-4886	162	1	[	[	X
cana-4886	162	2	9	9	NUM
cana-4886	162	3	]	]	PUNCT
cana-4886	162	4	p.	p.	NOUN
cana-4886	162	5	woodward	woodward	PROPN
cana-4886	162	6	and	and	CCONJ
cana-4886	162	7	p.	p.	PROPN
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cana-4886	162	9	,	,	PUNCT
cana-4886	162	10	“	"	PUNCT
cana-4886	162	11	the	the	DET
cana-4886	162	12	numerical	numerical	PROPN
cana-4886	162	13	simulation	simulation	NOUN
cana-4886	162	14	of	of	ADP
cana-4886	162	15	two	two	NUM
cana-4886	162	16	-	-	PUNCT
cana-4886	162	17	dimensional	dimensional	ADJ
cana-4886	162	18	fluid	fluid	NOUN
cana-4886	162	19	flow	flow	NOUN
cana-4886	162	20	with	with	ADP
cana-4886	162	21	strong	strong	ADJ
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cana-4886	162	23	,	,	PUNCT
cana-4886	162	24	”	"	PUNCT
cana-4886	162	25	journal	journal	NOUN
cana-4886	162	26	of	of	ADP
cana-4886	162	27	computational	computational	ADJ
cana-4886	162	28	physics	physics	NOUN
cana-4886	162	29	,	,	PUNCT
cana-4886	162	30	vol	vol	NOUN
cana-4886	162	31	.	.	PROPN
cana-4886	163	1	54	54	NUM
cana-4886	163	2	,	,	PUNCT
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cana-4886	163	5	1	1	NUM
cana-4886	163	6	,	,	PUNCT
cana-4886	163	7	pp	pp	ADJ
cana-4886	163	8	.	.	PUNCT
cana-4886	164	1	115–173	115–173	NUM
cana-4886	164	2	,	,	PUNCT
cana-4886	164	3	apr	apr	PROPN
cana-4886	164	4	.	.	PROPN
cana-4886	164	5	1984	1984	NUM
cana-4886	164	6	,	,	PUNCT
cana-4886	164	7	doi	doi	NOUN
cana-4886	164	8	:	:	PUNCT
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cana-4886	164	11	9991(84)90142	9991(84)90142	NUM
cana-4886	164	12	-	-	PUNCT
cana-4886	164	13	6	6	NUM
cana-4886	164	14	.	.	PUNCT
cana-4886	165	1	[	[	X
cana-4886	165	2	10	10	NUM
cana-4886	165	3	]	]	PUNCT
cana-4886	165	4	s.	s.	PROPN
cana-4886	165	5	a.	a.	PROPN
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cana-4886	165	8	v.	v.	ADP
cana-4886	165	9	m.	m.	NOUN
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cana-4886	165	11	,	,	PUNCT
cana-4886	165	12	“	"	PUNCT
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cana-4886	165	24	”	"	PUNCT
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cana-4886	165	27	computational	computational	ADJ
cana-4886	165	28	physics	physics	NOUN
cana-4886	165	29	,	,	PUNCT
cana-4886	165	30	vol	vol	NOUN
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cana-4886	166	2	,	,	PUNCT
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cana-4886	166	5	19	19	NUM
cana-4886	166	6	,	,	PUNCT
cana-4886	166	7	pp	pp	ADJ
cana-4886	166	8	.	.	PUNCT
cana-4886	167	1	7426–7451	7426–7451	NUM
cana-4886	167	2	,	,	PUNCT
cana-4886	167	3	jul	jul	PROPN
cana-4886	167	4	.	.	PROPN
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cana-4886	167	6	,	,	PUNCT
cana-4886	167	7	doi	doi	NOUN
cana-4886	167	8	:	:	PUNCT
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cana-4886	167	10	/	/	SYM
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cana-4886	168	5	a.	a.	PROPN
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cana-4886	168	9	m.	m.	NOUN
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cana-4886	168	11	,	,	PUNCT
cana-4886	168	12	“	"	PUNCT
cana-4886	168	13	compact	compact	ADJ
cana-4886	168	14	accurately	accurately	ADV
cana-4886	168	15	boundary	boundary	ADV
cana-4886	168	16	-	-	PUNCT
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cana-4886	168	19	technique	technique	NOUN
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cana-4886	168	24	”	"	PUNCT
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cana-4886	169	2	,	,	PUNCT
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cana-4886	169	5	19	19	NUM
cana-4886	169	6	,	,	PUNCT
cana-4886	169	7	pp	pp	ADJ
cana-4886	169	8	.	.	PUNCT
cana-4886	170	1	7426–7451	7426–7451	NUM
cana-4886	170	2	,	,	PUNCT
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cana-4886	170	4	.	.	PROPN
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cana-4886	170	6	,	,	PUNCT
cana-4886	170	7	doi	doi	NOUN
cana-4886	170	8	:	:	PUNCT
cana-4886	170	9	10.1016	10.1016	NUM
cana-4886	170	10	/	/	SYM
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cana-4886	170	12	.	.	PUNCT
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cana-4886	171	2	12	12	NUM
cana-4886	171	3	]	]	PUNCT
cana-4886	171	4	m.	m.	NOUN
cana-4886	171	5	yavuz	yavuz	PROPN
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cana-4886	171	9	,	,	PUNCT
cana-4886	171	10	“	"	PUNCT
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cana-4886	171	12	solutions	solution	NOUN
cana-4886	171	13	of	of	ADP
cana-4886	171	14	the	the	DET
cana-4886	171	15	model	model	NOUN
cana-4886	171	16	describing	describe	VERB
cana-4886	171	17	fluid	fluid	NOUN
cana-4886	171	18	flow	flow	NOUN
cana-4886	171	19	using	use	VERB
cana-4886	171	20	generalized	generalized	ADJ
cana-4886	171	21	ρ	ρ	ADJ
cana-4886	171	22	-	-	PUNCT
cana-4886	171	23	laplace	laplace	NOUN
cana-4886	171	24	transform	transform	NOUN
cana-4886	171	25	method	method	NOUN
cana-4886	171	26	and	and	CCONJ
cana-4886	171	27	heat	heat	NOUN
cana-4886	171	28	balance	balance	NOUN
cana-4886	171	29	integral	integral	ADJ
cana-4886	171	30	method	method	NOUN
cana-4886	171	31	,	,	PUNCT
cana-4886	171	32	”	"	PUNCT
cana-4886	171	33	axioms	axiom	NOUN
cana-4886	171	34	,	,	PUNCT
cana-4886	171	35	vol	vol	NOUN
cana-4886	171	36	.	.	NOUN
cana-4886	171	37	9	9	NUM
cana-4886	171	38	,	,	PUNCT
cana-4886	171	39	no	no	INTJ
cana-4886	171	40	.	.	NOUN
cana-4886	171	41	4	4	NUM
cana-4886	171	42	,	,	PUNCT
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