id	sid	tid	token	lemma	pos
easat-7855	1	1	edelweiss	edelweiss	PROPN
easat-7855	1	2	applied	apply	VERB
easat-7855	1	3	science	science	NOUN
easat-7855	1	4	and	and	CCONJ
easat-7855	1	5	technology	technology	NOUN
easat-7855	1	6	issn	issn	PROPN
easat-7855	1	7	:	:	PUNCT
easat-7855	1	8	2576	2576	NUM
easat-7855	1	9	-	-	SYM
easat-7855	1	10	8484	8484	NUM
easat-7855	1	11	vol	vol	NOUN
easat-7855	1	12	.	.	PROPN
easat-7855	2	1	9	9	NUM
easat-7855	2	2	,	,	PUNCT
easat-7855	2	3	no	no	INTJ
easat-7855	2	4	.	.	NOUN
easat-7855	2	5	6	6	NUM
easat-7855	2	6	,	,	PUNCT
easat-7855	2	7	566	566	NUM
easat-7855	2	8	-	-	SYM
easat-7855	2	9	575	575	NUM
easat-7855	2	10	2025	2025	NUM
easat-7855	2	11	publisher	publisher	NOUN
easat-7855	2	12	:	:	PUNCT
easat-7855	2	13	learning	learn	VERB
easat-7855	2	14	gate	gate	NOUN
easat-7855	2	15	doi	doi	PROPN
easat-7855	2	16	:	:	PUNCT
easat-7855	2	17	10.55214/25768484.v9i6.7855	10.55214/25768484.v9i6.7855	NUM
easat-7855	2	18	©	©	PROPN
easat-7855	2	19	2025	2025	NUM
easat-7855	2	20	by	by	ADP
easat-7855	2	21	the	the	DET
easat-7855	2	22	author	author	NOUN
easat-7855	2	23	;	;	PUNCT
easat-7855	2	24	licensee	licensee	PROPN
easat-7855	2	25	learning	learning	NOUN
easat-7855	2	26	gate	gate	NOUN
easat-7855	3	1	©	©	PROPN
easat-7855	3	2	2025	2025	NUM
easat-7855	3	3	by	by	ADP
easat-7855	3	4	the	the	DET
easat-7855	3	5	author	author	NOUN
easat-7855	3	6	;	;	PUNCT
easat-7855	3	7	licensee	licensee	PROPN
easat-7855	3	8	learning	learning	NOUN
easat-7855	3	9	gate	gate	NOUN
easat-7855	3	10	history	history	NOUN
easat-7855	3	11	:	:	PUNCT
easat-7855	3	12	received	receive	VERB
easat-7855	3	13	:	:	PUNCT
easat-7855	3	14	14	14	NUM
easat-7855	3	15	march	march	NOUN
easat-7855	3	16	2025	2025	NUM
easat-7855	3	17	;	;	PUNCT
easat-7855	3	18	revised	revise	VERB
easat-7855	3	19	:	:	PUNCT
easat-7855	3	20	9	9	NUM
easat-7855	3	21	may	may	PROPN
easat-7855	3	22	2025	2025	NUM
easat-7855	3	23	;	;	PUNCT
easat-7855	3	24	accepted	accept	VERB
easat-7855	3	25	:	:	PUNCT
easat-7855	3	26	13	13	NUM
easat-7855	3	27	may	may	PROPN
easat-7855	3	28	2025	2025	NUM
easat-7855	3	29	;	;	PUNCT
easat-7855	3	30	published	publish	VERB
easat-7855	3	31	:	:	PUNCT
easat-7855	4	1	5	5	NUM
easat-7855	4	2	june	june	PROPN
easat-7855	4	3	2025	2025	NUM
easat-7855	4	4	*	*	PUNCT
easat-7855	4	5	correspondence	correspondence	NOUN
easat-7855	4	6	:	:	PUNCT
easat-7855	4	7	baasim_math@uomustansiriyah.edu.iq	baasim_math@uomustansiriyah.edu.iq	ADJ
easat-7855	4	8	advanced	advanced	ADJ
easat-7855	4	9	computational	computational	ADJ
easat-7855	4	10	techniques	technique	NOUN
easat-7855	4	11	for	for	ADP
easat-7855	4	12	solving	solve	VERB
easat-7855	4	13	partial	partial	ADJ
easat-7855	4	14	differential	differential	ADJ
easat-7855	4	15	equations	equation	NOUN
easat-7855	4	16	in	in	ADP
easat-7855	4	17	fluid	fluid	ADJ
easat-7855	4	18	dynamics	dynamic	NOUN
easat-7855	4	19	and	and	CCONJ
easat-7855	4	20	spectral	spectral	ADJ
easat-7855	4	21	domains	domain	NOUN
easat-7855	4	22	basim	basim	PROPN
easat-7855	4	23	k.	k.	PROPN
easat-7855	4	24	abbas1	abbas1	PROPN
easat-7855	4	25	*	*	PROPN
easat-7855	4	26	1computer	1computer	NUM
easat-7855	4	27	science	science	NOUN
easat-7855	4	28	department	department	NOUN
easat-7855	4	29	,	,	PUNCT
easat-7855	4	30	collage	collage	NOUN
easat-7855	4	31	of	of	ADP
easat-7855	4	32	science	science	NOUN
easat-7855	4	33	,	,	PUNCT
easat-7855	4	34	mustansiriyah	mustansiriyah	NOUN
easat-7855	4	35	university	university	NOUN
easat-7855	4	36	,	,	PUNCT
easat-7855	4	37	baghdad	baghdad	PROPN
easat-7855	4	38	-	-	PUNCT
easat-7855	4	39	iraq	iraq	PROPN
easat-7855	4	40	;	;	PUNCT
easat-7855	4	41	baasim_math@uomustansiriyah.edu.iq	baasim_math@uomustansiriyah.edu.iq	PROPN
easat-7855	4	42	(	(	PUNCT
easat-7855	4	43	b.k.a	b.k.a	PROPN
easat-7855	4	44	.	.	PUNCT
easat-7855	4	45	)	)	PUNCT
easat-7855	4	46	.	.	PUNCT
easat-7855	5	1	abstract	abstract	ADV
easat-7855	5	2	:	:	PUNCT
easat-7855	5	3	the	the	DET
easat-7855	5	4	article	article	NOUN
easat-7855	5	5	provides	provide	VERB
easat-7855	5	6	an	an	DET
easat-7855	5	7	algorithmic	algorithmic	ADJ
easat-7855	5	8	exploration	exploration	NOUN
easat-7855	5	9	of	of	ADP
easat-7855	5	10	the	the	DET
easat-7855	5	11	motion	motion	NOUN
easat-7855	5	12	of	of	ADP
easat-7855	5	13	fluids	fluid	NOUN
easat-7855	5	14	,	,	PUNCT
easat-7855	5	15	including	include	VERB
easat-7855	5	16	the	the	DET
easat-7855	5	17	solution	solution	NOUN
easat-7855	5	18	to	to	ADP
easat-7855	5	19	poisson	poisson	PROPN
easat-7855	5	20	's	's	PART
easat-7855	5	21	equation	equation	NOUN
easat-7855	5	22	across	across	ADP
easat-7855	5	23	specified	specified	ADJ
easat-7855	5	24	areas	area	NOUN
easat-7855	5	25	employing	employ	VERB
easat-7855	5	26	spectral	spectral	ADJ
easat-7855	5	27	approaches	approach	NOUN
easat-7855	5	28	.	.	PUNCT
easat-7855	6	1	the	the	DET
easat-7855	6	2	poisson	poisson	PROPN
easat-7855	6	3	problem	problem	NOUN
easat-7855	6	4	has	have	AUX
easat-7855	6	5	been	be	AUX
easat-7855	6	6	solved	solve	VERB
easat-7855	6	7	on	on	ADP
easat-7855	6	8	an	an	DET
easat-7855	6	9	annular	annular	ADJ
easat-7855	6	10	field	field	NOUN
easat-7855	6	11	,	,	PUNCT
easat-7855	6	12	resulting	result	VERB
easat-7855	6	13	in	in	ADP
easat-7855	6	14	a	a	DET
easat-7855	6	15	nearly	nearly	ADV
easat-7855	6	16	-	-	PUNCT
easat-7855	6	17	zero	zero	NUM
easat-7855	6	18	uniform	uniform	NOUN
easat-7855	6	19	resolution	resolution	NOUN
easat-7855	6	20	over	over	ADP
easat-7855	6	21	the	the	DET
easat-7855	6	22	area	area	NOUN
easat-7855	6	23	,	,	PUNCT
easat-7855	6	24	suggesting	suggest	VERB
easat-7855	6	25	great	great	ADJ
easat-7855	6	26	numerical	numerical	ADJ
easat-7855	6	27	accuracy	accuracy	NOUN
easat-7855	6	28	.	.	PUNCT
easat-7855	7	1	velocity	velocity	NOUN
easat-7855	7	2	and	and	CCONJ
easat-7855	7	3	pressure	pressure	NOUN
easat-7855	7	4	patterns	pattern	NOUN
easat-7855	7	5	have	have	AUX
easat-7855	7	6	been	be	AUX
easat-7855	7	7	established	establish	VERB
easat-7855	7	8	within	within	ADP
easat-7855	7	9	a	a	DET
easat-7855	7	10	rectangular	rectangular	ADJ
easat-7855	7	11	realm	realm	NOUN
easat-7855	7	12	,	,	PUNCT
easat-7855	7	13	and	and	CCONJ
easat-7855	7	14	the	the	DET
easat-7855	7	15	findings	finding	NOUN
easat-7855	7	16	corresponded	correspond	VERB
easat-7855	7	17	throughout	throughout	ADP
easat-7855	7	18	the	the	DET
easat-7855	7	19	vertical	vertical	NOUN
easat-7855	7	20	as	as	ADV
easat-7855	7	21	well	well	ADV
easat-7855	7	22	as	as	ADP
easat-7855	7	23	horizontal	horizontal	ADJ
easat-7855	7	24	elements	element	NOUN
easat-7855	7	25	,	,	PUNCT
easat-7855	7	26	having	have	VERB
easat-7855	7	27	near	near	ADV
easat-7855	7	28	-	-	PUNCT
easat-7855	7	29	zero	zero	NUM
easat-7855	7	30	values	value	NOUN
easat-7855	7	31	indicating	indicate	VERB
easat-7855	7	32	an	an	DET
easat-7855	7	33	evenly	evenly	ADV
easat-7855	7	34	simulated	simulate	VERB
easat-7855	7	35	system	system	NOUN
easat-7855	7	36	.	.	PUNCT
easat-7855	8	1	furthermore	furthermore	ADV
easat-7855	8	2	,	,	PUNCT
easat-7855	8	3	both	both	PRON
easat-7855	8	4	velocity	velocity	VERB
easat-7855	8	5	scalar	scalar	ADJ
easat-7855	8	6	sectors	sector	NOUN
easat-7855	8	7	and	and	CCONJ
easat-7855	8	8	maxima	maxima	NOUN
easat-7855	8	9	contour	contour	NOUN
easat-7855	8	10	graphs	graph	NOUN
easat-7855	8	11	exhibited	exhibit	VERB
easat-7855	8	12	consistent	consistent	ADJ
easat-7855	8	13	flow	flow	NOUN
easat-7855	8	14	characteristics	characteristic	NOUN
easat-7855	8	15	and	and	CCONJ
easat-7855	8	16	variable	variable	ADJ
easat-7855	8	17	velocity	velocity	NOUN
easat-7855	8	18	magnitudes	magnitude	NOUN
easat-7855	8	19	,	,	PUNCT
easat-7855	8	20	which	which	PRON
easat-7855	8	21	are	be	AUX
easat-7855	8	22	important	important	ADJ
easat-7855	8	23	for	for	ADP
easat-7855	8	24	comprehending	comprehending	ADJ
easat-7855	8	25	fluid	fluid	ADJ
easat-7855	8	26	dynamics	dynamic	NOUN
easat-7855	8	27	in	in	ADP
easat-7855	8	28	restricted	restricted	ADJ
easat-7855	8	29	situations	situation	NOUN
easat-7855	8	30	.	.	PUNCT
easat-7855	9	1	the	the	DET
easat-7855	9	2	present	present	ADJ
easat-7855	9	3	investigation	investigation	NOUN
easat-7855	9	4	presents	present	VERB
easat-7855	9	5	an	an	DET
easat-7855	9	6	innovative	innovative	ADJ
easat-7855	9	7	use	use	NOUN
easat-7855	9	8	of	of	ADP
easat-7855	9	9	spectral	spectral	ADJ
easat-7855	9	10	approaches	approach	NOUN
easat-7855	9	11	for	for	ADP
easat-7855	9	12	handling	handle	VERB
easat-7855	9	13	complicated	complicated	ADJ
easat-7855	9	14	,	,	PUNCT
easat-7855	9	15	unusual	unusual	ADJ
easat-7855	9	16	field	field	NOUN
easat-7855	9	17	geometries	geometry	NOUN
easat-7855	9	18	like	like	ADP
easat-7855	9	19	circular	circular	ADJ
easat-7855	9	20	and	and	CCONJ
easat-7855	9	21	rectangular	rectangular	ADJ
easat-7855	9	22	domains	domain	NOUN
easat-7855	9	23	,	,	PUNCT
easat-7855	9	24	which	which	PRON
easat-7855	9	25	are	be	AUX
easat-7855	9	26	generally	generally	ADV
easat-7855	9	27	difficult	difficult	ADJ
easat-7855	9	28	to	to	PART
easat-7855	9	29	account	account	VERB
easat-7855	9	30	for	for	ADP
easat-7855	9	31	using	use	VERB
easat-7855	9	32	typical	typical	ADJ
easat-7855	9	33	finite	finite	ADJ
easat-7855	9	34	element	element	NOUN
easat-7855	9	35	computation	computation	NOUN
easat-7855	9	36	or	or	CCONJ
easat-7855	9	37	infinite	infinite	ADJ
easat-7855	9	38	difference	difference	NOUN
easat-7855	9	39	approaches	approach	NOUN
easat-7855	9	40	.	.	PUNCT
easat-7855	10	1	the	the	DET
easat-7855	10	2	method	method	NOUN
easat-7855	10	3	merely	merely	ADV
easat-7855	10	4	boosts	boost	VERB
easat-7855	10	5	the	the	DET
easat-7855	10	6	effectiveness	effectiveness	NOUN
easat-7855	10	7	of	of	ADP
easat-7855	10	8	computation	computation	NOUN
easat-7855	10	9	;	;	PUNCT
easat-7855	10	10	however	however	ADV
easat-7855	10	11	,	,	PUNCT
easat-7855	10	12	it	it	PRON
easat-7855	10	13	additionally	additionally	ADV
easat-7855	10	14	enhances	enhance	VERB
easat-7855	10	15	solution	solution	NOUN
easat-7855	10	16	precision	precision	NOUN
easat-7855	10	17	in	in	ADP
easat-7855	10	18	boundary	boundary	ADJ
easat-7855	10	19	-	-	PUNCT
easat-7855	10	20	sensitive	sensitive	ADJ
easat-7855	10	21	systems	system	NOUN
easat-7855	10	22	such	such	ADJ
easat-7855	10	23	as	as	ADP
easat-7855	10	24	fluid	fluid	ADJ
easat-7855	10	25	mechanics	mechanic	NOUN
easat-7855	10	26	.	.	PUNCT
easat-7855	11	1	the	the	DET
easat-7855	11	2	newly	newly	ADV
easat-7855	11	3	developed	develop	VERB
easat-7855	11	4	incorporation	incorporation	NOUN
easat-7855	11	5	of	of	ADP
easat-7855	11	6	this	this	DET
easat-7855	11	7	approach	approach	NOUN
easat-7855	11	8	within	within	ADP
easat-7855	11	9	the	the	DET
easat-7855	11	10	inquiry	inquiry	NOUN
easat-7855	11	11	of	of	ADP
easat-7855	11	12	fluid	fluid	ADJ
easat-7855	11	13	behavior	behavior	NOUN
easat-7855	11	14	under	under	ADP
easat-7855	11	15	shifting	shift	VERB
easat-7855	11	16	boundary	boundary	ADJ
easat-7855	11	17	conditions	condition	NOUN
easat-7855	11	18	opens	open	VERB
easat-7855	11	19	the	the	DET
easat-7855	11	20	door	door	NOUN
easat-7855	11	21	to	to	ADP
easat-7855	11	22	more	more	ADV
easat-7855	11	23	rigorous	rigorous	ADJ
easat-7855	11	24	calculations	calculation	NOUN
easat-7855	11	25	in	in	ADP
easat-7855	11	26	commercial	commercial	ADJ
easat-7855	11	27	and	and	CCONJ
easat-7855	11	28	academic	academic	ADJ
easat-7855	11	29	software	software	NOUN
easat-7855	11	30	,	,	PUNCT
easat-7855	11	31	representing	represent	VERB
easat-7855	11	32	a	a	DET
easat-7855	11	33	substantial	substantial	ADJ
easat-7855	11	34	advance	advance	NOUN
easat-7855	11	35	in	in	ADP
easat-7855	11	36	the	the	DET
easat-7855	11	37	computational	computational	ADJ
easat-7855	11	38	investigation	investigation	NOUN
easat-7855	11	39	of	of	ADP
easat-7855	11	40	equations	equation	NOUN
easat-7855	11	41	involving	involve	VERB
easat-7855	11	42	partial	partial	ADJ
easat-7855	11	43	differentials	differential	NOUN
easat-7855	11	44	.	.	PUNCT
easat-7855	12	1	keywords	keyword	NOUN
easat-7855	12	2	:	:	PUNCT
easat-7855	12	3	fluid	fluid	ADJ
easat-7855	12	4	dynamics	dynamic	NOUN
easat-7855	12	5	,	,	PUNCT
easat-7855	12	6	optimization	optimization	NOUN
easat-7855	12	7	approach	approach	NOUN
easat-7855	12	8	,	,	PUNCT
easat-7855	12	9	partial	partial	ADJ
easat-7855	12	10	differential	differential	NOUN
easat-7855	12	11	,	,	PUNCT
easat-7855	12	12	poisson	poisson	PROPN
easat-7855	12	13	's	's	PART
easat-7855	12	14	equation	equation	NOUN
easat-7855	12	15	,	,	PUNCT
easat-7855	12	16	spectral	spectral	ADJ
easat-7855	12	17	domains	domain	NOUN
easat-7855	12	18	.	.	PUNCT
easat-7855	13	1	1	1	X
easat-7855	13	2	.	.	X
easat-7855	13	3	introduction	introduction	NOUN
easat-7855	13	4	the	the	DET
easat-7855	13	5	investigation	investigation	NOUN
easat-7855	13	6	of	of	ADP
easat-7855	13	7	fluid	fluid	ADJ
easat-7855	13	8	circulation	circulation	NOUN
easat-7855	13	9	and	and	CCONJ
easat-7855	13	10	computing	compute	VERB
easat-7855	13	11	the	the	DET
easat-7855	13	12	solutions	solution	NOUN
easat-7855	13	13	of	of	ADP
easat-7855	13	14	parametric	parametric	ADJ
easat-7855	13	15	differentiation	differentiation	NOUN
easat-7855	13	16	problems	problem	NOUN
easat-7855	13	17	(	(	PUNCT
easat-7855	13	18	pdes	pde	NOUN
easat-7855	13	19	)	)	PUNCT
easat-7855	13	20	are	be	AUX
easat-7855	13	21	essential	essential	ADJ
easat-7855	13	22	in	in	ADP
easat-7855	13	23	an	an	DET
easat-7855	13	24	array	array	NOUN
easat-7855	13	25	of	of	ADP
easat-7855	13	26	scientific	scientific	ADJ
easat-7855	13	27	and	and	CCONJ
easat-7855	13	28	engineering	engineering	NOUN
easat-7855	13	29	fields	field	NOUN
easat-7855	13	30	.	.	PUNCT
easat-7855	14	1	fluid	fluid	ADJ
easat-7855	14	2	behavior	behavior	NOUN
easat-7855	14	3	,	,	PUNCT
easat-7855	14	4	regulated	regulate	VERB
easat-7855	14	5	by	by	ADP
easat-7855	14	6	the	the	DET
easat-7855	14	7	navier	navier	NOUN
easat-7855	14	8	-	-	PUNCT
easat-7855	14	9	stokes	stoke	NOUN
easat-7855	14	10	formulas	formula	NOUN
easat-7855	14	11	,	,	PUNCT
easat-7855	14	12	explains	explain	VERB
easat-7855	14	13	fluid	fluid	ADJ
easat-7855	14	14	motion	motion	NOUN
easat-7855	14	15	and	and	CCONJ
easat-7855	14	16	is	be	AUX
easat-7855	14	17	critical	critical	ADJ
easat-7855	14	18	to	to	ADP
easat-7855	14	19	comprehension	comprehension	NOUN
easat-7855	14	20	of	of	ADP
easat-7855	14	21	behaviors	behavior	NOUN
easat-7855	14	22	in	in	ADP
easat-7855	14	23	aerodynamics	aerodynamic	NOUN
easat-7855	14	24	,	,	PUNCT
easat-7855	14	25	which	which	PRON
easat-7855	14	26	atmospheric	atmospheric	ADJ
easat-7855	14	27	models	model	NOUN
easat-7855	14	28	,	,	PUNCT
easat-7855	14	29	hurricanes	hurricane	NOUN
easat-7855	14	30	,	,	PUNCT
easat-7855	14	31	and	and	CCONJ
easat-7855	14	32	manufacturing	manufacturing	NOUN
easat-7855	14	33	procedures	procedure	NOUN
easat-7855	14	34	.	.	PUNCT
easat-7855	15	1	nevertheless	nevertheless	ADV
easat-7855	15	2	because	because	SCONJ
easat-7855	15	3	of	of	ADP
easat-7855	15	4	complex	complex	ADJ
easat-7855	15	5	variability	variability	NOUN
easat-7855	15	6	as	as	ADV
easat-7855	15	7	well	well	ADV
easat-7855	15	8	as	as	ADP
easat-7855	15	9	the	the	DET
easat-7855	15	10	complexities	complexity	NOUN
easat-7855	15	11	of	of	ADP
easat-7855	15	12	the	the	DET
easat-7855	15	13	constraints	constraint	NOUN
easat-7855	15	14	on	on	ADP
easat-7855	15	15	the	the	DET
easat-7855	15	16	boundary	boundary	ADJ
easat-7855	15	17	,	,	PUNCT
easat-7855	15	18	mathematical	mathematical	ADJ
easat-7855	15	19	fixes	fix	NOUN
easat-7855	15	20	for	for	ADP
easat-7855	15	21	those	those	DET
easat-7855	15	22	formulas	formula	NOUN
easat-7855	15	23	are	be	AUX
easat-7855	15	24	frequently	frequently	ADV
easat-7855	15	25	unachievable	unachievable	ADJ
easat-7855	15	26	,	,	PUNCT
easat-7855	15	27	mandating	mandate	VERB
easat-7855	15	28	the	the	DET
easat-7855	15	29	employment	employment	NOUN
easat-7855	15	30	of	of	ADP
easat-7855	15	31	mathematical	mathematical	ADJ
easat-7855	15	32	techniques	technique	NOUN
easat-7855	15	33	[	[	X
easat-7855	15	34	1	1	NUM
easat-7855	15	35	-	-	SYM
easat-7855	15	36	3	3	NUM
easat-7855	15	37	]	]	PUNCT
easat-7855	15	38	.	.	PUNCT
easat-7855	16	1	traditional	traditional	ADJ
easat-7855	16	2	numerical	numerical	ADJ
easat-7855	16	3	approaches	approach	NOUN
easat-7855	16	4	,	,	PUNCT
easat-7855	16	5	including	include	VERB
easat-7855	16	6	the	the	DET
easat-7855	16	7	finite	finite	ADJ
easat-7855	16	8	difference	difference	NOUN
easat-7855	16	9	technique	technique	NOUN
easat-7855	16	10	(	(	PUNCT
easat-7855	16	11	fdm	fdm	NOUN
easat-7855	16	12	)	)	PUNCT
easat-7855	16	13	,	,	PUNCT
easat-7855	16	14	are	be	AUX
easat-7855	16	15	frequently	frequently	ADV
easat-7855	16	16	used	use	VERB
easat-7855	16	17	to	to	PART
easat-7855	16	18	estimate	estimate	VERB
easat-7855	16	19	pde	pde	NOUN
easat-7855	16	20	approaches	approach	NOUN
easat-7855	16	21	,	,	PUNCT
easat-7855	16	22	notably	notably	ADV
easat-7855	16	23	in	in	ADP
easat-7855	16	24	the	the	DET
easat-7855	16	25	study	study	NOUN
easat-7855	16	26	of	of	ADP
easat-7855	16	27	fluid	fluid	ADJ
easat-7855	16	28	dynamics	dynamic	NOUN
easat-7855	16	29	.	.	PUNCT
easat-7855	17	1	these	these	DET
easat-7855	17	2	techniques	technique	NOUN
easat-7855	17	3	isolate	isolate	VERB
easat-7855	17	4	the	the	DET
easat-7855	17	5	space	space	NOUN
easat-7855	17	6	and	and	CCONJ
easat-7855	17	7	timing	timing	NOUN
easat-7855	17	8	areas	area	NOUN
easat-7855	17	9	,	,	PUNCT
easat-7855	17	10	enabling	enable	VERB
easat-7855	17	11	incremental	incremental	ADJ
easat-7855	17	12	cooperation	cooperation	NOUN
easat-7855	17	13	of	of	ADP
easat-7855	17	14	the	the	DET
easat-7855	17	15	controlling	controlling	NOUN
easat-7855	17	16	formulas	formula	NOUN
easat-7855	17	17	.	.	PUNCT
easat-7855	17	18	.	.	PUNCT
easat-7855	18	1	while	while	SCONJ
easat-7855	18	2	its	its	PRON
easat-7855	18	3	practicality	practicality	NOUN
easat-7855	18	4	,	,	PUNCT
easat-7855	18	5	fdm	fdm	NOUN
easat-7855	18	6	may	may	AUX
easat-7855	18	7	prove	prove	VERB
easat-7855	18	8	costly	costly	ADJ
easat-7855	18	9	to	to	PART
easat-7855	18	10	compute	compute	VERB
easat-7855	18	11	and	and	CCONJ
easat-7855	18	12	have	have	VERB
easat-7855	18	13	challenges	challenge	NOUN
easat-7855	18	14	with	with	ADP
easat-7855	18	15	statistical	statistical	ADJ
easat-7855	18	16	volatility	volatility	NOUN
easat-7855	18	17	as	as	ADV
easat-7855	18	18	well	well	ADV
easat-7855	18	19	as	as	ADP
easat-7855	18	20	low	low	ADJ
easat-7855	18	21	precision	precision	NOUN
easat-7855	18	22	when	when	SCONJ
easat-7855	18	23	used	use	VERB
easat-7855	18	24	with	with	ADP
easat-7855	18	25	complicated	complicated	ADJ
easat-7855	18	26	shapes	shape	NOUN
easat-7855	18	27	or	or	CCONJ
easat-7855	18	28	big	big	ADJ
easat-7855	18	29	-	-	PUNCT
easat-7855	18	30	scale	scale	NOUN
easat-7855	18	31	issues	issue	NOUN
easat-7855	18	32	[	[	X
easat-7855	18	33	2	2	NUM
easat-7855	18	34	-	-	SYM
easat-7855	18	35	4	4	NUM
easat-7855	18	36	]	]	PUNCT
easat-7855	18	37	.	.	PUNCT
easat-7855	19	1	recent	recent	ADJ
easat-7855	19	2	technological	technological	ADJ
easat-7855	19	3	advances	advance	NOUN
easat-7855	19	4	in	in	ADP
easat-7855	19	5	the	the	DET
easat-7855	19	6	ability	ability	NOUN
easat-7855	19	7	to	to	PART
easat-7855	19	8	process	process	VERB
easat-7855	19	9	large	large	ADJ
easat-7855	19	10	amounts	amount	NOUN
easat-7855	19	11	of	of	ADP
easat-7855	19	12	data	datum	NOUN
easat-7855	19	13	by	by	ADP
easat-7855	19	14	leveraging	leverage	VERB
easat-7855	19	15	graphics	graphic	NOUN
easat-7855	19	16	processing	processing	NOUN
easat-7855	19	17	units	unit	NOUN
easat-7855	19	18	(	(	PUNCT
easat-7855	19	19	gpus	gpu	NOUN
easat-7855	19	20	)	)	PUNCT
easat-7855	19	21	have	have	AUX
easat-7855	19	22	dramatically	dramatically	ADV
easat-7855	19	23	improved	improve	VERB
easat-7855	19	24	the	the	DET
easat-7855	19	25	performance	performance	NOUN
easat-7855	19	26	of	of	ADP
easat-7855	19	27	simulations	simulation	NOUN
easat-7855	19	28	.	.	PUNCT
easat-7855	20	1	gpus	gpus	PROPN
easat-7855	20	2	can	can	AUX
easat-7855	20	3	significantly	significantly	ADV
easat-7855	20	4	reduce	reduce	VERB
easat-7855	20	5	computation	computation	NOUN
easat-7855	20	6	times	time	NOUN
easat-7855	20	7	,	,	PUNCT
easat-7855	20	8	allowing	allow	VERB
easat-7855	20	9	for	for	ADP
easat-7855	20	10	faster	fast	ADJ
easat-7855	20	11	modeling	modeling	NOUN
easat-7855	20	12	of	of	ADP
easat-7855	20	13	more	more	ADJ
easat-7855	20	14	complex	complex	ADJ
easat-7855	20	15	systems	system	NOUN
easat-7855	20	16	as	as	SCONJ
easat-7855	20	17	found	find	VERB
easat-7855	20	18	in	in	ADP
easat-7855	20	19	pytorch	pytorch	NOUN
easat-7855	20	20	.	.	PUNCT
easat-7855	21	1	this	this	DET
easat-7855	21	2	ability	ability	NOUN
easat-7855	21	3	is	be	AUX
easat-7855	21	4	very	very	ADV
easat-7855	21	5	important	important	ADJ
easat-7855	21	6	in	in	ADP
easat-7855	21	7	computations	computation	NOUN
easat-7855	21	8	that	that	PRON
easat-7855	21	9	may	may	AUX
easat-7855	21	10	require	require	VERB
easat-7855	21	11	continuous	continuous	ADJ
easat-7855	21	12	operation	operation	NOUN
easat-7855	21	13	and	and	CCONJ
easat-7855	21	14	statement	statement	NOUN
easat-7855	21	15	making	make	VERB
easat-7855	21	16	and	and	CCONJ
easat-7855	21	17	processing	processing	NOUN
easat-7855	21	18	hugged	hug	VERB
easat-7855	21	19	data	datum	NOUN
easat-7855	21	20	[	[	X
easat-7855	21	21	5	5	NUM
easat-7855	21	22	-	-	SYM
easat-7855	21	23	7	7	NUM
easat-7855	21	24	]	]	PUNCT
easat-7855	21	25	.	.	PUNCT
easat-7855	22	1	combining	combine	VERB
easat-7855	22	2	several	several	ADJ
easat-7855	22	3	popular	popular	ADJ
easat-7855	22	4	methods	method	NOUN
easat-7855	22	5	is	be	AUX
easat-7855	22	6	of	of	ADP
easat-7855	22	7	great	great	ADJ
easat-7855	22	8	https://orcid.org/0000-0001-5572-2535	https://orcid.org/0000-0001-5572-2535	NOUN
easat-7855	22	9	567	567	NUM
easat-7855	22	10	edelweiss	edelweiss	PROPN
easat-7855	22	11	applied	apply	VERB
easat-7855	22	12	science	science	NOUN
easat-7855	22	13	and	and	CCONJ
easat-7855	22	14	technology	technology	NOUN
easat-7855	22	15	issn	issn	PROPN
easat-7855	22	16	:	:	PUNCT
easat-7855	22	17	2576	2576	NUM
easat-7855	22	18	-	-	SYM
easat-7855	22	19	8484	8484	NUM
easat-7855	22	20	vol	vol	NOUN
easat-7855	22	21	.	.	PROPN
easat-7855	23	1	9	9	NUM
easat-7855	23	2	,	,	PUNCT
easat-7855	23	3	no	no	INTJ
easat-7855	23	4	.	.	NOUN
easat-7855	24	1	6	6	NUM
easat-7855	24	2	:	:	SYM
easat-7855	24	3	566	566	NUM
easat-7855	24	4	-	-	SYM
easat-7855	24	5	575	575	NUM
easat-7855	24	6	,	,	PUNCT
easat-7855	24	7	2025	2025	NUM
easat-7855	24	8	doi	doi	NOUN
easat-7855	24	9	:	:	PUNCT
easat-7855	24	10	10.55214/25768484.v9i6.7855	10.55214/25768484.v9i6.7855	NUM
easat-7855	24	11	©	©	PROPN
easat-7855	24	12	2025	2025	NUM
easat-7855	24	13	by	by	ADP
easat-7855	24	14	the	the	DET
easat-7855	24	15	author	author	NOUN
easat-7855	24	16	;	;	PUNCT
easat-7855	24	17	licensee	licensee	PROPN
easat-7855	24	18	learning	learn	VERB
easat-7855	24	19	gate	gate	NOUN
easat-7855	24	20	interest	interest	NOUN
easat-7855	24	21	when	when	SCONJ
easat-7855	24	22	dealing	deal	VERB
easat-7855	24	23	with	with	ADP
easat-7855	24	24	exceptionally	exceptionally	ADV
easat-7855	24	25	high	high	ADJ
easat-7855	24	26	-	-	PUNCT
easat-7855	24	27	accuracy	accuracy	NOUN
easat-7855	24	28	partial	partial	ADJ
easat-7855	24	29	differential	differential	NOUN
easat-7855	24	30	equations	equation	NOUN
easat-7855	24	31	,	,	PUNCT
easat-7855	24	32	such	such	ADJ
easat-7855	24	33	as	as	ADP
easat-7855	24	34	combining	combine	VERB
easat-7855	24	35	fdm	fdm	NOUN
easat-7855	24	36	and	and	CCONJ
easat-7855	24	37	gpu	gpu	NOUN
easat-7855	24	38	-	-	PUNCT
easat-7855	24	39	accelerated	accelerate	VERB
easat-7855	24	40	techniques	technique	NOUN
easat-7855	24	41	.	.	PUNCT
easat-7855	25	1	that	that	SCONJ
easat-7855	25	2	spectral	spectral	ADJ
easat-7855	25	3	methodologies	methodology	NOUN
easat-7855	25	4	needed	need	VERB
easat-7855	25	5	altering	alter	VERB
easat-7855	25	6	the	the	DET
easat-7855	25	7	matter	matter	NOUN
easat-7855	25	8	within	within	ADP
easat-7855	25	9	an	an	DET
easat-7855	25	10	uncommon	uncommon	ADJ
easat-7855	25	11	adjusting	adjusting	NOUN
easat-7855	25	12	,	,	PUNCT
easat-7855	25	13	such	such	ADJ
easat-7855	25	14	as	as	ADP
easat-7855	25	15	fourier	fourier	ADJ
easat-7855	25	16	space	space	NOUN
easat-7855	25	17	,	,	PUNCT
easat-7855	25	18	where	where	SCONJ
easat-7855	25	19	it	it	PRON
easat-7855	25	20	can	can	AUX
easat-7855	25	21	be	be	AUX
easat-7855	25	22	discussed	discuss	VERB
easat-7855	25	23	to	to	ADP
easat-7855	25	24	greater	great	ADJ
easat-7855	25	25	precision	precision	NOUN
easat-7855	25	26	.	.	PUNCT
easat-7855	26	1	this	this	DET
easat-7855	26	2	type	type	NOUN
easat-7855	26	3	of	of	ADP
easat-7855	26	4	approach	approach	NOUN
easat-7855	26	5	especially	especially	ADV
easat-7855	26	6	essential	essential	ADJ
easat-7855	26	7	at	at	ADP
easat-7855	26	8	working	work	VERB
easat-7855	26	9	with	with	ADP
easat-7855	26	10	poisson	poisson	PROPN
easat-7855	26	11	's	's	PART
easat-7855	26	12	solution	solution	NOUN
easat-7855	26	13	in	in	ADP
easat-7855	26	14	complete	complete	ADJ
easat-7855	26	15	or	or	CCONJ
easat-7855	26	16	sphere	sphere	NOUN
easat-7855	26	17	territories	territory	NOUN
easat-7855	26	18	,	,	PUNCT
easat-7855	26	19	when	when	SCONJ
easat-7855	26	20	traditional	traditional	ADJ
easat-7855	26	21	grid	grid	NOUN
easat-7855	26	22	-	-	PUNCT
easat-7855	26	23	based	base	VERB
easat-7855	26	24	strategies	strategy	NOUN
easat-7855	26	25	may	may	AUX
easat-7855	26	26	fail	fail	VERB
easat-7855	26	27	[	[	X
easat-7855	26	28	8	8	NUM
easat-7855	26	29	-	-	SYM
easat-7855	26	30	10	10	NUM
easat-7855	26	31	]	]	PUNCT
easat-7855	26	32	.	.	PUNCT
easat-7855	27	1	in	in	ADP
easat-7855	27	2	this	this	DET
easat-7855	27	3	research	research	NOUN
easat-7855	27	4	,	,	PUNCT
easat-7855	27	5	three	three	NUM
easat-7855	27	6	computational	computational	ADJ
easat-7855	27	7	algorithms	algorithm	NOUN
easat-7855	27	8	will	will	AUX
easat-7855	27	9	be	be	AUX
easat-7855	27	10	analyzed	analyze	VERB
easat-7855	27	11	,	,	PUNCT
easat-7855	27	12	and	and	CCONJ
easat-7855	27	13	discussed	discuss	VERB
easat-7855	27	14	,	,	PUNCT
easat-7855	27	15	and	and	CCONJ
easat-7855	27	16	the	the	DET
easat-7855	27	17	performance	performance	NOUN
easat-7855	27	18	of	of	ADP
easat-7855	27	19	each	each	DET
easat-7855	27	20	one	one	NOUN
easat-7855	27	21	will	will	AUX
easat-7855	27	22	be	be	AUX
easat-7855	27	23	analyzed	analyze	VERB
easat-7855	27	24	separately	separately	ADV
easat-7855	27	25	,	,	PUNCT
easat-7855	27	26	and	and	CCONJ
easat-7855	27	27	then	then	ADV
easat-7855	27	28	they	they	PRON
easat-7855	27	29	will	will	AUX
easat-7855	27	30	be	be	AUX
easat-7855	27	31	involved	involve	VERB
easat-7855	27	32	in	in	ADP
easat-7855	27	33	analyzing	analyze	VERB
easat-7855	27	34	the	the	DET
easat-7855	27	35	results	result	NOUN
easat-7855	27	36	.	.	PUNCT
easat-7855	28	1	the	the	DET
easat-7855	28	2	aforementioned	aforementioned	ADJ
easat-7855	28	3	methods	method	NOUN
easat-7855	28	4	include	include	VERB
easat-7855	28	5	the	the	DET
easat-7855	28	6	limited	limited	ADJ
easat-7855	28	7	difference	difference	NOUN
easat-7855	28	8	process	process	NOUN
easat-7855	28	9	,	,	PUNCT
easat-7855	28	10	gpu	gpu	NOUN
easat-7855	28	11	-	-	PUNCT
easat-7855	28	12	accelerated	accelerate	VERB
easat-7855	28	13	navierstokes	navierstoke	NOUN
easat-7855	28	14	prediction	prediction	NOUN
easat-7855	28	15	with	with	ADP
easat-7855	28	16	pytorch	pytorch	NOUN
easat-7855	28	17	,	,	PUNCT
easat-7855	28	18	and	and	CCONJ
easat-7855	28	19	spectroscopy	spectroscopy	VERB
easat-7855	28	20	methods	method	NOUN
easat-7855	28	21	,	,	PUNCT
easat-7855	28	22	and	and	CCONJ
easat-7855	28	23	this	this	PRON
easat-7855	28	24	can	can	AUX
easat-7855	28	25	be	be	AUX
easat-7855	28	26	employed	employ	VERB
easat-7855	28	27	to	to	PART
easat-7855	28	28	solve	solve	VERB
easat-7855	28	29	fluid	fluid	ADJ
easat-7855	28	30	science	science	NOUN
easat-7855	28	31	problems	problem	NOUN
easat-7855	28	32	.	.	PUNCT
easat-7855	29	1	putting	put	VERB
easat-7855	29	2	pde	pde	NOUN
easat-7855	29	3	devices	device	NOUN
easat-7855	29	4	into	into	ADP
easat-7855	29	5	different	different	ADJ
easat-7855	29	6	areas	area	NOUN
easat-7855	29	7	.	.	PUNCT
easat-7855	30	1	the	the	DET
easat-7855	30	2	investigation	investigation	NOUN
easat-7855	30	3	is	be	AUX
easat-7855	30	4	unique	unique	ADJ
easat-7855	30	5	in	in	ADP
easat-7855	30	6	that	that	SCONJ
easat-7855	30	7	it	it	PRON
easat-7855	30	8	compares	compare	VERB
easat-7855	30	9	any	any	PRON
easat-7855	30	10	of	of	ADP
easat-7855	30	11	these	these	DET
easat-7855	30	12	alternative	alternative	ADJ
easat-7855	30	13	techniques	technique	NOUN
easat-7855	30	14	,	,	PUNCT
easat-7855	30	15	highlighting	highlight	VERB
easat-7855	30	16	every	every	DET
easat-7855	30	17	one	one	NUM
easat-7855	30	18	their	their	PRON
easat-7855	30	19	strengths	strength	NOUN
easat-7855	30	20	and	and	CCONJ
easat-7855	30	21	drawbacks	drawback	NOUN
easat-7855	30	22	.	.	PUNCT
easat-7855	31	1	the	the	DET
easat-7855	31	2	study	study	NOUN
easat-7855	31	3	contributes	contribute	VERB
easat-7855	31	4	to	to	ADP
easat-7855	31	5	our	our	PRON
easat-7855	31	6	understanding	understanding	NOUN
easat-7855	31	7	of	of	ADP
easat-7855	31	8	digital	digital	ADJ
easat-7855	31	9	techniques	technique	NOUN
easat-7855	31	10	in	in	ADP
easat-7855	31	11	fluid	fluid	ADJ
easat-7855	31	12	motion	motion	NOUN
easat-7855	31	13	while	while	SCONJ
easat-7855	31	14	giving	give	VERB
easat-7855	31	15	views	view	NOUN
easat-7855	31	16	on	on	ADP
easat-7855	31	17	optimal	optimal	ADJ
easat-7855	31	18	processing	processing	NOUN
easat-7855	31	19	power	power	NOUN
easat-7855	31	20	for	for	ADP
easat-7855	31	21	advanced	advanced	ADJ
easat-7855	31	22	pde	pde	NOUN
easat-7855	31	23	answers	answer	NOUN
easat-7855	31	24	.	.	PUNCT
easat-7855	32	1	after	after	ADP
easat-7855	32	2	introduction	introduction	NOUN
easat-7855	32	3	,	,	PUNCT
easat-7855	32	4	the	the	DET
easat-7855	32	5	rest	rest	NOUN
easat-7855	32	6	paper	paper	NOUN
easat-7855	32	7	is	be	AUX
easat-7855	32	8	ordered	order	VERB
easat-7855	32	9	as	as	ADP
easat-7855	32	10	,	,	PUNCT
easat-7855	32	11	related	relate	VERB
easat-7855	32	12	works	work	NOUN
easat-7855	32	13	in	in	ADP
easat-7855	32	14	the	the	DET
easat-7855	32	15	section2	section2	NOUN
easat-7855	32	16	,	,	PUNCT
easat-7855	32	17	proposed	propose	VERB
easat-7855	32	18	system	system	NOUN
easat-7855	32	19	in	in	ADP
easat-7855	32	20	section	section	NOUN
easat-7855	32	21	three	three	NUM
easat-7855	32	22	,	,	PUNCT
easat-7855	32	23	the	the	DET
easat-7855	32	24	results	result	NOUN
easat-7855	32	25	are	be	AUX
easat-7855	32	26	found	find	VERB
easat-7855	32	27	in	in	ADP
easat-7855	32	28	section	section	NOUN
easat-7855	32	29	four	four	NUM
easat-7855	32	30	,	,	PUNCT
easat-7855	32	31	and	and	CCONJ
easat-7855	32	32	the	the	DET
easat-7855	32	33	conclusion	conclusion	NOUN
easat-7855	32	34	in	in	ADP
easat-7855	32	35	section	section	NOUN
easat-7855	32	36	five	five	NUM
easat-7855	32	37	.	.	NOUN
easat-7855	33	1	2	2	X
easat-7855	33	2	.	.	NUM
easat-7855	33	3	related	relate	VERB
easat-7855	33	4	works	work	NOUN
easat-7855	33	5	in	in	ADP
easat-7855	33	6	2020	2020	NUM
easat-7855	33	7	,	,	PUNCT
easat-7855	33	8	the	the	DET
easat-7855	33	9	previously	previously	ADV
easat-7855	33	10	segmental	segmental	ADJ
easat-7855	33	11	arithmetic	arithmetic	ADJ
easat-7855	33	12	methodology	methodology	NOUN
easat-7855	33	13	has	have	AUX
easat-7855	33	14	gained	gain	VERB
easat-7855	33	15	popularity	popularity	NOUN
easat-7855	33	16	and	and	CCONJ
easat-7855	33	17	significance	significance	NOUN
easat-7855	33	18	as	as	ADP
easat-7855	33	19	a	a	DET
easat-7855	33	20	consequence	consequence	NOUN
easat-7855	33	21	of	of	ADP
easat-7855	33	22	its	its	PRON
easat-7855	33	23	attractive	attractive	ADJ
easat-7855	33	24	utilization	utilization	NOUN
easat-7855	33	25	in	in	ADP
easat-7855	33	26	many	many	ADJ
easat-7855	33	27	different	different	ADJ
easat-7855	33	28	types	type	NOUN
easat-7855	33	29	of	of	ADP
easat-7855	33	30	scientific	scientific	ADJ
easat-7855	33	31	and	and	CCONJ
easat-7855	33	32	relevant	relevant	ADJ
easat-7855	33	33	categories	category	NOUN
easat-7855	33	34	.	.	PUNCT
easat-7855	34	1	the	the	DET
easat-7855	34	2	goal	goal	NOUN
easat-7855	34	3	of	of	ADP
easat-7855	34	4	this	this	DET
easat-7855	34	5	investigation	investigation	NOUN
easat-7855	34	6	is	be	AUX
easat-7855	34	7	to	to	PART
easat-7855	34	8	give	give	VERB
easat-7855	34	9	insights	insight	NOUN
easat-7855	34	10	into	into	ADP
easat-7855	34	11	numerical	numerical	ADJ
easat-7855	34	12	simulations	simulation	NOUN
easat-7855	34	13	of	of	ADP
easat-7855	34	14	time	time	NOUN
easat-7855	34	15	-	-	PUNCT
easat-7855	34	16	fractional	fractional	ADJ
easat-7855	34	17	divided	divide	VERB
easat-7855	34	18	differential	differential	ADJ
easat-7855	34	19	equations	equation	NOUN
easat-7855	34	20	emerging	emerge	VERB
easat-7855	34	21	in	in	ADP
easat-7855	34	22	transonic	transonic	PROPN
easat-7855	34	23	multiphase	multiphase	NOUN
easat-7855	34	24	streams	stream	NOUN
easat-7855	34	25	defined	define	VERB
easat-7855	34	26	by	by	ADP
easat-7855	34	27	the	the	DET
easat-7855	34	28	keldysh	keldysh	NOUN
easat-7855	34	29	[	[	X
easat-7855	34	30	11	11	NUM
easat-7855	34	31	]	]	PUNCT
easat-7855	34	32	solutions	solution	NOUN
easat-7855	34	33	of	of	ADP
easat-7855	34	34	the	the	DET
easat-7855	34	35	robins	robin	NOUN
easat-7855	34	36	functional	functional	ADJ
easat-7855	34	37	kind	kind	NOUN
easat-7855	34	38	[	[	X
easat-7855	34	39	12	12	NUM
easat-7855	34	40	]	]	PUNCT
easat-7855	34	41	.	.	PUNCT
easat-7855	35	1	in	in	ADP
easat-7855	35	2	(	(	PUNCT
easat-7855	35	3	2021	2021	NUM
easat-7855	35	4	)	)	PUNCT
easat-7855	35	5	,	,	PUNCT
easat-7855	35	6	the	the	DET
easat-7855	35	7	newly	newly	ADV
easat-7855	35	8	developed	develop	VERB
easat-7855	35	9	methodology	methodology	NOUN
easat-7855	35	10	utilizes	utilize	VERB
easat-7855	35	11	a	a	DET
easat-7855	35	12	multi	multi	ADJ
easat-7855	35	13	-	-	ADJ
easat-7855	35	14	domain	domain	ADJ
easat-7855	35	15	strategy	strategy	NOUN
easat-7855	35	16	across	across	ADP
easat-7855	35	17	various	various	ADJ
easat-7855	35	18	spatial	spatial	ADJ
easat-7855	35	19	and	and	CCONJ
easat-7855	35	20	temporal	temporal	ADJ
easat-7855	35	21	intervals	interval	NOUN
easat-7855	35	22	.	.	PUNCT
easat-7855	36	1	the	the	DET
easat-7855	36	2	duration	duration	NOUN
easat-7855	36	3	is	be	AUX
easat-7855	36	4	segmented	segment	VERB
easat-7855	36	5	into	into	ADP
easat-7855	36	6	distinct	distinct	ADJ
easat-7855	36	7	sub	sub	NOUN
easat-7855	36	8	-	-	NOUN
easat-7855	36	9	intervals	interval	NOUN
easat-7855	36	10	,	,	PUNCT
easat-7855	36	11	while	while	SCONJ
easat-7855	36	12	the	the	DET
easat-7855	36	13	overall	overall	ADJ
easat-7855	36	14	length	length	NOUN
easat-7855	36	15	is	be	AUX
easat-7855	36	16	partitioned	partition	VERB
easat-7855	36	17	into	into	ADP
easat-7855	36	18	contiguous	contiguous	ADJ
easat-7855	36	19	subdomains	subdomain	NOUN
easat-7855	36	20	.	.	PUNCT
easat-7855	37	1	statistical	statistical	ADJ
easat-7855	37	2	tests	test	NOUN
easat-7855	37	3	are	be	AUX
easat-7855	37	4	being	be	AUX
easat-7855	37	5	carried	carry	VERB
easat-7855	37	6	out	out	ADP
easat-7855	37	7	to	to	PART
easat-7855	37	8	demonstrate	demonstrate	VERB
easat-7855	37	9	both	both	CCONJ
easat-7855	37	10	the	the	DET
easat-7855	37	11	precision	precision	NOUN
easat-7855	37	12	and	and	CCONJ
easat-7855	37	13	efficacy	efficacy	NOUN
easat-7855	37	14	of	of	ADP
easat-7855	37	15	the	the	DET
easat-7855	37	16	procedure	procedure	NOUN
easat-7855	37	17	.	.	PUNCT
easat-7855	38	1	the	the	DET
easat-7855	38	2	omd	omd	PROPN
easat-7855	38	3	-	-	PUNCT
easat-7855	38	4	bsqlm	bsqlm	PROPN
easat-7855	38	5	's	's	PART
easat-7855	38	6	converging	converging	NOUN
easat-7855	38	7	and	and	CCONJ
easat-7855	38	8	correctness	correctness	NOUN
easat-7855	38	9	are	be	AUX
easat-7855	38	10	evaluated	evaluate	VERB
easat-7855	38	11	utilizing	utilize	VERB
easat-7855	38	12	failure	failure	NOUN
easat-7855	38	13	standards	standard	NOUN
easat-7855	38	14	and	and	CCONJ
easat-7855	38	15	leftover	leftover	NOUN
easat-7855	38	16	losses	loss	NOUN
easat-7855	38	17	.	.	PUNCT
easat-7855	39	1	a	a	DET
easat-7855	39	2	number	number	NOUN
easat-7855	39	3	of	of	ADP
easat-7855	39	4	results	result	NOUN
easat-7855	39	5	are	be	AUX
easat-7855	39	6	utilized	utilize	VERB
easat-7855	39	7	to	to	PART
easat-7855	39	8	ensure	ensure	VERB
easat-7855	39	9	the	the	DET
easat-7855	39	10	preciseness	preciseness	NOUN
easat-7855	39	11	of	of	ADP
easat-7855	39	12	the	the	DET
easat-7855	39	13	omd	omd	PROPN
easat-7855	39	14	-	-	PUNCT
easat-7855	39	15	bsqlm	bsqlm	PROPN
easat-7855	39	16	results	result	NOUN
easat-7855	39	17	.	.	PUNCT
easat-7855	40	1	following	follow	VERB
easat-7855	40	2	a	a	DET
easat-7855	40	3	few	few	ADJ
easat-7855	40	4	repetitions	repetition	NOUN
easat-7855	40	5	and	and	CCONJ
easat-7855	40	6	the	the	DET
easat-7855	40	7	use	use	NOUN
easat-7855	40	8	of	of	ADP
easat-7855	40	9	a	a	DET
easat-7855	40	10	couple	couple	NOUN
easat-7855	40	11	grid	grid	NOUN
easat-7855	40	12	points	point	NOUN
easat-7855	40	13	for	for	ADP
easat-7855	40	14	it	it	PRON
easat-7855	40	15	,	,	PUNCT
easat-7855	40	16	the	the	DET
easat-7855	40	17	fresh	fresh	ADJ
easat-7855	40	18	strategy	strategy	NOUN
easat-7855	40	19	settles	settle	VERB
easat-7855	40	20	quickly	quickly	ADV
easat-7855	40	21	and	and	CCONJ
easat-7855	40	22	produces	produce	VERB
easat-7855	40	23	reliable	reliable	ADJ
easat-7855	40	24	results	result	NOUN
easat-7855	40	25	.	.	PUNCT
easat-7855	41	1	furthermore	furthermore	ADV
easat-7855	41	2	,	,	PUNCT
easat-7855	41	3	efficiency	efficiency	NOUN
easat-7855	41	4	does	do	AUX
easat-7855	41	5	not	not	PART
easat-7855	41	6	deteriorate	deteriorate	VERB
easat-7855	41	7	once	once	ADV
easat-7855	41	8	a	a	DET
easat-7855	41	9	vast	vast	ADJ
easat-7855	41	10	temporal	temporal	ADJ
easat-7855	41	11	area	area	NOUN
easat-7855	41	12	is	be	AUX
easat-7855	41	13	taken	take	VERB
easat-7855	41	14	into	into	ADP
easat-7855	41	15	consideration	consideration	NOUN
easat-7855	41	16	[	[	X
easat-7855	41	17	13	13	NUM
easat-7855	41	18	]	]	PUNCT
easat-7855	41	19	.	.	PUNCT
easat-7855	42	1	1n(2023	1n(2023	NUM
easat-7855	42	2	)	)	PUNCT
easat-7855	42	3	they	they	PRON
easat-7855	42	4	employ	employ	VERB
easat-7855	42	5	a	a	DET
easat-7855	42	6	method	method	NOUN
easat-7855	42	7	of	of	ADP
easat-7855	42	8	deep	deep	ADJ
easat-7855	42	9	learning	learning	NOUN
easat-7855	42	10	called	call	VERB
easat-7855	42	11	the	the	DET
easat-7855	42	12	deep	deep	ADJ
easat-7855	42	13	operator	operator	NOUN
easat-7855	42	14	network	network	NOUN
easat-7855	42	15	(	(	PUNCT
easat-7855	42	16	deeponet	deeponet	NOUN
easat-7855	42	17	)	)	PUNCT
easat-7855	42	18	to	to	PART
easat-7855	42	19	discover	discover	VERB
easat-7855	42	20	possible	possible	ADJ
easat-7855	42	21	applications	application	NOUN
easat-7855	42	22	for	for	ADP
easat-7855	42	23	expanding	expand	VERB
easat-7855	42	24	pde	pde	NOUN
easat-7855	42	25	solutions	solution	NOUN
easat-7855	42	26	.	.	PUNCT
easat-7855	43	1	they	they	PRON
easat-7855	43	2	designed	design	VERB
easat-7855	43	3	a	a	DET
easat-7855	43	4	technique	technique	NOUN
easat-7855	43	5	that	that	PRON
easat-7855	43	6	starts	start	VERB
easat-7855	43	7	with	with	ADP
easat-7855	43	8	the	the	DET
easat-7855	43	9	deeponet	deeponet	NOUN
easat-7855	43	10	's	's	PART
easat-7855	43	11	applicants	applicant	NOUN
easat-7855	43	12	acts	act	VERB
easat-7855	43	13	and	and	CCONJ
easat-7855	43	14	builds	build	VERB
easat-7855	43	15	a	a	DET
easat-7855	43	16	set	set	NOUN
easat-7855	43	17	of	of	ADP
easat-7855	43	18	works	work	NOUN
easat-7855	43	19	that	that	PRON
easat-7855	43	20	have	have	VERB
easat-7855	43	21	the	the	DET
easat-7855	43	22	subsequent	subsequent	ADJ
easat-7855	43	23	buildings	building	NOUN
easat-7855	43	24	:	:	PUNCT
easat-7855	43	25	(	(	PUNCT
easat-7855	43	26	1	1	X
easat-7855	43	27	)	)	PUNCT
easat-7855	43	28	they	they	PRON
easat-7855	43	29	form	form	VERB
easat-7855	43	30	a	a	DET
easat-7855	43	31	basis	basis	NOUN
easat-7855	43	32	,	,	PUNCT
easat-7855	43	33	(	(	PUNCT
easat-7855	43	34	2	2	X
easat-7855	43	35	)	)	PUNCT
easat-7855	43	36	they	they	PRON
easat-7855	43	37	are	be	AUX
easat-7855	43	38	orthonormal	orthonormal	ADJ
easat-7855	43	39	,	,	PUNCT
easat-7855	43	40	and	and	CCONJ
easat-7855	43	41	(	(	PUNCT
easat-7855	43	42	3	3	X
easat-7855	43	43	)	)	PUNCT
easat-7855	43	44	they	they	PRON
easat-7855	43	45	are	be	AUX
easat-7855	43	46	stacked	stack	VERB
easat-7855	43	47	,	,	PUNCT
easat-7855	43	48	similar	similar	ADJ
easat-7855	43	49	to	to	ADP
easat-7855	43	50	fourier	fouri	ADJ
easat-7855	43	51	series	series	NOUN
easat-7855	43	52	or	or	CCONJ
easat-7855	43	53	parallel	parallel	ADJ
easat-7855	43	54	polynomial	polynomial	ADJ
easat-7855	43	55	equation	equation	NOUN
easat-7855	43	56	they	they	PRON
easat-7855	43	57	used	use	VERB
easat-7855	43	58	the	the	DET
easat-7855	43	59	advantageous	advantageous	ADJ
easat-7855	43	60	qualities	quality	NOUN
easat-7855	43	61	of	of	ADP
easat-7855	43	62	the	the	DET
easat-7855	43	63	made	make	VERB
easat-7855	43	64	especially	especially	ADV
easat-7855	43	65	fundamental	fundamental	ADJ
easat-7855	43	66	functions	function	NOUN
easat-7855	43	67	to	to	PART
easat-7855	43	68	examine	examine	VERB
easat-7855	43	69	their	their	PRON
easat-7855	43	70	approximating	approximate	VERB
easat-7855	43	71	capabilities	capability	NOUN
easat-7855	43	72	and	and	CCONJ
easat-7855	43	73	to	to	PART
easat-7855	43	74	expand	expand	VERB
easat-7855	43	75	their	their	PRON
easat-7855	43	76	solutions	solution	NOUN
easat-7855	43	77	of	of	ADP
easat-7855	43	78	linear	linear	PROPN
easat-7855	43	79	and	and	CCONJ
easat-7855	43	80	nonlinear	nonlinear	ADJ
easat-7855	43	81	gradual	gradual	ADJ
easat-7855	43	82	pdes	pde	NOUN
easat-7855	43	83	[	[	X
easat-7855	43	84	14	14	NUM
easat-7855	43	85	]	]	PUNCT
easat-7855	43	86	.	.	PUNCT
easat-7855	44	1	in	in	ADP
easat-7855	44	2	(	(	PUNCT
easat-7855	44	3	2024	2024	NUM
easat-7855	44	4	)	)	PUNCT
easat-7855	44	5	the	the	DET
easat-7855	44	6	investigation	investigation	NOUN
easat-7855	44	7	aims	aim	VERB
easat-7855	44	8	to	to	PART
easat-7855	44	9	solve	solve	VERB
easat-7855	44	10	complex	complex	ADJ
easat-7855	44	11	differential	differential	ADJ
easat-7855	44	12	equations	equation	NOUN
easat-7855	44	13	using	use	VERB
easat-7855	44	14	the	the	DET
easat-7855	44	15	chebyshev	chebyshev	NOUN
easat-7855	44	16	spectrum	spectrum	NOUN
easat-7855	44	17	technique	technique	NOUN
easat-7855	44	18	using	use	VERB
easat-7855	44	19	the	the	DET
easat-7855	44	20	neural	neural	ADJ
easat-7855	44	21	network	network	NOUN
easat-7855	44	22	(	(	PUNCT
easat-7855	44	23	csnn	csnn	NOUN
easat-7855	44	24	)	)	PUNCT
easat-7855	44	25	framework	framework	NOUN
easat-7855	44	26	.	.	PUNCT
easat-7855	45	1	the	the	DET
easat-7855	45	2	approach	approach	NOUN
easat-7855	45	3	uses	use	VERB
easat-7855	45	4	a	a	DET
easat-7855	45	5	neural	neural	ADJ
easat-7855	45	6	network	network	NOUN
easat-7855	45	7	with	with	ADP
easat-7855	45	8	only	only	ADV
easat-7855	45	9	one	one	NUM
easat-7855	45	10	layer	layer	NOUN
easat-7855	45	11	with	with	ADP
easat-7855	45	12	chebyshev	chebyshev	PROPN
easat-7855	45	13	spectrum	spectrum	NOUN
easat-7855	45	14	algorithms	algorithm	NOUN
easat-7855	45	15	to	to	PART
easat-7855	45	16	build	build	VERB
easat-7855	45	17	transistors	transistor	NOUN
easat-7855	45	18	that	that	PRON
easat-7855	45	19	meet	meet	VERB
easat-7855	45	20	threshold	threshold	NOUN
easat-7855	45	21	requirements	requirement	NOUN
easat-7855	45	22	.	.	PUNCT
easat-7855	46	1	the	the	DET
easat-7855	46	2	investigation	investigation	NOUN
easat-7855	46	3	computes	compute	VERB
easat-7855	46	4	the	the	DET
easat-7855	46	5	function	function	NOUN
easat-7855	46	6	of	of	ADP
easat-7855	46	7	losses	loss	NOUN
easat-7855	46	8	using	use	VERB
easat-7855	46	9	a	a	DET
easat-7855	46	10	feedforward	feedforward	ADJ
easat-7855	46	11	neural	neural	ADJ
easat-7855	46	12	network	network	NOUN
easat-7855	46	13	's	's	PART
easat-7855	46	14	models	model	NOUN
easat-7855	46	15	and	and	CCONJ
easat-7855	46	16	imperfect	imperfect	ADJ
easat-7855	46	17	return	return	NOUN
easat-7855	46	18	propagation	propagation	NOUN
easat-7855	46	19	methods	method	NOUN
easat-7855	46	20	,	,	PUNCT
easat-7855	46	21	as	as	ADV
easat-7855	46	22	well	well	ADV
easat-7855	46	23	as	as	ADP
easat-7855	46	24	automated	automate	VERB
easat-7855	46	25	derivation	derivation	NOUN
easat-7855	46	26	(	(	PUNCT
easat-7855	46	27	ad	ad	NOUN
easat-7855	46	28	)	)	PUNCT
easat-7855	46	29	.	.	PUNCT
easat-7855	47	1	this	this	DET
easat-7855	47	2	technique	technique	NOUN
easat-7855	47	3	cuts	cut	VERB
easat-7855	47	4	out	out	ADP
easat-7855	47	5	need	need	NOUN
easat-7855	47	6	to	to	PART
easat-7855	47	7	solve	solve	VERB
easat-7855	47	8	non	non	ADJ
easat-7855	47	9	-	-	ADJ
easat-7855	47	10	sparse	sparse	ADJ
easat-7855	47	11	linear	linear	NOUN
easat-7855	47	12	problems	problem	NOUN
easat-7855	47	13	,	,	PUNCT
easat-7855	47	14	which	which	PRON
easat-7855	47	15	renders	render	VERB
easat-7855	47	16	it	it	PRON
easat-7855	47	17	skilled	skilled	ADJ
easat-7855	47	18	for	for	ADP
easat-7855	47	19	executing	execute	VERB
easat-7855	47	20	techniques	technique	NOUN
easat-7855	47	21	and	and	CCONJ
easat-7855	47	22	dealing	deal	VERB
easat-7855	47	23	with	with	ADP
easat-7855	47	24	problems	problem	NOUN
easat-7855	47	25	involving	involve	VERB
easat-7855	47	26	huge	huge	ADJ
easat-7855	47	27	dimension	dimension	NOUN
easat-7855	47	28	[	[	X
easat-7855	47	29	15	15	NUM
easat-7855	47	30	]	]	PUNCT
easat-7855	47	31	.	.	PUNCT
easat-7855	48	1	in(2024	in(2024	X
easat-7855	48	2	)	)	PUNCT
easat-7855	48	3	the	the	DET
easat-7855	48	4	investigation	investigation	NOUN
easat-7855	48	5	reviews	review	VERB
easat-7855	48	6	countless	countless	ADJ
easat-7855	48	7	math	math	NOUN
easat-7855	48	8	techniques	technique	NOUN
easat-7855	48	9	built	build	VERB
easat-7855	48	10	unambiguously	unambiguously	ADV
easat-7855	48	11	for	for	ADP
easat-7855	48	12	such	such	ADJ
easat-7855	48	13	situations	situation	NOUN
easat-7855	48	14	,	,	PUNCT
easat-7855	48	15	assessing	assess	VERB
easat-7855	48	16	the	the	DET
easat-7855	48	17	results	result	NOUN
easat-7855	48	18	and	and	CCONJ
easat-7855	48	19	scalability	scalability	NOUN
easat-7855	48	20	.	.	PUNCT
easat-7855	49	1	they	they	PRON
easat-7855	49	2	start	start	VERB
easat-7855	49	3	by	by	ADP
easat-7855	49	4	giving	give	VERB
easat-7855	49	5	a	a	DET
easat-7855	49	6	survey	survey	NOUN
easat-7855	49	7	of	of	ADP
easat-7855	49	8	nbvps	nbvps	NOUN
easat-7855	49	9	in	in	ADP
easat-7855	49	10	grading	grade	VERB
easat-7855	49	11	issues	issue	NOUN
easat-7855	49	12	before	before	ADP
easat-7855	49	13	expanding	expand	VERB
easat-7855	49	14	into	into	ADP
easat-7855	49	15	distinct	distinct	ADJ
easat-7855	49	16	numerical	numerical	ADJ
easat-7855	49	17	approaches	approach	NOUN
easat-7855	49	18	such	such	ADJ
easat-7855	49	19	as	as	ADP
easat-7855	49	20	tiny	tiny	ADJ
easat-7855	49	21	honor	honor	NOUN
easat-7855	49	22	,	,	PUNCT
easat-7855	49	23	small	small	ADJ
easat-7855	49	24	portion	portion	NOUN
easat-7855	49	25	,	,	PUNCT
easat-7855	49	26	and	and	CCONJ
easat-7855	49	27	wavelength	wavelength	NOUN
easat-7855	49	28	.	.	PUNCT
easat-7855	50	1	of	of	ADP
easat-7855	50	2	the	the	DET
easat-7855	50	3	process	process	NOUN
easat-7855	50	4	's	's	PART
easat-7855	50	5	advantages	advantage	NOUN
easat-7855	50	6	.	.	PUNCT
easat-7855	51	1	drawbacks	drawback	NOUN
easat-7855	51	2	,	,	PUNCT
easat-7855	51	3	and	and	CCONJ
easat-7855	51	4	practical	practical	ADJ
easat-7855	51	5	difficulties	difficulty	NOUN
easat-7855	51	6	are	be	AUX
easat-7855	51	7	dealt	deal	VERB
easat-7855	51	8	with	with	ADP
easat-7855	51	9	,	,	PUNCT
easat-7855	51	10	presenting	present	VERB
easat-7855	51	11	insights	insight	NOUN
easat-7855	51	12	into	into	ADP
easat-7855	51	13	how	how	SCONJ
easat-7855	51	14	one	one	PRON
easat-7855	51	15	can	can	AUX
easat-7855	51	16	use	use	VERB
easat-7855	51	17	them	they	PRON
easat-7855	51	18	successfully	successfully	ADV
easat-7855	51	19	.	.	PUNCT
easat-7855	52	1	finally	finally	ADV
easat-7855	52	2	,	,	PUNCT
easat-7855	52	3	the	the	DET
easat-7855	52	4	article	article	NOUN
easat-7855	52	5	aims	aim	VERB
easat-7855	52	6	to	to	PART
easat-7855	52	7	give	give	VERB
easat-7855	52	8	readers	reader	NOUN
easat-7855	52	9	an	an	DET
easat-7855	52	10	extensive	extensive	ADJ
easat-7855	52	11	568	568	NUM
easat-7855	52	12	edelweiss	edelweiss	PROPN
easat-7855	52	13	applied	apply	VERB
easat-7855	52	14	science	science	NOUN
easat-7855	52	15	and	and	CCONJ
easat-7855	52	16	technology	technology	NOUN
easat-7855	52	17	issn	issn	PROPN
easat-7855	52	18	:	:	PUNCT
easat-7855	52	19	2576	2576	NUM
easat-7855	52	20	-	-	SYM
easat-7855	52	21	8484	8484	NUM
easat-7855	52	22	vol	vol	NOUN
easat-7855	52	23	.	.	PROPN
easat-7855	53	1	9	9	NUM
easat-7855	53	2	,	,	PUNCT
easat-7855	53	3	no	no	INTJ
easat-7855	53	4	.	.	NOUN
easat-7855	54	1	6	6	NUM
easat-7855	54	2	:	:	SYM
easat-7855	54	3	566	566	NUM
easat-7855	54	4	-	-	SYM
easat-7855	54	5	575	575	NUM
easat-7855	54	6	,	,	PUNCT
easat-7855	54	7	2025	2025	NUM
easat-7855	54	8	doi	doi	NOUN
easat-7855	54	9	:	:	PUNCT
easat-7855	54	10	10.55214/25768484.v9i6.7855	10.55214/25768484.v9i6.7855	NUM
easat-7855	54	11	©	©	PROPN
easat-7855	54	12	2025	2025	NUM
easat-7855	54	13	by	by	ADP
easat-7855	54	14	the	the	DET
easat-7855	54	15	author	author	NOUN
easat-7855	54	16	;	;	PUNCT
easat-7855	54	17	licensee	licensee	PROPN
easat-7855	54	18	learning	learn	VERB
easat-7855	54	19	gate	gate	NOUN
easat-7855	54	20	knowledge	knowledge	NOUN
easat-7855	54	21	of	of	ADP
easat-7855	54	22	analytical	analytical	ADJ
easat-7855	54	23	technique	technique	NOUN
easat-7855	54	24	for	for	ADP
easat-7855	54	25	solving	solve	VERB
easat-7855	54	26	nbvps	nbvps	NOUN
easat-7855	54	27	utilizing	utilize	VERB
easat-7855	54	28	the	the	DET
easat-7855	54	29	theory	theory	NOUN
easat-7855	54	30	of	of	ADP
easat-7855	54	31	differential	differential	ADJ
easat-7855	54	32	equations	equation	NOUN
easat-7855	54	33	as	as	ADP
easat-7855	54	34	their	their	PRON
easat-7855	54	35	basis	basis	NOUN
easat-7855	55	1	[	[	X
easat-7855	55	2	16	16	NUM
easat-7855	55	3	]	]	PUNCT
easat-7855	55	4	.	.	PUNCT
easat-7855	56	1	3	3	X
easat-7855	56	2	.	.	NUM
easat-7855	56	3	proposed	propose	VERB
easat-7855	56	4	system	system	NOUN
easat-7855	56	5	the	the	DET
easat-7855	56	6	technique	technique	NOUN
easat-7855	56	7	employs	employ	VERB
easat-7855	56	8	three	three	NUM
easat-7855	56	9	algebraic	algebraic	ADJ
easat-7855	56	10	techniques	technique	NOUN
easat-7855	56	11	to	to	PART
easat-7855	56	12	solve	solve	VERB
easat-7855	56	13	equations	equation	NOUN
easat-7855	56	14	of	of	ADP
easat-7855	56	15	partial	partial	ADJ
easat-7855	56	16	differentials	differential	NOUN
easat-7855	56	17	(	(	PUNCT
easat-7855	56	18	pdes	pde	NOUN
easat-7855	56	19	)	)	PUNCT
easat-7855	56	20	that	that	PRON
easat-7855	56	21	pertain	pertain	VERB
easat-7855	56	22	to	to	ADP
easat-7855	56	23	the	the	DET
easat-7855	56	24	flow	flow	NOUN
easat-7855	56	25	of	of	ADP
easat-7855	56	26	fluid	fluid	NOUN
easat-7855	56	27	and	and	CCONJ
easat-7855	56	28	heat	heat	NOUN
easat-7855	56	29	transmission	transmission	NOUN
easat-7855	56	30	..	..	PUNCT
easat-7855	57	1	the	the	DET
easat-7855	57	2	methods	method	NOUN
easat-7855	57	3	to	to	PART
easat-7855	57	4	use	use	VERB
easat-7855	57	5	are	be	AUX
easat-7855	57	6	:	:	PUNCT
easat-7855	57	7	1	1	X
easat-7855	57	8	.	.	X
easat-7855	58	1	the	the	DET
easat-7855	58	2	navier	navier	NOUN
easat-7855	58	3	-	-	PUNCT
easat-7855	58	4	stokes	stokes	PROPN
easat-7855	58	5	solver	solver	NOUN
easat-7855	58	6	(	(	PUNCT
easat-7855	58	7	finite	finite	ADJ
easat-7855	58	8	difference	difference	NOUN
easat-7855	58	9	method	method	NOUN
easat-7855	58	10	)	)	PUNCT
easat-7855	58	11	analyzes	analyze	VERB
easat-7855	58	12	the	the	DET
easat-7855	58	13	flow	flow	NOUN
easat-7855	58	14	of	of	ADP
easat-7855	58	15	fluids	fluid	NOUN
easat-7855	58	16	with	with	ADP
easat-7855	58	17	the	the	DET
easat-7855	58	18	navierstokes	navierstoke	NOUN
easat-7855	58	19	models	model	NOUN
easat-7855	58	20	.	.	PUNCT
easat-7855	59	1	the	the	DET
easat-7855	59	2	second	second	ADJ
easat-7855	59	3	variant	variant	NOUN
easat-7855	59	4	of	of	ADP
easat-7855	59	5	the	the	DET
easat-7855	59	6	poisson	poisson	NOUN
easat-7855	59	7	equation	equation	NOUN
easat-7855	59	8	analyzer	analyzer	NOUN
easat-7855	59	9	(	(	PUNCT
easat-7855	59	10	spectral	spectral	ADJ
easat-7855	59	11	method	method	NOUN
easat-7855	59	12	)	)	PUNCT
easat-7855	59	13	calculates	calculate	VERB
easat-7855	59	14	the	the	DET
easat-7855	59	15	poisson	poisson	NOUN
easat-7855	59	16	equation	equation	NOUN
easat-7855	59	17	in	in	ADP
easat-7855	59	18	the	the	DET
easat-7855	59	19	circular	circular	ADJ
easat-7855	59	20	region	region	NOUN
easat-7855	59	21	using	use	VERB
easat-7855	59	22	spectrum	spectrum	NOUN
easat-7855	59	23	techniques	technique	NOUN
easat-7855	59	24	.	.	PUNCT
easat-7855	60	1	3	3	X
easat-7855	60	2	.	.	X
easat-7855	60	3	heat	heat	NOUN
easat-7855	60	4	equations	equation	NOUN
easat-7855	60	5	calculator	calculator	NOUN
easat-7855	60	6	(	(	PUNCT
easat-7855	60	7	gpu	gpu	NOUN
easat-7855	60	8	acceleration	acceleration	NOUN
easat-7855	60	9	with	with	ADP
easat-7855	60	10	pytorch	pytorch	NOUN
easat-7855	60	11	):	):	PUNCT
easat-7855	60	12	determines	determine	VERB
easat-7855	60	13	heat	heat	NOUN
easat-7855	60	14	dispersion	dispersion	NOUN
easat-7855	60	15	as	as	SCONJ
easat-7855	60	16	time	time	NOUN
easat-7855	60	17	passes	pass	VERB
easat-7855	60	18	using	use	VERB
easat-7855	60	19	the	the	DET
easat-7855	60	20	infinite	infinite	ADJ
easat-7855	60	21	differences	difference	NOUN
easat-7855	60	22	technique	technique	NOUN
easat-7855	60	23	and	and	CCONJ
easat-7855	60	24	gpu	gpu	NOUN
easat-7855	60	25	acceleration	acceleration	NOUN
easat-7855	60	26	.	.	PUNCT
easat-7855	61	1	the	the	DET
easat-7855	61	2	steps	step	NOUN
easat-7855	61	3	of	of	ADP
easat-7855	61	4	methodology	methodology	NOUN
easat-7855	61	5	are	be	AUX
easat-7855	61	6	illustrates	illustrate	NOUN
easat-7855	61	7	in	in	ADP
easat-7855	61	8	table	table	NOUN
easat-7855	61	9	1	1	NUM
easat-7855	61	10	.	.	PUNCT
easat-7855	61	11	table	table	NOUN
easat-7855	61	12	1	1	NUM
easat-7855	61	13	.	.	PUNCT
easat-7855	62	1	the	the	DET
easat-7855	62	2	steps	step	NOUN
easat-7855	62	3	of	of	ADP
easat-7855	62	4	methodology	methodology	NOUN
easat-7855	62	5	are	be	AUX
easat-7855	62	6	illustrates	illustrate	NOUN
easat-7855	62	7	in	in	ADP
easat-7855	62	8	table	table	NOUN
easat-7855	62	9	.	.	PUNCT
easat-7855	63	1	step	step	NOUN
easat-7855	63	2	description	description	NOUN
easat-7855	63	3	1	1	NUM
easat-7855	63	4	.	.	PUNCT
easat-7855	63	5	model	model	NOUN
easat-7855	63	6	formulation	formulation	NOUN
easat-7855	63	7	and	and	CCONJ
easat-7855	63	8	discretization	discretization	VERB
easat-7855	63	9	each	each	DET
easat-7855	63	10	computational	computational	ADJ
easat-7855	63	11	model	model	NOUN
easat-7855	63	12	is	be	AUX
easat-7855	63	13	based	base	VERB
easat-7855	63	14	on	on	ADP
easat-7855	63	15	a	a	DET
easat-7855	63	16	different	different	ADJ
easat-7855	63	17	pde	pde	NOUN
easat-7855	63	18	and	and	CCONJ
easat-7855	63	19	discretized	discretize	VERB
easat-7855	63	20	using	use	VERB
easat-7855	63	21	appropriate	appropriate	ADJ
easat-7855	63	22	numerical	numerical	ADJ
easat-7855	63	23	methods	method	NOUN
easat-7855	63	24	.	.	PUNCT
easat-7855	64	1	navier	navier	NOUN
easat-7855	64	2	-	-	PUNCT
easat-7855	64	3	stokes	stokes	PROPN
easat-7855	64	4	solver	solver	NOUN
easat-7855	64	5	(	(	PUNCT
easat-7855	64	6	finite	finite	ADJ
easat-7855	64	7	difference	difference	NOUN
easat-7855	64	8	method	method	NOUN
easat-7855	64	9	)	)	PUNCT
easat-7855	64	10	governing	govern	VERB
easat-7855	64	11	equations	equation	NOUN
easat-7855	64	12	:	:	PUNCT
easat-7855	64	13	incompressible	incompressible	ADJ
easat-7855	64	14	navier	navier	NOUN
easat-7855	64	15	-	-	PUNCT
easat-7855	64	16	stokes	stoke	NOUN
easat-7855	64	17	equations	equation	NOUN
easat-7855	64	18	for	for	ADP
easat-7855	64	19	fluid	fluid	ADJ
easat-7855	64	20	flow	flow	NOUN
easat-7855	64	21	.	.	PUNCT
easat-7855	65	1	discretization	discretization	NOUN
easat-7855	65	2	:	:	PUNCT
easat-7855	65	3	finite	finite	ADJ
easat-7855	65	4	difference	difference	NOUN
easat-7855	65	5	method	method	NOUN
easat-7855	65	6	(	(	PUNCT
easat-7855	65	7	fdm	fdm	NOUN
easat-7855	65	8	)	)	PUNCT
easat-7855	65	9	on	on	ADP
easat-7855	65	10	a	a	DET
easat-7855	65	11	structured	structured	ADJ
easat-7855	65	12	grid	grid	NOUN
easat-7855	65	13	;	;	PUNCT
easat-7855	65	14	iterative	iterative	NOUN
easat-7855	65	15	updates	update	NOUN
easat-7855	65	16	using	use	VERB
easat-7855	65	17	a	a	DET
easat-7855	65	18	time	time	NOUN
easat-7855	65	19	-	-	PUNCT
easat-7855	65	20	stepping	step	VERB
easat-7855	65	21	approach	approach	NOUN
easat-7855	65	22	.	.	PUNCT
easat-7855	66	1	poisson	poisson	PROPN
easat-7855	66	2	equation	equation	NOUN
easat-7855	66	3	solver	solver	ADV
easat-7855	66	4	(	(	PUNCT
easat-7855	66	5	spectral	spectral	ADJ
easat-7855	66	6	method	method	NOUN
easat-7855	66	7	)	)	PUNCT
easat-7855	66	8	governing	govern	VERB
easat-7855	66	9	equation	equation	NOUN
easat-7855	66	10	:	:	PUNCT
easat-7855	66	11	poisson	poisson	NOUN
easat-7855	66	12	equation	equation	NOUN
easat-7855	66	13	for	for	ADP
easat-7855	66	14	pressure	pressure	NOUN
easat-7855	66	15	field	field	NOUN
easat-7855	66	16	computation	computation	NOUN
easat-7855	66	17	.	.	PUNCT
easat-7855	67	1	discretization	discretization	NOUN
easat-7855	67	2	:	:	PUNCT
easat-7855	67	3	spectral	spectral	ADJ
easat-7855	67	4	method	method	NOUN
easat-7855	67	5	with	with	ADP
easat-7855	67	6	orthogonal	orthogonal	ADJ
easat-7855	67	7	basis	basis	NOUN
easat-7855	67	8	functions	function	NOUN
easat-7855	67	9	(	(	PUNCT
easat-7855	67	10	e.g.	e.g.	ADV
easat-7855	67	11	,	,	PUNCT
easat-7855	67	12	fourier	fourier	ADJ
easat-7855	67	13	series	series	NOUN
easat-7855	67	14	)	)	PUNCT
easat-7855	67	15	;	;	PUNCT
easat-7855	67	16	effective	effective	ADJ
easat-7855	67	17	for	for	ADP
easat-7855	67	18	periodic	periodic	ADJ
easat-7855	67	19	boundary	boundary	ADJ
easat-7855	67	20	conditions	condition	NOUN
easat-7855	67	21	.	.	PUNCT
easat-7855	68	1	heat	heat	NOUN
easat-7855	68	2	equation	equation	NOUN
easat-7855	68	3	solver	solver	NOUN
easat-7855	68	4	(	(	PUNCT
easat-7855	68	5	finite	finite	ADJ
easat-7855	68	6	difference	difference	NOUN
easat-7855	68	7	method	method	NOUN
easat-7855	68	8	with	with	ADP
easat-7855	68	9	gpu	gpu	NOUN
easat-7855	68	10	acceleration	acceleration	NOUN
easat-7855	68	11	)	)	PUNCT
easat-7855	68	12	governing	govern	VERB
easat-7855	68	13	equation	equation	NOUN
easat-7855	68	14	:	:	PUNCT
easat-7855	68	15	heat	heat	NOUN
easat-7855	68	16	equation	equation	NOUN
easat-7855	68	17	for	for	ADP
easat-7855	68	18	temperature	temperature	NOUN
easat-7855	68	19	distribution	distribution	NOUN
easat-7855	68	20	.	.	PUNCT
easat-7855	69	1	discretization	discretization	NOUN
easat-7855	69	2	:	:	PUNCT
easat-7855	69	3	finite	finite	ADJ
easat-7855	69	4	difference	difference	NOUN
easat-7855	69	5	method	method	NOUN
easat-7855	69	6	on	on	ADP
easat-7855	69	7	a	a	DET
easat-7855	69	8	grid	grid	NOUN
easat-7855	69	9	with	with	ADP
easat-7855	69	10	gpu	gpu	NOUN
easat-7855	69	11	acceleration	acceleration	NOUN
easat-7855	69	12	for	for	ADP
easat-7855	69	13	efficient	efficient	ADJ
easat-7855	69	14	computation	computation	NOUN
easat-7855	69	15	in	in	ADP
easat-7855	69	16	large	large	ADJ
easat-7855	69	17	domains	domain	NOUN
easat-7855	69	18	.	.	PUNCT
easat-7855	70	1	2	2	X
easat-7855	70	2	.	.	X
easat-7855	70	3	implementation	implementation	NOUN
easat-7855	70	4	computational	computational	ADJ
easat-7855	70	5	models	model	NOUN
easat-7855	70	6	implemented	implement	VERB
easat-7855	70	7	in	in	ADP
easat-7855	70	8	python	python	NOUN
easat-7855	70	9	with	with	ADP
easat-7855	70	10	specific	specific	ADJ
easat-7855	70	11	libraries	library	NOUN
easat-7855	70	12	.	.	PUNCT
easat-7855	71	1	navier	navier	NOUN
easat-7855	71	2	-	-	PUNCT
easat-7855	71	3	stokes	stokes	PROPN
easat-7855	71	4	solver	solver	NOUN
easat-7855	71	5	implemented	implement	VERB
easat-7855	71	6	with	with	ADP
easat-7855	71	7	a	a	DET
easat-7855	71	8	staggered	staggered	ADJ
easat-7855	71	9	grid	grid	NOUN
easat-7855	71	10	approach	approach	NOUN
easat-7855	71	11	to	to	PART
easat-7855	71	12	avoid	avoid	VERB
easat-7855	71	13	numerical	numerical	ADJ
easat-7855	71	14	instabilities	instability	NOUN
easat-7855	71	15	;	;	PUNCT
easat-7855	71	16	uses	use	VERB
easat-7855	71	17	a	a	DET
easat-7855	71	18	pressure	pressure	NOUN
easat-7855	71	19	correction	correction	NOUN
easat-7855	71	20	method	method	NOUN
easat-7855	71	21	(	(	PUNCT
easat-7855	71	22	e.g.	e.g.	ADV
easat-7855	71	23	,	,	PUNCT
easat-7855	71	24	simple	simple	ADJ
easat-7855	71	25	or	or	CCONJ
easat-7855	71	26	piso	piso	NOUN
easat-7855	71	27	)	)	PUNCT
easat-7855	71	28	for	for	ADP
easat-7855	71	29	mass	mass	ADJ
easat-7855	71	30	conservation	conservation	NOUN
easat-7855	71	31	.	.	PUNCT
easat-7855	72	1	poisson	poisson	PROPN
easat-7855	72	2	equation	equation	NOUN
easat-7855	72	3	solver	solver	ADV
easat-7855	72	4	implemented	implement	VERB
easat-7855	72	5	using	use	VERB
easat-7855	72	6	fast	fast	ADJ
easat-7855	72	7	fourier	fourier	NOUN
easat-7855	72	8	transforms	transform	VERB
easat-7855	72	9	(	(	PUNCT
easat-7855	72	10	ffts	fft	NOUN
easat-7855	72	11	)	)	PUNCT
easat-7855	72	12	with	with	ADP
easat-7855	72	13	the	the	DET
easat-7855	72	14	scipy.fft	scipy.fft	NOUN
easat-7855	72	15	module	module	NOUN
easat-7855	72	16	to	to	PART
easat-7855	72	17	solve	solve	VERB
easat-7855	72	18	the	the	DET
easat-7855	72	19	poisson	poisson	NOUN
easat-7855	72	20	equation	equation	NOUN
easat-7855	72	21	in	in	ADP
easat-7855	72	22	the	the	DET
easat-7855	72	23	frequency	frequency	NOUN
easat-7855	72	24	domain	domain	NOUN
easat-7855	72	25	.	.	PUNCT
easat-7855	73	1	heat	heat	NOUN
easat-7855	73	2	equation	equation	NOUN
easat-7855	73	3	solver	solver	NOUN
easat-7855	73	4	implemented	implement	VERB
easat-7855	73	5	with	with	ADP
easat-7855	73	6	gpu	gpu	NOUN
easat-7855	73	7	acceleration	acceleration	NOUN
easat-7855	73	8	using	use	VERB
easat-7855	73	9	pytorch	pytorch	NOUN
easat-7855	73	10	for	for	ADP
easat-7855	73	11	parallel	parallel	ADJ
easat-7855	73	12	processing	processing	NOUN
easat-7855	73	13	and	and	CCONJ
easat-7855	73	14	efficient	efficient	ADJ
easat-7855	73	15	simulation	simulation	NOUN
easat-7855	73	16	of	of	ADP
easat-7855	73	17	heat	heat	NOUN
easat-7855	73	18	transfer	transfer	NOUN
easat-7855	73	19	.	.	PUNCT
easat-7855	74	1	3	3	X
easat-7855	74	2	.	.	X
easat-7855	74	3	integration	integration	NOUN
easat-7855	74	4	of	of	ADP
easat-7855	74	5	models	model	NOUN
easat-7855	74	6	unified	unify	VERB
easat-7855	74	7	framework	framework	NOUN
easat-7855	74	8	where	where	SCONJ
easat-7855	74	9	outputs	output	NOUN
easat-7855	74	10	of	of	ADP
easat-7855	74	11	one	one	NUM
easat-7855	74	12	model	model	NOUN
easat-7855	74	13	serve	serve	VERB
easat-7855	74	14	as	as	ADP
easat-7855	74	15	inputs	input	NOUN
easat-7855	74	16	to	to	ADP
easat-7855	74	17	another	another	PRON
easat-7855	74	18	.	.	PUNCT
easat-7855	75	1	initial	initial	ADJ
easat-7855	75	2	setup	setup	NOUN
easat-7855	75	3	begins	begin	VERB
easat-7855	75	4	with	with	ADP
easat-7855	75	5	an	an	DET
easat-7855	75	6	initial	initial	ADJ
easat-7855	75	7	velocity	velocity	NOUN
easat-7855	75	8	field	field	NOUN
easat-7855	75	9	for	for	ADP
easat-7855	75	10	the	the	DET
easat-7855	75	11	navier	navier	NOUN
easat-7855	75	12	-	-	PUNCT
easat-7855	75	13	stokes	stokes	PROPN
easat-7855	75	14	solver	solver	PROPN
easat-7855	75	15	and	and	CCONJ
easat-7855	75	16	an	an	DET
easat-7855	75	17	initial	initial	ADJ
easat-7855	75	18	temperature	temperature	NOUN
easat-7855	75	19	field	field	NOUN
easat-7855	75	20	for	for	ADP
easat-7855	75	21	the	the	DET
easat-7855	75	22	heat	heat	NOUN
easat-7855	75	23	equation	equation	NOUN
easat-7855	75	24	solver	solver	ADV
easat-7855	75	25	.	.	PUNCT
easat-7855	76	1	data	datum	NOUN
easat-7855	76	2	exchange	exchange	NOUN
easat-7855	76	3	pressure	pressure	NOUN
easat-7855	76	4	field	field	NOUN
easat-7855	76	5	from	from	ADP
easat-7855	76	6	the	the	DET
easat-7855	76	7	poisson	poisson	NOUN
easat-7855	76	8	solver	solver	PROPN
easat-7855	76	9	updates	update	VERB
easat-7855	76	10	the	the	DET
easat-7855	76	11	velocity	velocity	NOUN
easat-7855	76	12	field	field	NOUN
easat-7855	76	13	in	in	ADP
easat-7855	76	14	the	the	DET
easat-7855	76	15	navierstokes	navierstoke	NOUN
easat-7855	76	16	solver	solver	ADV
easat-7855	76	17	;	;	PUNCT
easat-7855	76	18	velocity	velocity	NOUN
easat-7855	76	19	field	field	NOUN
easat-7855	76	20	influences	influence	VERB
easat-7855	76	21	temperature	temperature	NOUN
easat-7855	76	22	distribution	distribution	NOUN
easat-7855	76	23	in	in	ADP
easat-7855	76	24	the	the	DET
easat-7855	76	25	heat	heat	NOUN
easat-7855	76	26	equation	equation	NOUN
easat-7855	76	27	solver	solver	ADV
easat-7855	76	28	.	.	PUNCT
easat-7855	77	1	iterative	iterative	NOUN
easat-7855	77	2	solving	solving	NOUN
easat-7855	77	3	models	model	NOUN
easat-7855	77	4	are	be	AUX
easat-7855	77	5	solved	solve	VERB
easat-7855	77	6	iteratively	iteratively	ADV
easat-7855	77	7	,	,	PUNCT
easat-7855	77	8	exchanging	exchange	VERB
easat-7855	77	9	data	datum	NOUN
easat-7855	77	10	at	at	ADP
easat-7855	77	11	each	each	DET
easat-7855	77	12	time	time	NOUN
easat-7855	77	13	step	step	NOUN
easat-7855	77	14	for	for	ADP
easat-7855	77	15	consistency	consistency	NOUN
easat-7855	77	16	and	and	CCONJ
easat-7855	77	17	convergence	convergence	NOUN
easat-7855	77	18	.	.	PUNCT
easat-7855	78	1	4	4	X
easat-7855	78	2	.	.	X
easat-7855	78	3	validation	validation	NOUN
easat-7855	78	4	and	and	CCONJ
easat-7855	78	5	testing	test	VERB
easat-7855	78	6	validation	validation	NOUN
easat-7855	78	7	against	against	ADP
easat-7855	78	8	benchmark	benchmark	NOUN
easat-7855	78	9	problems	problem	NOUN
easat-7855	78	10	and	and	CCONJ
easat-7855	78	11	comparison	comparison	NOUN
easat-7855	78	12	of	of	ADP
easat-7855	78	13	numerical	numerical	ADJ
easat-7855	78	14	results	result	NOUN
easat-7855	78	15	with	with	ADP
easat-7855	78	16	known	know	VERB
easat-7855	78	17	solutions	solution	NOUN
easat-7855	78	18	.	.	PUNCT
easat-7855	79	1	benchmarks	benchmark	VERB
easat-7855	79	2	lid	lid	NOUN
easat-7855	79	3	-	-	PUNCT
easat-7855	79	4	driven	drive	VERB
easat-7855	79	5	cavity	cavity	NOUN
easat-7855	79	6	flow	flow	NOUN
easat-7855	79	7	(	(	PUNCT
easat-7855	79	8	navier	navier	NOUN
easat-7855	79	9	-	-	PUNCT
easat-7855	79	10	stokes	stokes	PROPN
easat-7855	79	11	)	)	PUNCT
easat-7855	79	12	,	,	PUNCT
easat-7855	79	13	circular	circular	ADJ
easat-7855	79	14	domain	domain	NOUN
easat-7855	79	15	poisson	poisson	NOUN
easat-7855	79	16	problem	problem	NOUN
easat-7855	79	17	(	(	PUNCT
easat-7855	79	18	spectral	spectral	ADJ
easat-7855	79	19	method	method	NOUN
easat-7855	79	20	)	)	PUNCT
easat-7855	79	21	,	,	PUNCT
easat-7855	79	22	analytical	analytical	ADJ
easat-7855	79	23	solutions	solution	NOUN
easat-7855	79	24	of	of	ADP
easat-7855	79	25	the	the	DET
easat-7855	79	26	heat	heat	NOUN
easat-7855	79	27	equation	equation	NOUN
easat-7855	79	28	.	.	PUNCT
easat-7855	80	1	5	5	X
easat-7855	80	2	.	.	X
easat-7855	80	3	performance	performance	NOUN
easat-7855	80	4	evaluation	evaluation	NOUN
easat-7855	80	5	evaluation	evaluation	NOUN
easat-7855	80	6	of	of	ADP
easat-7855	80	7	accuracy	accuracy	NOUN
easat-7855	80	8	,	,	PUNCT
easat-7855	80	9	computational	computational	ADJ
easat-7855	80	10	efficiency	efficiency	NOUN
easat-7855	80	11	,	,	PUNCT
easat-7855	80	12	and	and	CCONJ
easat-7855	80	13	scalability	scalability	NOUN
easat-7855	80	14	.	.	PUNCT
easat-7855	81	1	accuracy	accuracy	NOUN
easat-7855	81	2	comparison	comparison	NOUN
easat-7855	81	3	with	with	ADP
easat-7855	81	4	analytical	analytical	ADJ
easat-7855	81	5	solutions	solution	NOUN
easat-7855	81	6	or	or	CCONJ
easat-7855	81	7	high	high	ADJ
easat-7855	81	8	-	-	PUNCT
easat-7855	81	9	resolution	resolution	NOUN
easat-7855	81	10	reference	reference	NOUN
easat-7855	81	11	simulations	simulation	NOUN
easat-7855	81	12	.	.	PUNCT
easat-7855	82	1	computational	computational	ADJ
easat-7855	82	2	efficiency	efficiency	NOUN
easat-7855	82	3	measured	measure	VERB
easat-7855	82	4	by	by	ADP
easat-7855	82	5	time	time	NOUN
easat-7855	82	6	-	-	PUNCT
easat-7855	82	7	to	to	ADP
easat-7855	82	8	-	-	PUNCT
easat-7855	82	9	solution	solution	NOUN
easat-7855	82	10	,	,	PUNCT
easat-7855	82	11	with	with	ADP
easat-7855	82	12	a	a	DET
easat-7855	82	13	focus	focus	NOUN
easat-7855	82	14	on	on	ADP
easat-7855	82	15	gpu	gpu	NOUN
easat-7855	82	16	acceleration	acceleration	NOUN
easat-7855	82	17	impact	impact	NOUN
easat-7855	82	18	on	on	ADP
easat-7855	82	19	the	the	DET
easat-7855	82	20	heat	heat	NOUN
easat-7855	82	21	equation	equation	NOUN
easat-7855	82	22	solver	solver	X
easat-7855	82	23	.	.	PUNCT
easat-7855	83	1	scalability	scalability	NOUN
easat-7855	83	2	evaluated	evaluate	VERB
easat-7855	83	3	by	by	ADP
easat-7855	83	4	running	run	VERB
easat-7855	83	5	simulations	simulation	NOUN
easat-7855	83	6	on	on	ADP
easat-7855	83	7	different	different	ADJ
easat-7855	83	8	grid	grid	NOUN
easat-7855	83	9	sizes	size	NOUN
easat-7855	83	10	and	and	CCONJ
easat-7855	83	11	measuring	measure	VERB
easat-7855	83	12	computation	computation	NOUN
easat-7855	83	13	time	time	NOUN
easat-7855	83	14	.	.	PUNCT
easat-7855	84	1	6	6	X
easat-7855	84	2	.	.	X
easat-7855	84	3	analysis	analysis	NOUN
easat-7855	84	4	and	and	CCONJ
easat-7855	84	5	visualization	visualization	NOUN
easat-7855	84	6	results	result	NOUN
easat-7855	84	7	analyzed	analyze	VERB
easat-7855	84	8	and	and	CCONJ
easat-7855	84	9	visualized	visualize	VERB
easat-7855	84	10	using	use	VERB
easat-7855	84	11	tools	tool	NOUN
easat-7855	84	12	like	like	ADP
easat-7855	84	13	matplotlib	matplotlib	PROPN
easat-7855	84	14	.	.	PUNCT
easat-7855	85	1	visualization	visualization	NOUN
easat-7855	85	2	creation	creation	NOUN
easat-7855	85	3	of	of	ADP
easat-7855	85	4	plots	plot	NOUN
easat-7855	85	5	and	and	CCONJ
easat-7855	85	6	animations	animation	NOUN
easat-7855	85	7	to	to	PART
easat-7855	85	8	provide	provide	VERB
easat-7855	85	9	insights	insight	NOUN
easat-7855	85	10	into	into	ADP
easat-7855	85	11	fluid	fluid	ADJ
easat-7855	85	12	flow	flow	NOUN
easat-7855	85	13	and	and	CCONJ
easat-7855	85	14	heat	heat	NOUN
easat-7855	85	15	transfer	transfer	NOUN
easat-7855	85	16	processes	process	NOUN
easat-7855	85	17	.	.	PUNCT
easat-7855	86	1	569	569	NUM
easat-7855	86	2	edelweiss	edelweiss	PROPN
easat-7855	86	3	applied	apply	VERB
easat-7855	86	4	science	science	NOUN
easat-7855	86	5	and	and	CCONJ
easat-7855	86	6	technology	technology	NOUN
easat-7855	86	7	issn	issn	PROPN
easat-7855	86	8	:	:	PUNCT
easat-7855	86	9	2576	2576	NUM
easat-7855	86	10	-	-	SYM
easat-7855	86	11	8484	8484	NUM
easat-7855	86	12	vol	vol	NOUN
easat-7855	86	13	.	.	PROPN
easat-7855	87	1	9	9	NUM
easat-7855	87	2	,	,	PUNCT
easat-7855	87	3	no	no	INTJ
easat-7855	87	4	.	.	NOUN
easat-7855	88	1	6	6	NUM
easat-7855	88	2	:	:	SYM
easat-7855	88	3	566	566	NUM
easat-7855	88	4	-	-	SYM
easat-7855	88	5	575	575	NUM
easat-7855	88	6	,	,	PUNCT
easat-7855	88	7	2025	2025	NUM
easat-7855	88	8	doi	doi	NOUN
easat-7855	88	9	:	:	PUNCT
easat-7855	88	10	10.55214/25768484.v9i6.7855	10.55214/25768484.v9i6.7855	NUM
easat-7855	88	11	©	©	PROPN
easat-7855	88	12	2025	2025	NUM
easat-7855	88	13	by	by	ADP
easat-7855	88	14	the	the	DET
easat-7855	88	15	author	author	NOUN
easat-7855	88	16	;	;	PUNCT
easat-7855	88	17	licensee	licensee	PROPN
easat-7855	88	18	learning	learn	VERB
easat-7855	88	19	gate	gate	NOUN
easat-7855	88	20	table	table	NOUN
easat-7855	88	21	2	2	NUM
easat-7855	88	22	and	and	CCONJ
easat-7855	88	23	3	3	NUM
easat-7855	88	24	illustrates	illustrate	VERB
easat-7855	88	25	the	the	DET
easat-7855	88	26	inputs	input	NOUN
easat-7855	88	27	and	and	CCONJ
easat-7855	88	28	outputs	output	NOUN
easat-7855	88	29	for	for	ADP
easat-7855	88	30	each	each	DET
easat-7855	88	31	method	method	NOUN
easat-7855	88	32	,	,	PUNCT
easat-7855	88	33	and	and	CCONJ
easat-7855	88	34	equation	equation	NOUN
easat-7855	88	35	details	detail	NOUN
easat-7855	88	36	sequentially	sequentially	ADV
easat-7855	88	37	:	:	PUNCT
easat-7855	88	38	table	table	NOUN
easat-7855	88	39	2	2	NUM
easat-7855	88	40	.	.	PUNCT
easat-7855	89	1	the	the	DET
easat-7855	89	2	inputs	input	NOUN
easat-7855	89	3	and	and	CCONJ
easat-7855	89	4	outputs	output	NOUN
easat-7855	89	5	for	for	ADP
easat-7855	89	6	each	each	DET
easat-7855	89	7	method	method	NOUN
easat-7855	89	8	.	.	PUNCT
easat-7855	90	1	technique	technique	NOUN
easat-7855	90	2	inputs	input	NOUN
easat-7855	90	3	outputs	output	NOUN
easat-7855	90	4	description	description	NOUN
easat-7855	90	5	finite	finite	NOUN
easat-7855	90	6	difference	difference	NOUN
easat-7855	90	7	method	method	NOUN
easat-7855	90	8	(	(	PUNCT
easat-7855	90	9	fdm	fdm	NOUN
easat-7855	90	10	)	)	PUNCT
easat-7855	90	11	for	for	ADP
easat-7855	90	12	navier	navier	NOUN
easat-7855	90	13	-	-	PUNCT
easat-7855	90	14	stokes	stokes	PROPN
easat-7855	90	15	grid	grid	NOUN
easat-7855	90	16	size	size	NOUN
easat-7855	90	17	,	,	PUNCT
easat-7855	90	18	time	time	NOUN
easat-7855	90	19	steps	step	NOUN
easat-7855	90	20	,	,	PUNCT
easat-7855	90	21	viscosity	viscosity	NOUN
easat-7855	90	22	,	,	PUNCT
easat-7855	90	23	density	density	NOUN
easat-7855	90	24	velocity	velocity	NOUN
easat-7855	90	25	field	field	NOUN
easat-7855	90	26	(	(	PUNCT
easat-7855	90	27	u	u	NOUN
easat-7855	90	28	,	,	PUNCT
easat-7855	90	29	v	v	NOUN
easat-7855	90	30	)	)	PUNCT
easat-7855	90	31	,	,	PUNCT
easat-7855	90	32	pressure	pressure	NOUN
easat-7855	90	33	field	field	NOUN
easat-7855	90	34	(	(	PUNCT
easat-7855	90	35	p	p	NOUN
easat-7855	90	36	)	)	PUNCT
easat-7855	90	37	,	,	PUNCT
easat-7855	90	38	vorticity	vorticity	NOUN
easat-7855	90	39	,	,	PUNCT
easat-7855	90	40	streamlines	streamline	NOUN
easat-7855	90	41	simulates	simulate	NOUN
easat-7855	90	42	fluid	fluid	ADJ
easat-7855	90	43	flow	flow	NOUN
easat-7855	90	44	in	in	ADP
easat-7855	90	45	a	a	DET
easat-7855	90	46	lid	lid	NOUN
easat-7855	90	47	-	-	PUNCT
easat-7855	90	48	driven	drive	VERB
easat-7855	90	49	cavity	cavity	NOUN
easat-7855	90	50	using	use	VERB
easat-7855	90	51	a	a	DET
easat-7855	90	52	traditional	traditional	ADJ
easat-7855	90	53	finite	finite	ADJ
easat-7855	90	54	difference	difference	NOUN
easat-7855	90	55	method	method	NOUN
easat-7855	90	56	to	to	PART
easat-7855	90	57	solve	solve	VERB
easat-7855	90	58	navierstokes	navierstoke	NOUN
easat-7855	90	59	equations	equation	NOUN
easat-7855	90	60	.	.	PUNCT
easat-7855	91	1	gpu	gpu	NOUN
easat-7855	91	2	-	-	PUNCT
easat-7855	91	3	accelerated	accelerate	VERB
easat-7855	91	4	navier	navier	NOUN
easat-7855	91	5	-	-	PUNCT
easat-7855	91	6	stokes	stoke	NOUN
easat-7855	91	7	using	use	VERB
easat-7855	91	8	pytorch	pytorch	NOUN
easat-7855	91	9	grid	grid	NOUN
easat-7855	91	10	size	size	NOUN
easat-7855	91	11	,	,	PUNCT
easat-7855	91	12	time	time	NOUN
easat-7855	91	13	steps	step	NOUN
easat-7855	91	14	,	,	PUNCT
easat-7855	91	15	viscosity	viscosity	NOUN
easat-7855	91	16	velocity	velocity	NOUN
easat-7855	91	17	field	field	NOUN
easat-7855	91	18	(	(	PUNCT
easat-7855	91	19	u	u	NOUN
easat-7855	91	20	,	,	PUNCT
easat-7855	91	21	v	v	NOUN
easat-7855	91	22	)	)	PUNCT
easat-7855	91	23	,	,	PUNCT
easat-7855	91	24	pressure	pressure	NOUN
easat-7855	91	25	field	field	NOUN
easat-7855	91	26	(	(	PUNCT
easat-7855	91	27	p	p	NOUN
easat-7855	91	28	)	)	PUNCT
easat-7855	91	29	utilizes	utilize	VERB
easat-7855	91	30	pytorch	pytorch	NOUN
easat-7855	91	31	for	for	ADP
easat-7855	91	32	gpu	gpu	NOUN
easat-7855	91	33	-	-	PUNCT
easat-7855	91	34	accelerated	accelerate	VERB
easat-7855	91	35	computation	computation	NOUN
easat-7855	91	36	of	of	ADP
easat-7855	91	37	fluid	fluid	ADJ
easat-7855	91	38	flow	flow	NOUN
easat-7855	91	39	,	,	PUNCT
easat-7855	91	40	enhancing	enhance	VERB
easat-7855	91	41	computational	computational	ADJ
easat-7855	91	42	speed	speed	NOUN
easat-7855	91	43	and	and	CCONJ
easat-7855	91	44	scalability	scalability	NOUN
easat-7855	91	45	.	.	PUNCT
easat-7855	92	1	spectral	spectral	ADJ
easat-7855	92	2	method	method	NOUN
easat-7855	92	3	for	for	ADP
easat-7855	92	4	poisson	poisson	NOUN
easat-7855	92	5	's	's	PART
easat-7855	92	6	equation	equation	NOUN
easat-7855	92	7	in	in	ADP
easat-7855	92	8	circular	circular	ADJ
easat-7855	92	9	domain	domain	NOUN
easat-7855	92	10	grid	grid	NOUN
easat-7855	92	11	size	size	NOUN
easat-7855	92	12	,	,	PUNCT
easat-7855	92	13	radius	radius	NOUN
easat-7855	92	14	,	,	PUNCT
easat-7855	92	15	max	max	PROPN
easat-7855	92	16	iterations	iteration	NOUN
easat-7855	92	17	solution	solution	NOUN
easat-7855	92	18	to	to	ADP
easat-7855	92	19	poisson	poisson	PROPN
easat-7855	92	20	’s	’s	PART
easat-7855	92	21	equation	equation	NOUN
easat-7855	92	22	(	(	PUNCT
easat-7855	92	23	u	u	NOUN
easat-7855	92	24	)	)	PUNCT
easat-7855	92	25	,	,	PUNCT
easat-7855	92	26	cartesian	cartesian	ADJ
easat-7855	92	27	grid	grid	NOUN
easat-7855	92	28	(	(	PUNCT
easat-7855	92	29	x	x	NOUN
easat-7855	92	30	,	,	PUNCT
easat-7855	92	31	y	y	NOUN
easat-7855	92	32	)	)	PUNCT
easat-7855	92	33	solves	solve	VERB
easat-7855	92	34	poisson	poisson	NOUN
easat-7855	92	35	’s	’s	PART
easat-7855	92	36	equation	equation	NOUN
easat-7855	92	37	in	in	ADP
easat-7855	92	38	a	a	DET
easat-7855	92	39	circular	circular	ADJ
easat-7855	92	40	domain	domain	NOUN
easat-7855	92	41	using	use	VERB
easat-7855	92	42	fourier	fourier	NOUN
easat-7855	92	43	transforms	transform	NOUN
easat-7855	92	44	,	,	PUNCT
easat-7855	92	45	allowing	allow	VERB
easat-7855	92	46	for	for	ADP
easat-7855	92	47	high	high	ADJ
easat-7855	92	48	precision	precision	NOUN
easat-7855	92	49	in	in	ADP
easat-7855	92	50	solving	solve	VERB
easat-7855	92	51	pdes	pde	NOUN
easat-7855	92	52	with	with	ADP
easat-7855	92	53	periodic	periodic	ADJ
easat-7855	92	54	boundary	boundary	ADJ
easat-7855	92	55	conditions	condition	NOUN
easat-7855	92	56	.	.	PUNCT
easat-7855	93	1	table	table	NOUN
easat-7855	93	2	3	3	NUM
easat-7855	93	3	.	.	PUNCT
easat-7855	94	1	equation	equation	NOUN
easat-7855	94	2	details	detail	NOUN
easat-7855	94	3	that	that	PRON
easat-7855	94	4	used	use	VERB
easat-7855	94	5	.	.	PUNCT
easat-7855	95	1	4	4	X
easat-7855	95	2	.	.	NOUN
easat-7855	95	3	results	result	NOUN
easat-7855	95	4	and	and	CCONJ
easat-7855	95	5	discussion	discussion	VERB
easat-7855	95	6	the	the	DET
easat-7855	95	7	outcomes	outcome	NOUN
easat-7855	95	8	of	of	ADP
easat-7855	95	9	the	the	DET
easat-7855	95	10	unified	unified	ADJ
easat-7855	95	11	mathematical	mathematical	ADJ
easat-7855	95	12	paradigm	paradigm	NOUN
easat-7855	95	13	are	be	AUX
easat-7855	95	14	provided	provide	VERB
easat-7855	95	15	and	and	CCONJ
easat-7855	95	16	addressed	address	VERB
easat-7855	95	17	in	in	ADP
easat-7855	95	18	this	this	DET
easat-7855	95	19	part	part	NOUN
easat-7855	95	20	of	of	ADP
easat-7855	95	21	the	the	DET
easat-7855	95	22	paper	paper	NOUN
easat-7855	95	23	.	.	PUNCT
easat-7855	96	1	the	the	DET
easat-7855	96	2	mathematical	mathematical	ADJ
easat-7855	96	3	models	model	NOUN
easat-7855	96	4	encompass	encompass	VERB
easat-7855	96	5	the	the	DET
easat-7855	96	6	flow	flow	NOUN
easat-7855	96	7	of	of	ADP
easat-7855	96	8	fluid	fluid	ADJ
easat-7855	96	9	motion	motion	NOUN
easat-7855	96	10	,	,	PUNCT
easat-7855	96	11	pressure	pressure	NOUN
easat-7855	96	12	shipment	shipment	NOUN
easat-7855	96	13	,	,	PUNCT
easat-7855	96	14	and	and	CCONJ
easat-7855	96	15	the	the	DET
easat-7855	96	16	transfer	transfer	NOUN
easat-7855	96	17	of	of	ADP
easat-7855	96	18	heat	heat	NOUN
easat-7855	96	19	in	in	ADP
easat-7855	96	20	a	a	DET
easat-7855	96	21	variety	variety	NOUN
easat-7855	96	22	of	of	ADP
easat-7855	96	23	circumstances	circumstance	NOUN
easat-7855	96	24	.	.	PUNCT
easat-7855	97	1	the	the	DET
easat-7855	97	2	functioning	functioning	NOUN
easat-7855	97	3	of	of	ADP
easat-7855	97	4	the	the	DET
easat-7855	97	5	suggested	suggest	VERB
easat-7855	97	6	system	system	NOUN
easat-7855	97	7	is	be	AUX
easat-7855	97	8	evaluated	evaluate	VERB
easat-7855	97	9	on	on	ADP
easat-7855	97	10	the	the	DET
easat-7855	97	11	basis	basis	NOUN
easat-7855	97	12	of	of	ADP
easat-7855	97	13	precision	precision	NOUN
easat-7855	97	14	,	,	PUNCT
easat-7855	97	15	computational	computational	ADJ
easat-7855	97	16	productivity	productivity	NOUN
easat-7855	97	17	,	,	PUNCT
easat-7855	97	18	and	and	CCONJ
easat-7855	97	19	adaptability	adaptability	NOUN
easat-7855	97	20	,	,	PUNCT
easat-7855	97	21	as	as	SCONJ
easat-7855	97	22	shown	show	VERB
easat-7855	97	23	in	in	ADP
easat-7855	97	24	table3	table3	PROPN
easat-7855	97	25	.	.	PUNCT
easat-7855	98	1	table	table	NOUN
easat-7855	98	2	3	3	NUM
easat-7855	98	3	:	:	PUNCT
easat-7855	99	1	the	the	DET
easat-7855	99	2	results	result	NOUN
easat-7855	99	3	and	and	CCONJ
easat-7855	99	4	performance	performance	NOUN
easat-7855	99	5	of	of	ADP
easat-7855	99	6	the	the	DET
easat-7855	99	7	computational	computational	ADJ
easat-7855	99	8	models	model	NOUN
easat-7855	99	9	,	,	PUNCT
easat-7855	99	10	the	the	DET
easat-7855	99	11	tables	table	NOUN
easat-7855	99	12	4	4	NUM
easat-7855	99	13	-	-	SYM
easat-7855	99	14	9	9	NUM
easat-7855	99	15	are	be	AUX
easat-7855	99	16	illustrate	illustrate	ADJ
easat-7855	99	17	the	the	DET
easat-7855	99	18	velocity	velocity	NOUN
easat-7855	99	19	,	,	PUNCT
easat-7855	99	20	temperature	temperature	NOUN
easat-7855	99	21	distribution	distribution	NOUN
easat-7855	99	22	,	,	PUNCT
easat-7855	99	23	integrated	integrate	VERB
easat-7855	99	24	system	system	NOUN
easat-7855	99	25	performance	performance	NOUN
easat-7855	99	26	,	,	PUNCT
easat-7855	99	27	and	and	CCONJ
easat-7855	99	28	scalability	scalability	NOUN
easat-7855	99	29	analysis	analysis	NOUN
easat-7855	99	30	field	field	NOUN
easat-7855	99	31	simulation	simulation	NOUN
easat-7855	99	32	sequentially	sequentially	ADV
easat-7855	99	33	.	.	PUNCT
easat-7855	100	1	equation	equation	NOUN
easat-7855	100	2	numerical	numerical	PROPN
easat-7855	100	3	method	method	PROPN
easat-7855	100	4	computational	computational	ADJ
easat-7855	100	5	approach	approach	NOUN
easat-7855	100	6	expected	expect	VERB
easat-7855	100	7	outputs	output	NOUN
easat-7855	100	8	navier	navier	NOUN
easat-7855	100	9	-	-	PUNCT
easat-7855	100	10	stokes	stoke	NOUN
easat-7855	100	11	equation	equation	NOUN
easat-7855	100	12	𝜕𝑢	𝜕𝑢	NOUN
easat-7855	100	13	𝜕𝑡	𝜕𝑡	NOUN
easat-7855	101	1	+	+	CCONJ
easat-7855	101	2	(	(	PUNCT
easat-7855	101	3	𝑢.	𝑢.	NOUN
easat-7855	101	4	∇)𝑢	∇)𝑢	PROPN
easat-7855	101	5	=	=	SYM
easat-7855	101	6	−1	−1	NOUN
easat-7855	101	7	𝑝	𝑝	NOUN
easat-7855	101	8	∇𝑝	∇𝑝	ADJ
easat-7855	101	9	+	+	CCONJ
easat-7855	101	10	𝑣∇2𝑢	𝑣∇2𝑢	NOUN
easat-7855	101	11	+	+	CCONJ
easat-7855	101	12	𝑓	𝑓	DET
easat-7855	101	13	finite	finite	ADJ
easat-7855	101	14	difference	difference	NOUN
easat-7855	101	15	method	method	NOUN
easat-7855	101	16	(	(	PUNCT
easat-7855	101	17	fdm	fdm	NOUN
easat-7855	101	18	)	)	PUNCT
easat-7855	101	19	central	central	ADJ
easat-7855	101	20	difference	difference	NOUN
easat-7855	101	21	and	and	CCONJ
easat-7855	101	22	timestepping	timesteppe	VERB
easat-7855	101	23	techniques	technique	NOUN
easat-7855	101	24	for	for	ADP
easat-7855	101	25	velocity	velocity	NOUN
easat-7855	101	26	and	and	CCONJ
easat-7855	101	27	pressure	pressure	NOUN
easat-7855	101	28	calculations	calculation	NOUN
easat-7855	101	29	simulating	simulate	VERB
easat-7855	101	30	fluid	fluid	ADJ
easat-7855	101	31	motion	motion	NOUN
easat-7855	101	32	with	with	ADP
easat-7855	101	33	non	non	ADJ
easat-7855	101	34	-	-	ADJ
easat-7855	101	35	turbulent	turbulent	ADJ
easat-7855	101	36	flow	flow	NOUN
easat-7855	101	37	poisson	poisson	NOUN
easat-7855	101	38	equation	equation	NOUN
easat-7855	101	39	𝛁𝟐∅	𝛁𝟐∅	PROPN
easat-7855	101	40	=	=	SYM
easat-7855	101	41	𝒇(𝒙	𝒇(𝒙	NUM
easat-7855	101	42	,	,	PUNCT
easat-7855	101	43	𝒚	𝒚	NOUN
easat-7855	101	44	)	)	PUNCT
easat-7855	101	45	spectral	spectral	ADJ
easat-7855	101	46	methods	method	NOUN
easat-7855	101	47	fourier	fourier	NOUN
easat-7855	101	48	transform	transform	VERB
easat-7855	101	49	and	and	CCONJ
easat-7855	101	50	solving	solve	VERB
easat-7855	101	51	the	the	DET
easat-7855	101	52	equation	equation	NOUN
easat-7855	101	53	in	in	ADP
easat-7855	101	54	frequency	frequency	NOUN
easat-7855	101	55	space	space	NOUN
easat-7855	101	56	pressure	pressure	NOUN
easat-7855	101	57	or	or	CCONJ
easat-7855	101	58	temperature	temperature	NOUN
easat-7855	101	59	distribution	distribution	NOUN
easat-7855	101	60	in	in	ADP
easat-7855	101	61	a	a	DET
easat-7855	101	62	spatial	spatial	ADJ
easat-7855	101	63	domain	domain	NOUN
easat-7855	101	64	continuity	continuity	NOUN
easat-7855	101	65	equation	equation	NOUN
easat-7855	101	66	𝝏𝒑	𝝏𝒑	PRON
easat-7855	101	67	𝝏𝒕	𝝏𝒕	X
easat-7855	101	68	+	+	CCONJ
easat-7855	101	69	𝛁.	𝛁.	NUM
easat-7855	101	70	(	(	PUNCT
easat-7855	101	71	𝒑𝒖	𝒑𝒖	NOUN
easat-7855	101	72	)	)	PUNCT
easat-7855	101	73	=	=	SYM
easat-7855	101	74	𝟎	𝟎	NUM
easat-7855	101	75	finite	finite	ADJ
easat-7855	101	76	difference	difference	NOUN
easat-7855	101	77	method	method	NOUN
easat-7855	101	78	(	(	PUNCT
easat-7855	101	79	fdm	fdm	NOUN
easat-7855	101	80	)	)	PUNCT
easat-7855	101	81	computational	computational	ADJ
easat-7855	101	82	grid	grid	NOUN
easat-7855	101	83	to	to	PART
easat-7855	101	84	calculate	calculate	VERB
easat-7855	101	85	density	density	NOUN
easat-7855	101	86	gradients	gradient	NOUN
easat-7855	101	87	density	density	NOUN
easat-7855	101	88	distribution	distribution	NOUN
easat-7855	101	89	across	across	ADP
easat-7855	101	90	a	a	DET
easat-7855	101	91	specific	specific	ADJ
easat-7855	101	92	domain	domain	NOUN
easat-7855	101	93	heat	heat	NOUN
easat-7855	101	94	equation	equation	NOUN
easat-7855	101	95	𝝏𝑻	𝝏𝑻	X
easat-7855	101	96	𝝏𝒕	𝝏𝒕	X
easat-7855	101	97	=	=	SYM
easat-7855	101	98	𝜶𝛁𝟐𝑻	𝜶𝛁𝟐𝑻	ADJ
easat-7855	101	99	gpu	gpu	NOUN
easat-7855	101	100	acceleration	acceleration	NOUN
easat-7855	101	101	(	(	PUNCT
easat-7855	101	102	pytorch	pytorch	NOUN
easat-7855	101	103	)	)	PUNCT
easat-7855	101	104	implementing	implement	VERB
easat-7855	101	105	simulations	simulation	NOUN
easat-7855	101	106	using	use	VERB
easat-7855	101	107	gpus	gpu	NOUN
easat-7855	101	108	for	for	ADP
easat-7855	101	109	enhanced	enhanced	ADJ
easat-7855	101	110	performance	performance	NOUN
easat-7855	101	111	temperature	temperature	NOUN
easat-7855	101	112	distribution	distribution	NOUN
easat-7855	101	113	over	over	ADP
easat-7855	101	114	time	time	NOUN
easat-7855	101	115	in	in	ADP
easat-7855	101	116	a	a	DET
easat-7855	101	117	given	give	VERB
easat-7855	101	118	domain	domain	NOUN
easat-7855	101	119	570	570	NUM
easat-7855	101	120	edelweiss	edelweiss	PROPN
easat-7855	101	121	applied	apply	VERB
easat-7855	101	122	science	science	NOUN
easat-7855	101	123	and	and	CCONJ
easat-7855	101	124	technology	technology	NOUN
easat-7855	101	125	issn	issn	PROPN
easat-7855	101	126	:	:	PUNCT
easat-7855	101	127	2576	2576	NUM
easat-7855	101	128	-	-	SYM
easat-7855	101	129	8484	8484	NUM
easat-7855	101	130	vol	vol	NOUN
easat-7855	101	131	.	.	PROPN
easat-7855	101	132	9	9	NUM
easat-7855	101	133	,	,	PUNCT
easat-7855	101	134	no	no	INTJ
easat-7855	101	135	.	.	NOUN
easat-7855	102	1	6	6	NUM
easat-7855	102	2	:	:	SYM
easat-7855	102	3	566	566	NUM
easat-7855	102	4	-	-	SYM
easat-7855	102	5	575	575	NUM
easat-7855	102	6	,	,	PUNCT
easat-7855	102	7	2025	2025	NUM
easat-7855	102	8	doi	doi	NOUN
easat-7855	102	9	:	:	PUNCT
easat-7855	102	10	10.55214/25768484.v9i6.7855	10.55214/25768484.v9i6.7855	NUM
easat-7855	102	11	©	©	PROPN
easat-7855	102	12	2025	2025	NUM
easat-7855	102	13	by	by	ADP
easat-7855	102	14	the	the	DET
easat-7855	102	15	author	author	NOUN
easat-7855	102	16	;	;	PUNCT
easat-7855	102	17	licensee	licensee	PROPN
easat-7855	102	18	learning	learn	VERB
easat-7855	102	19	gate	gate	NOUN
easat-7855	102	20	table	table	NOUN
easat-7855	102	21	4	4	NUM
easat-7855	102	22	.	.	PUNCT
easat-7855	103	1	the	the	DET
easat-7855	103	2	results	result	NOUN
easat-7855	103	3	and	and	CCONJ
easat-7855	103	4	performance	performance	NOUN
easat-7855	103	5	of	of	ADP
easat-7855	103	6	the	the	DET
easat-7855	103	7	computational	computational	ADJ
easat-7855	103	8	models	model	NOUN
easat-7855	103	9	.	.	PUNCT
easat-7855	104	1	section	section	NOUN
easat-7855	104	2	details	detail	NOUN
easat-7855	104	3	1	1	NUM
easat-7855	104	4	.	.	PUNCT
easat-7855	104	5	navier	navier	NOUN
easat-7855	104	6	-	-	PUNCT
easat-7855	104	7	stokes	stokes	PROPN
easat-7855	104	8	solver	solver	NOUN
easat-7855	104	9	results	result	NOUN
easat-7855	104	10	case	case	NOUN
easat-7855	104	11	study	study	NOUN
easat-7855	104	12	:	:	PUNCT
easat-7855	104	13	lid	lid	NOUN
easat-7855	104	14	-	-	PUNCT
easat-7855	104	15	driven	drive	VERB
easat-7855	104	16	cavity	cavity	NOUN
easat-7855	104	17	flow	flow	VERB
easat-7855	104	18	•	•	NOUN
easat-7855	104	19	velocity	velocity	NOUN
easat-7855	104	20	field	field	NOUN
easat-7855	104	21	:	:	PUNCT
easat-7855	104	22	expected	expect	VERB
easat-7855	104	23	formation	formation	NOUN
easat-7855	104	24	of	of	ADP
easat-7855	104	25	primary	primary	ADJ
easat-7855	104	26	and	and	CCONJ
easat-7855	104	27	secondary	secondary	ADJ
easat-7855	104	28	vortices	vortex	NOUN
easat-7855	104	29	,	,	PUNCT
easat-7855	104	30	aligning	align	VERB
easat-7855	104	31	with	with	ADP
easat-7855	104	32	benchmark	benchmark	ADJ
easat-7855	104	33	data	datum	NOUN
easat-7855	104	34	.	.	PUNCT
easat-7855	105	1	•	•	NUM
easat-7855	105	2	convergence	convergence	NOUN
easat-7855	105	3	:	:	PUNCT
easat-7855	105	4	converged	converge	VERB
easat-7855	105	5	with	with	ADP
easat-7855	105	6	residuals	residual	NOUN
easat-7855	105	7	below	below	ADP
easat-7855	105	8	tolerance	tolerance	NOUN
easat-7855	105	9	;	;	PUNCT
easat-7855	105	10	effective	effective	ADJ
easat-7855	105	11	pressure	pressure	NOUN
easat-7855	105	12	correction	correction	NOUN
easat-7855	105	13	.	.	PUNCT
easat-7855	106	1	•	•	NUM
easat-7855	106	2	discussion	discussion	NOUN
easat-7855	106	3	:	:	PUNCT
easat-7855	106	4	staggered	staggered	ADJ
easat-7855	106	5	grid	grid	NOUN
easat-7855	106	6	and	and	CCONJ
easat-7855	106	7	pressure	pressure	NOUN
easat-7855	106	8	correction	correction	NOUN
easat-7855	106	9	methods	method	NOUN
easat-7855	106	10	effectively	effectively	ADV
easat-7855	106	11	resolve	resolve	VERB
easat-7855	106	12	flow	flow	NOUN
easat-7855	106	13	patterns	pattern	NOUN
easat-7855	106	14	,	,	PUNCT
easat-7855	106	15	demonstrating	demonstrate	VERB
easat-7855	106	16	solver	solver	ADJ
easat-7855	106	17	accuracy	accuracy	NOUN
easat-7855	106	18	.	.	PUNCT
easat-7855	107	1	2	2	X
easat-7855	107	2	.	.	X
easat-7855	107	3	poisson	poisson	PROPN
easat-7855	107	4	equation	equation	NOUN
easat-7855	107	5	solver	solver	NOUN
easat-7855	107	6	results	result	VERB
easat-7855	107	7	case	case	NOUN
easat-7855	107	8	study	study	NOUN
easat-7855	107	9	:	:	PUNCT
easat-7855	107	10	circular	circular	ADJ
easat-7855	107	11	domain	domain	NOUN
easat-7855	107	12	pressure	pressure	NOUN
easat-7855	107	13	distribution	distribution	NOUN
easat-7855	107	14	•	•	NOUN
easat-7855	107	15	pressure	pressure	NOUN
easat-7855	107	16	field	field	NOUN
easat-7855	107	17	:	:	PUNCT
easat-7855	107	18	numerical	numerical	ADJ
easat-7855	107	19	results	result	NOUN
easat-7855	107	20	closely	closely	ADV
easat-7855	107	21	match	match	VERB
easat-7855	107	22	the	the	DET
easat-7855	107	23	analytical	analytical	ADJ
easat-7855	107	24	solution	solution	NOUN
easat-7855	107	25	.	.	PUNCT
easat-7855	108	1	•	•	NUM
easat-7855	108	2	efficiency	efficiency	NOUN
easat-7855	108	3	:	:	PUNCT
easat-7855	108	4	ffts	fft	NOUN
easat-7855	108	5	reduced	reduce	VERB
easat-7855	108	6	computation	computation	NOUN
easat-7855	108	7	time	time	NOUN
easat-7855	108	8	significantly	significantly	ADV
easat-7855	108	9	.	.	PUNCT
easat-7855	109	1	•	•	NUM
easat-7855	109	2	discussion	discussion	NOUN
easat-7855	109	3	:	:	PUNCT
easat-7855	109	4	spectral	spectral	ADJ
easat-7855	109	5	method	method	NOUN
easat-7855	109	6	excels	excel	VERB
easat-7855	109	7	in	in	ADP
easat-7855	109	8	accuracy	accuracy	NOUN
easat-7855	109	9	and	and	CCONJ
easat-7855	109	10	efficiency	efficiency	NOUN
easat-7855	109	11	for	for	ADP
easat-7855	109	12	periodic	periodic	ADJ
easat-7855	109	13	boundary	boundary	ADJ
easat-7855	109	14	conditions	condition	NOUN
easat-7855	109	15	and	and	CCONJ
easat-7855	109	16	complex	complex	ADJ
easat-7855	109	17	geometries	geometry	NOUN
easat-7855	109	18	.	.	PUNCT
easat-7855	110	1	3	3	X
easat-7855	110	2	.	.	X
easat-7855	110	3	heat	heat	NOUN
easat-7855	110	4	equation	equation	NOUN
easat-7855	110	5	solver	solver	NOUN
easat-7855	110	6	results	result	NOUN
easat-7855	110	7	case	case	NOUN
easat-7855	110	8	study	study	NOUN
easat-7855	110	9	:	:	PUNCT
easat-7855	110	10	heat	heat	NOUN
easat-7855	110	11	conduction	conduction	NOUN
easat-7855	110	12	in	in	ADP
easat-7855	110	13	a	a	DET
easat-7855	110	14	metal	metal	NOUN
easat-7855	110	15	plate	plate	NOUN
easat-7855	110	16	•	•	NOUN
easat-7855	110	17	temperature	temperature	NOUN
easat-7855	110	18	distribution	distribution	NOUN
easat-7855	110	19	:	:	PUNCT
easat-7855	110	20	smooth	smooth	ADJ
easat-7855	110	21	diffusion	diffusion	NOUN
easat-7855	110	22	from	from	ADP
easat-7855	110	23	hot	hot	ADJ
easat-7855	110	24	spot	spot	NOUN
easat-7855	110	25	;	;	PUNCT
easat-7855	110	26	well	well	ADV
easat-7855	110	27	-	-	PUNCT
easat-7855	110	28	visualized	visualize	VERB
easat-7855	110	29	.	.	PUNCT
easat-7855	111	1	•	•	NUM
easat-7855	111	2	performance	performance	NOUN
easat-7855	111	3	:	:	PUNCT
easat-7855	111	4	significant	significant	ADJ
easat-7855	111	5	speedup	speedup	NOUN
easat-7855	111	6	with	with	ADP
easat-7855	111	7	gpu	gpu	NOUN
easat-7855	111	8	acceleration	acceleration	NOUN
easat-7855	111	9	;	;	PUNCT
easat-7855	111	10	handles	handle	VERB
easat-7855	111	11	large	large	ADJ
easat-7855	111	12	grids	grid	NOUN
easat-7855	111	13	efficiently	efficiently	ADV
easat-7855	111	14	.	.	PUNCT
easat-7855	112	1	•	•	NUM
easat-7855	112	2	discussion	discussion	NOUN
easat-7855	112	3	:	:	PUNCT
easat-7855	112	4	accurate	accurate	ADJ
easat-7855	112	5	and	and	CCONJ
easat-7855	112	6	fast	fast	ADJ
easat-7855	112	7	simulations	simulation	NOUN
easat-7855	112	8	,	,	PUNCT
easat-7855	112	9	suitable	suitable	ADJ
easat-7855	112	10	for	for	ADP
easat-7855	112	11	large	large	ADJ
easat-7855	112	12	-	-	PUNCT
easat-7855	112	13	scale	scale	NOUN
easat-7855	112	14	problems	problem	NOUN
easat-7855	112	15	.	.	PUNCT
easat-7855	113	1	4	4	X
easat-7855	113	2	.	.	X
easat-7855	113	3	integrated	integrate	VERB
easat-7855	113	4	system	system	NOUN
easat-7855	113	5	performance	performance	NOUN
easat-7855	113	6	scenario	scenario	NOUN
easat-7855	113	7	:	:	PUNCT
easat-7855	113	8	coupled	couple	VERB
easat-7855	113	9	fluid	fluid	ADJ
easat-7855	113	10	flow	flow	NOUN
easat-7855	113	11	and	and	CCONJ
easat-7855	113	12	heat	heat	NOUN
easat-7855	113	13	transfer	transfer	NOUN
easat-7855	113	14	•	•	NOUN
easat-7855	113	15	simulation	simulation	NOUN
easat-7855	113	16	workflow	workflow	NOUN
easat-7855	113	17	:	:	PUNCT
easat-7855	113	18	simulated	simulate	VERB
easat-7855	113	19	cooling	cooling	NOUN
easat-7855	113	20	in	in	ADP
easat-7855	113	21	a	a	DET
easat-7855	113	22	heat	heat	NOUN
easat-7855	113	23	exchanger	exchanger	NOUN
easat-7855	113	24	;	;	PUNCT
easat-7855	113	25	data	datum	NOUN
easat-7855	113	26	exchange	exchange	NOUN
easat-7855	113	27	ensured	ensure	VERB
easat-7855	113	28	consistency	consistency	NOUN
easat-7855	113	29	.	.	PUNCT
easat-7855	114	1	•	•	NUM
easat-7855	114	2	results	result	NOUN
easat-7855	114	3	:	:	PUNCT
easat-7855	114	4	accurate	accurate	ADJ
easat-7855	114	5	simulation	simulation	NOUN
easat-7855	114	6	of	of	ADP
easat-7855	114	7	coupled	couple	VERB
easat-7855	114	8	phenomena	phenomenon	NOUN
easat-7855	114	9	with	with	ADP
easat-7855	114	10	proper	proper	ADJ
easat-7855	114	11	data	datum	NOUN
easat-7855	114	12	exchange	exchange	NOUN
easat-7855	114	13	.	.	PUNCT
easat-7855	115	1	•	•	NUM
easat-7855	115	2	discussion	discussion	NOUN
easat-7855	115	3	:	:	PUNCT
easat-7855	115	4	comprehensive	comprehensive	ADJ
easat-7855	115	5	simulation	simulation	NOUN
easat-7855	115	6	of	of	ADP
easat-7855	115	7	multi	multi	ADJ
easat-7855	115	8	-	-	ADJ
easat-7855	115	9	physics	physics	ADJ
easat-7855	115	10	scenarios	scenario	NOUN
easat-7855	115	11	,	,	PUNCT
easat-7855	115	12	applicable	applicable	ADJ
easat-7855	115	13	to	to	ADP
easat-7855	115	14	engineering	engineering	NOUN
easat-7855	115	15	problems	problem	NOUN
easat-7855	115	16	.	.	PUNCT
easat-7855	116	1	5	5	X
easat-7855	116	2	.	.	X
easat-7855	116	3	validation	validation	NOUN
easat-7855	116	4	and	and	CCONJ
easat-7855	116	5	comparison	comparison	NOUN
easat-7855	116	6	validation	validation	NOUN
easat-7855	116	7	:	:	PUNCT
easat-7855	116	8	results	result	NOUN
easat-7855	116	9	validated	validate	VERB
easat-7855	116	10	against	against	ADP
easat-7855	116	11	analytical	analytical	ADJ
easat-7855	116	12	solutions	solution	NOUN
easat-7855	116	13	and	and	CCONJ
easat-7855	116	14	benchmarks	benchmark	NOUN
easat-7855	116	15	;	;	PUNCT
easat-7855	116	16	close	close	ADJ
easat-7855	116	17	agreement	agreement	NOUN
easat-7855	116	18	confirms	confirm	VERB
easat-7855	116	19	accuracy	accuracy	NOUN
easat-7855	116	20	.	.	PUNCT
easat-7855	117	1	comparison	comparison	NOUN
easat-7855	117	2	:	:	PUNCT
easat-7855	117	3	superior	superior	ADJ
easat-7855	117	4	accuracy	accuracy	NOUN
easat-7855	117	5	and	and	CCONJ
easat-7855	117	6	efficiency	efficiency	NOUN
easat-7855	117	7	compared	compare	VERB
easat-7855	117	8	to	to	ADP
easat-7855	117	9	standalone	standalone	ADJ
easat-7855	117	10	solvers	solver	NOUN
easat-7855	117	11	and	and	CCONJ
easat-7855	117	12	other	other	ADJ
easat-7855	117	13	methods	method	NOUN
easat-7855	117	14	,	,	PUNCT
easat-7855	117	15	especially	especially	ADV
easat-7855	117	16	for	for	ADP
easat-7855	117	17	complex	complex	ADJ
easat-7855	117	18	scenarios	scenario	NOUN
easat-7855	117	19	.	.	PUNCT
easat-7855	118	1	6	6	X
easat-7855	118	2	.	.	X
easat-7855	118	3	scalability	scalability	NOUN
easat-7855	118	4	and	and	CCONJ
easat-7855	118	5	computational	computational	ADJ
easat-7855	118	6	efficiency	efficiency	NOUN
easat-7855	118	7	scalability	scalability	NOUN
easat-7855	118	8	:	:	PUNCT
easat-7855	118	9	tested	test	VERB
easat-7855	118	10	with	with	ADP
easat-7855	118	11	increased	increase	VERB
easat-7855	118	12	grid	grid	NOUN
easat-7855	118	13	size	size	NOUN
easat-7855	118	14	and	and	CCONJ
easat-7855	118	15	time	time	NOUN
easat-7855	118	16	steps	step	NOUN
easat-7855	118	17	;	;	PUNCT
easat-7855	118	18	linear	linear	ADJ
easat-7855	118	19	increase	increase	NOUN
easat-7855	118	20	in	in	ADP
easat-7855	118	21	computation	computation	NOUN
easat-7855	118	22	time	time	NOUN
easat-7855	118	23	.	.	PUNCT
easat-7855	119	1	gpu	gpu	NOUN
easat-7855	119	2	acceleration	acceleration	NOUN
easat-7855	119	3	improved	improve	VERB
easat-7855	119	4	overall	overall	ADJ
easat-7855	119	5	efficiency	efficiency	NOUN
easat-7855	119	6	.	.	PUNCT
easat-7855	120	1	efficiency	efficiency	NOUN
easat-7855	120	2	:	:	PUNCT
easat-7855	120	3	significant	significant	ADJ
easat-7855	120	4	speedup	speedup	NOUN
easat-7855	120	5	in	in	ADP
easat-7855	120	6	time	time	NOUN
easat-7855	120	7	-	-	PUNCT
easat-7855	120	8	to	to	ADP
easat-7855	120	9	-	-	PUNCT
easat-7855	120	10	solution	solution	NOUN
easat-7855	120	11	with	with	ADP
easat-7855	120	12	gpu	gpu	NOUN
easat-7855	120	13	acceleration	acceleration	NOUN
easat-7855	120	14	and	and	CCONJ
easat-7855	120	15	efficient	efficient	ADJ
easat-7855	120	16	methods	method	NOUN
easat-7855	120	17	.	.	PUNCT
easat-7855	121	1	table	table	NOUN
easat-7855	121	2	5	5	NUM
easat-7855	121	3	.	.	PUNCT
easat-7855	121	4	velocity	velocity	NOUN
easat-7855	121	5	field	field	NOUN
easat-7855	121	6	comparison	comparison	NOUN
easat-7855	121	7	for	for	ADP
easat-7855	121	8	lid	lid	NOUN
easat-7855	121	9	-	-	PUNCT
easat-7855	121	10	driven	drive	VERB
easat-7855	121	11	cavity	cavity	NOUN
easat-7855	121	12	flow	flow	NOUN
easat-7855	121	13	.	.	PUNCT
easat-7855	122	1	grid	grid	NOUN
easat-7855	122	2	size	size	NOUN
easat-7855	122	3	primary	primary	ADJ
easat-7855	122	4	vortex	vortex	NOUN
easat-7855	122	5	center	center	NOUN
easat-7855	122	6	(	(	PUNCT
easat-7855	122	7	x	x	NOUN
easat-7855	122	8	,	,	PUNCT
easat-7855	122	9	y	y	NOUN
easat-7855	122	10	)	)	PUNCT
easat-7855	122	11	velocity	velocity	NOUN
easat-7855	122	12	at	at	ADP
easat-7855	122	13	center	center	NOUN
easat-7855	122	14	(	(	PUNCT
easat-7855	122	15	u	u	NOUN
easat-7855	122	16	,	,	PUNCT
easat-7855	122	17	v	v	NOUN
easat-7855	122	18	)	)	PUNCT
easat-7855	122	19	convergence	convergence	NOUN
easat-7855	122	20	iterations	iteration	NOUN
easat-7855	122	21	residual	residual	ADJ
easat-7855	122	22	32x32	32x32	NUM
easat-7855	122	23	(	(	PUNCT
easat-7855	122	24	0.617	0.617	NUM
easat-7855	122	25	,	,	PUNCT
easat-7855	122	26	0.734	0.734	NUM
easat-7855	122	27	)	)	PUNCT
easat-7855	122	28	(	(	PUNCT
easat-7855	122	29	0.062	0.062	NUM
easat-7855	122	30	,	,	PUNCT
easat-7855	122	31	-0.041	-0.041	NUM
easat-7855	122	32	)	)	PUNCT
easat-7855	122	33	500	500	NUM
easat-7855	122	34	1.0e-4	1.0e-4	NUM
easat-7855	122	35	64x64	64x64	NUM
easat-7855	122	36	(	(	PUNCT
easat-7855	122	37	0.619	0.619	NUM
easat-7855	122	38	,	,	PUNCT
easat-7855	122	39	0.735	0.735	NUM
easat-7855	122	40	)	)	PUNCT
easat-7855	122	41	(	(	PUNCT
easat-7855	122	42	0.060	0.060	NUM
easat-7855	122	43	,	,	PUNCT
easat-7855	122	44	-0.043	-0.043	NUM
easat-7855	122	45	)	)	PUNCT
easat-7855	122	46	480	480	NUM
easat-7855	122	47	9.5e-5	9.5e-5	NUM
easat-7855	122	48	128x128	128x128	NUM
easat-7855	122	49	(	(	PUNCT
easat-7855	122	50	0.620	0.620	NUM
easat-7855	122	51	,	,	PUNCT
easat-7855	122	52	0.736	0.736	NUM
easat-7855	122	53	)	)	PUNCT
easat-7855	122	54	(	(	PUNCT
easat-7855	122	55	0.058	0.058	NUM
easat-7855	122	56	,	,	PUNCT
easat-7855	122	57	-0.044	-0.044	PROPN
easat-7855	122	58	)	)	PUNCT
easat-7855	122	59	460	460	NUM
easat-7855	122	60	8.0e-5	8.0e-5	NUM
easat-7855	122	61	table	table	NOUN
easat-7855	122	62	6	6	NUM
easat-7855	122	63	.	.	PUNCT
easat-7855	122	64	pressure	pressure	NOUN
easat-7855	122	65	field	field	NOUN
easat-7855	122	66	accuracy	accuracy	NOUN
easat-7855	122	67	in	in	ADP
easat-7855	122	68	circular	circular	ADJ
easat-7855	122	69	domain	domain	NOUN
easat-7855	122	70	.	.	PUNCT
easat-7855	123	1	method	method	PROPN
easat-7855	123	2	maximum	maximum	ADJ
easat-7855	123	3	error	error	NOUN
easat-7855	123	4	rms	rm	NOUN
easat-7855	123	5	error	error	NOUN
easat-7855	123	6	computation	computation	NOUN
easat-7855	123	7	time	time	NOUN
easat-7855	123	8	(	(	PUNCT
easat-7855	123	9	s	s	NOUN
easat-7855	123	10	)	)	PUNCT
easat-7855	123	11	grid	grid	NOUN
easat-7855	123	12	size	size	NOUN
easat-7855	123	13	finite	finite	NOUN
easat-7855	123	14	difference	difference	NOUN
easat-7855	123	15	0.0056	0.0056	NUM
easat-7855	123	16	0.0024	0.0024	NUM
easat-7855	123	17	120	120	NUM
easat-7855	123	18	128x128	128x128	NUM
easat-7855	123	19	spectral	spectral	PROPN
easat-7855	123	20	method	method	NOUN
easat-7855	123	21	0.0003	0.0003	NUM
easat-7855	123	22	0.0001	0.0001	NUM
easat-7855	123	23	15	15	NUM
easat-7855	123	24	128x128	128x128	NUM
easat-7855	123	25	table	table	NOUN
easat-7855	123	26	7	7	NUM
easat-7855	123	27	.	.	PUNCT
easat-7855	123	28	temperature	temperature	NOUN
easat-7855	123	29	distribution	distribution	NOUN
easat-7855	123	30	in	in	ADP
easat-7855	123	31	metal	metal	NOUN
easat-7855	123	32	plate	plate	NOUN
easat-7855	123	33	(	(	PUNCT
easat-7855	123	34	gpu	gpu	X
easat-7855	123	35	vs	vs	ADP
easat-7855	123	36	cpu	cpu	NOUN
easat-7855	123	37	)	)	PUNCT
easat-7855	123	38	.	.	PUNCT
easat-7855	124	1	solver	solver	PROPN
easat-7855	124	2	grid	grid	NOUN
easat-7855	124	3	size	size	NOUN
easat-7855	124	4	time	time	NOUN
easat-7855	124	5	step	step	NOUN
easat-7855	124	6	max	max	PROPN
easat-7855	124	7	temperature	temperature	NOUN
easat-7855	124	8	(	(	PUNCT
easat-7855	124	9	°	°	ADP
easat-7855	124	10	c	c	NOUN
easat-7855	124	11	)	)	PUNCT
easat-7855	124	12	computation	computation	NOUN
easat-7855	124	13	time	time	NOUN
easat-7855	124	14	(	(	PUNCT
easat-7855	124	15	s	s	NOUN
easat-7855	124	16	)	)	PUNCT
easat-7855	124	17	cpu	cpu	NOUN
easat-7855	124	18	-	-	PUNCT
easat-7855	124	19	based	base	VERB
easat-7855	124	20	solver	solver	NOUN
easat-7855	124	21	256x256	256x256	PROPN
easat-7855	124	22	0.01	0.01	NUM
easat-7855	124	23	105.2	105.2	NUM
easat-7855	124	24	240	240	NUM
easat-7855	124	25	gpu	gpu	NOUN
easat-7855	124	26	-	-	PUNCT
easat-7855	124	27	accelerated	accelerate	VERB
easat-7855	124	28	256x256	256x256	PROPN
easat-7855	124	29	0.01	0.01	NUM
easat-7855	124	30	105.2	105.2	NUM
easat-7855	124	31	25	25	NUM
easat-7855	124	32	table	table	NOUN
easat-7855	124	33	8	8	NUM
easat-7855	124	34	.	.	PUNCT
easat-7855	124	35	integrated	integrate	VERB
easat-7855	124	36	system	system	NOUN
easat-7855	124	37	performance	performance	NOUN
easat-7855	124	38	(	(	PUNCT
easat-7855	124	39	coupled	couple	VERB
easat-7855	124	40	fluid	fluid	ADJ
easat-7855	124	41	flow	flow	NOUN
easat-7855	124	42	and	and	CCONJ
easat-7855	124	43	heat	heat	NOUN
easat-7855	124	44	transfer	transfer	NOUN
easat-7855	124	45	)	)	PUNCT
easat-7855	124	46	.	.	PUNCT
easat-7855	125	1	scenario	scenario	NOUN
easat-7855	125	2	time	time	NOUN
easat-7855	125	3	to	to	ADP
easat-7855	125	4	solution	solution	NOUN
easat-7855	125	5	(	(	PUNCT
easat-7855	125	6	s	s	NOUN
easat-7855	125	7	)	)	PUNCT
easat-7855	125	8	temperature	temperature	NOUN
easat-7855	125	9	deviation	deviation	NOUN
easat-7855	125	10	(	(	PUNCT
easat-7855	125	11	°	°	ADP
easat-7855	125	12	c	c	NOUN
easat-7855	125	13	)	)	PUNCT
easat-7855	125	14	velocity	velocity	NOUN
easat-7855	125	15	deviation	deviation	NOUN
easat-7855	125	16	(	(	PUNCT
easat-7855	125	17	m	m	NOUN
easat-7855	125	18	/	/	SYM
easat-7855	125	19	s	s	PART
easat-7855	125	20	)	)	PUNCT
easat-7855	125	21	convergence	convergence	NOUN
easat-7855	125	22	time	time	NOUN
easat-7855	125	23	(	(	PUNCT
easat-7855	125	24	iterations	iteration	NOUN
easat-7855	125	25	)	)	PUNCT
easat-7855	125	26	heat	heat	NOUN
easat-7855	125	27	exchanger	exchanger	NOUN
easat-7855	125	28	low	low	ADJ
easat-7855	125	29	flow	flow	NOUN
easat-7855	125	30	rate	rate	NOUN
easat-7855	125	31	180	180	NUM
easat-7855	125	32	2.3	2.3	NUM
easat-7855	125	33	0.05	0.05	NUM
easat-7855	125	34	600	600	NUM
easat-7855	125	35	heat	heat	NOUN
easat-7855	125	36	exchanger	exchanger	NOUN
easat-7855	125	37	high	high	ADJ
easat-7855	125	38	flow	flow	NOUN
easat-7855	125	39	rate	rate	NOUN
easat-7855	125	40	300	300	NUM
easat-7855	125	41	1.7	1.7	NUM
easat-7855	125	42	0.02	0.02	NUM
easat-7855	125	43	700	700	NUM
easat-7855	125	44	571	571	NUM
easat-7855	125	45	edelweiss	edelweiss	PROPN
easat-7855	125	46	applied	apply	VERB
easat-7855	125	47	science	science	NOUN
easat-7855	125	48	and	and	CCONJ
easat-7855	125	49	technology	technology	NOUN
easat-7855	125	50	issn	issn	PROPN
easat-7855	125	51	:	:	PUNCT
easat-7855	125	52	2576	2576	NUM
easat-7855	125	53	-	-	SYM
easat-7855	125	54	8484	8484	NUM
easat-7855	125	55	vol	vol	NOUN
easat-7855	125	56	.	.	PROPN
easat-7855	126	1	9	9	NUM
easat-7855	126	2	,	,	PUNCT
easat-7855	126	3	no	no	INTJ
easat-7855	126	4	.	.	NOUN
easat-7855	127	1	6	6	NUM
easat-7855	127	2	:	:	SYM
easat-7855	127	3	566	566	NUM
easat-7855	127	4	-	-	SYM
easat-7855	127	5	575	575	NUM
easat-7855	127	6	,	,	PUNCT
easat-7855	127	7	2025	2025	NUM
easat-7855	127	8	doi	doi	NOUN
easat-7855	127	9	:	:	PUNCT
easat-7855	127	10	10.55214/25768484.v9i6.7855	10.55214/25768484.v9i6.7855	NUM
easat-7855	127	11	©	©	PROPN
easat-7855	127	12	2025	2025	NUM
easat-7855	127	13	by	by	ADP
easat-7855	127	14	the	the	DET
easat-7855	127	15	author	author	NOUN
easat-7855	127	16	;	;	PUNCT
easat-7855	127	17	licensee	licensee	PROPN
easat-7855	127	18	learning	learn	VERB
easat-7855	127	19	gate	gate	NOUN
easat-7855	127	20	table	table	NOUN
easat-7855	127	21	9	9	NUM
easat-7855	127	22	.	.	PUNCT
easat-7855	127	23	table	table	NOUN
easat-7855	127	24	5	5	NUM
easat-7855	127	25	:	:	PUNCT
easat-7855	127	26	scalability	scalability	NOUN
easat-7855	127	27	analysis	analysis	NOUN
easat-7855	127	28	of	of	ADP
easat-7855	127	29	integrated	integrated	ADJ
easat-7855	127	30	system	system	NOUN
easat-7855	127	31	.	.	PUNCT
easat-7855	128	1	grid	grid	NOUN
easat-7855	128	2	size	size	NOUN
easat-7855	128	3	number	number	NOUN
easat-7855	128	4	of	of	ADP
easat-7855	128	5	time	time	NOUN
easat-7855	128	6	steps	step	NOUN
easat-7855	128	7	total	total	ADJ
easat-7855	128	8	computation	computation	NOUN
easat-7855	128	9	time	time	NOUN
easat-7855	128	10	(	(	PUNCT
easat-7855	128	11	s	s	NOUN
easat-7855	128	12	)	)	PUNCT
easat-7855	128	13	speedup	speedup	NOUN
easat-7855	128	14	(	(	PUNCT
easat-7855	128	15	gpu	gpu	X
easat-7855	128	16	vs	vs	ADP
easat-7855	128	17	cpu	cpu	PROPN
easat-7855	128	18	)	)	PUNCT
easat-7855	128	19	64x64	64x64	NUM
easat-7855	128	20	1000	1000	NUM
easat-7855	128	21	120	120	NUM
easat-7855	128	22	4x	4x	NOUN
easat-7855	128	23	128x128	128x128	NUM
easat-7855	128	24	1000	1000	NUM
easat-7855	128	25	300	300	NUM
easat-7855	128	26	4x	4x	NOUN
easat-7855	128	27	256x256	256x256	PROPN
easat-7855	128	28	1000	1000	NUM
easat-7855	128	29	800	800	NUM
easat-7855	128	30	5x	5x	NOUN
easat-7855	128	31	the	the	DET
easat-7855	128	32	figure	figure	NOUN
easat-7855	128	33	1	1	NUM
easat-7855	128	34	,	,	PUNCT
easat-7855	128	35	depicts	depict	VERB
easat-7855	128	36	the	the	DET
easat-7855	128	37	outcomes	outcome	NOUN
easat-7855	128	38	of	of	ADP
easat-7855	128	39	the	the	DET
easat-7855	128	40	fluid	fluid	ADJ
easat-7855	128	41	dynamic	dynamic	ADJ
easat-7855	128	42	model	model	NOUN
easat-7855	128	43	.	.	PUNCT
easat-7855	129	1	initially	initially	ADV
easat-7855	129	2	it	it	PRON
easat-7855	129	3	shows	show	VERB
easat-7855	129	4	pressures	pressure	NOUN
easat-7855	129	5	as	as	ADP
easat-7855	129	6	a	a	DET
easat-7855	129	7	color	color	NOUN
easat-7855	129	8	heat	heat	NOUN
easat-7855	129	9	map	map	NOUN
easat-7855	129	10	.	.	PUNCT
easat-7855	130	1	in	in	ADP
easat-7855	130	2	addition	addition	NOUN
easat-7855	130	3	,	,	PUNCT
easat-7855	130	4	it	it	PRON
easat-7855	130	5	displays	display	VERB
easat-7855	130	6	the	the	DET
easat-7855	130	7	speed	speed	NOUN
easat-7855	130	8	of	of	ADP
easat-7855	130	9	the	the	DET
easat-7855	130	10	field	field	NOUN
easat-7855	130	11	of	of	ADP
easat-7855	130	12	view	view	NOUN
easat-7855	130	13	,	,	PUNCT
easat-7855	130	14	with	with	ADP
easat-7855	130	15	arrow	arrow	NOUN
easat-7855	130	16	indicating	indicate	VERB
easat-7855	130	17	orientation	orientation	NOUN
easat-7855	130	18	and	and	CCONJ
easat-7855	130	19	strength	strength	NOUN
easat-7855	130	20	.	.	PUNCT
easat-7855	131	1	furthermore	furthermore	ADV
easat-7855	131	2	,	,	PUNCT
easat-7855	131	3	it	it	PRON
easat-7855	131	4	shows	show	VERB
easat-7855	131	5	the	the	DET
easat-7855	131	6	speed	speed	NOUN
easat-7855	131	7	's	's	PART
easat-7855	131	8	magnitude	magnitude	NOUN
easat-7855	131	9	as	as	ADP
easat-7855	131	10	a	a	DET
easat-7855	131	11	colored	colored	ADJ
easat-7855	131	12	heatmap	heatmap	NOUN
easat-7855	131	13	.	.	PUNCT
easat-7855	132	1	fourthly	fourthly	ADV
easat-7855	132	2	,	,	PUNCT
easat-7855	132	3	it	it	PRON
easat-7855	132	4	shows	show	VERB
easat-7855	132	5	outlines	outline	NOUN
easat-7855	132	6	to	to	PART
easat-7855	132	7	help	help	VERB
easat-7855	132	8	comprehend	comprehend	VERB
easat-7855	132	9	the	the	DET
easat-7855	132	10	flow	flow	NOUN
easat-7855	132	11	of	of	ADP
easat-7855	132	12	fluid	fluid	ADJ
easat-7855	132	13	pathways	pathway	NOUN
easat-7855	132	14	.	.	PUNCT
easat-7855	133	1	finally	finally	ADV
easat-7855	133	2	,	,	PUNCT
easat-7855	133	3	it	it	PRON
easat-7855	133	4	displays	display	VERB
easat-7855	133	5	a	a	DET
easat-7855	133	6	vorticity	vorticity	NOUN
easat-7855	133	7	as	as	ADP
easat-7855	133	8	a	a	DET
easat-7855	133	9	color	color	NOUN
easat-7855	133	10	heatmap	heatmap	NOUN
easat-7855	133	11	to	to	PART
easat-7855	133	12	represent	represent	VERB
easat-7855	133	13	the	the	DET
easat-7855	133	14	liquid	liquid	NOUN
easat-7855	133	15	's	's	PART
easat-7855	133	16	rotation	rotation	NOUN
easat-7855	133	17	properties	property	NOUN
easat-7855	133	18	.	.	PUNCT
easat-7855	134	1	figure	figure	NOUN
easat-7855	134	2	1	1	NUM
easat-7855	134	3	.	.	PUNCT
easat-7855	135	1	distribution	distribution	NOUN
easat-7855	135	2	of	of	ADP
easat-7855	135	3	vorticity	vorticity	NOUN
easat-7855	135	4	showing	show	VERB
easat-7855	135	5	rotation	rotation	NOUN
easat-7855	135	6	intensity	intensity	NOUN
easat-7855	135	7	in	in	ADP
easat-7855	135	8	the	the	DET
easat-7855	135	9	flow	flow	NOUN
easat-7855	135	10	field	field	NOUN
easat-7855	135	11	.	.	PUNCT
easat-7855	136	1	572	572	NUM
easat-7855	136	2	edelweiss	edelweiss	PROPN
easat-7855	136	3	applied	apply	VERB
easat-7855	136	4	science	science	NOUN
easat-7855	136	5	and	and	CCONJ
easat-7855	136	6	technology	technology	NOUN
easat-7855	136	7	issn	issn	PROPN
easat-7855	136	8	:	:	PUNCT
easat-7855	136	9	2576	2576	NUM
easat-7855	136	10	-	-	SYM
easat-7855	136	11	8484	8484	NUM
easat-7855	136	12	vol	vol	NOUN
easat-7855	136	13	.	.	PROPN
easat-7855	137	1	9	9	NUM
easat-7855	137	2	,	,	PUNCT
easat-7855	137	3	no	no	INTJ
easat-7855	137	4	.	.	NOUN
easat-7855	138	1	6	6	NUM
easat-7855	138	2	:	:	SYM
easat-7855	138	3	566	566	NUM
easat-7855	138	4	-	-	SYM
easat-7855	138	5	575	575	NUM
easat-7855	138	6	,	,	PUNCT
easat-7855	138	7	2025	2025	NUM
easat-7855	138	8	doi	doi	NOUN
easat-7855	138	9	:	:	PUNCT
easat-7855	138	10	10.55214/25768484.v9i6.7855	10.55214/25768484.v9i6.7855	NUM
easat-7855	138	11	©	©	PROPN
easat-7855	138	12	2025	2025	NUM
easat-7855	138	13	by	by	ADP
easat-7855	138	14	the	the	DET
easat-7855	138	15	author	author	NOUN
easat-7855	138	16	;	;	PUNCT
easat-7855	138	17	licensee	licensee	PROPN
easat-7855	138	18	learning	learn	VERB
easat-7855	138	19	gate	gate	NOUN
easat-7855	138	20	figure	figure	NOUN
easat-7855	138	21	2	2	NUM
easat-7855	138	22	.	.	PUNCT
easat-7855	138	23	pressure	pressure	NOUN
easat-7855	138	24	distribution	distribution	NOUN
easat-7855	138	25	across	across	ADP
easat-7855	138	26	the	the	DET
easat-7855	138	27	domain	domain	NOUN
easat-7855	138	28	.	.	PUNCT
easat-7855	139	1	figure	figure	NOUN
easat-7855	139	2	3	3	NUM
easat-7855	139	3	.	.	PUNCT
easat-7855	139	4	velocity	velocity	NOUN
easat-7855	139	5	vectors	vector	NOUN
easat-7855	139	6	indicating	indicate	VERB
easat-7855	139	7	direction	direction	NOUN
easat-7855	139	8	and	and	CCONJ
easat-7855	139	9	magnitude	magnitude	NOUN
easat-7855	139	10	of	of	ADP
easat-7855	139	11	flow	flow	NOUN
easat-7855	139	12	.	.	PUNCT
easat-7855	140	1	573	573	NUM
easat-7855	140	2	edelweiss	edelweiss	PROPN
easat-7855	140	3	applied	apply	VERB
easat-7855	140	4	science	science	NOUN
easat-7855	140	5	and	and	CCONJ
easat-7855	140	6	technology	technology	NOUN
easat-7855	140	7	issn	issn	PROPN
easat-7855	140	8	:	:	PUNCT
easat-7855	140	9	2576	2576	NUM
easat-7855	140	10	-	-	SYM
easat-7855	140	11	8484	8484	NUM
easat-7855	140	12	vol	vol	NOUN
easat-7855	140	13	.	.	PROPN
easat-7855	141	1	9	9	NUM
easat-7855	141	2	,	,	PUNCT
easat-7855	141	3	no	no	INTJ
easat-7855	141	4	.	.	NOUN
easat-7855	142	1	6	6	NUM
easat-7855	142	2	:	:	SYM
easat-7855	142	3	566	566	NUM
easat-7855	142	4	-	-	SYM
easat-7855	142	5	575	575	NUM
easat-7855	142	6	,	,	PUNCT
easat-7855	142	7	2025	2025	NUM
easat-7855	142	8	doi	doi	NOUN
easat-7855	142	9	:	:	PUNCT
easat-7855	142	10	10.55214/25768484.v9i6.7855	10.55214/25768484.v9i6.7855	NUM
easat-7855	142	11	©	©	PROPN
easat-7855	142	12	2025	2025	NUM
easat-7855	142	13	by	by	ADP
easat-7855	142	14	the	the	DET
easat-7855	142	15	author	author	NOUN
easat-7855	142	16	;	;	PUNCT
easat-7855	142	17	licensee	licensee	PROPN
easat-7855	142	18	learning	learn	VERB
easat-7855	142	19	gate	gate	NOUN
easat-7855	142	20	figure	figure	NOUN
easat-7855	142	21	4	4	NUM
easat-7855	142	22	.	.	PUNCT
easat-7855	143	1	contour	contour	NOUN
easat-7855	143	2	of	of	ADP
easat-7855	143	3	velocity	velocity	NOUN
easat-7855	143	4	magnitude	magnitude	NOUN
easat-7855	143	5	showing	show	VERB
easat-7855	143	6	speed	speed	NOUN
easat-7855	143	7	variations	variation	NOUN
easat-7855	143	8	.	.	PUNCT
easat-7855	144	1	figure	figure	NOUN
easat-7855	144	2	5	5	NUM
easat-7855	144	3	.	.	PUNCT
easat-7855	145	1	streamlines	streamline	NOUN
easat-7855	145	2	depicting	depict	VERB
easat-7855	145	3	flow	flow	NOUN
easat-7855	145	4	paths	path	NOUN
easat-7855	145	5	colored	color	VERB
easat-7855	145	6	by	by	ADP
easat-7855	145	7	velocity	velocity	NOUN
easat-7855	145	8	magnitude	magnitude	NOUN
easat-7855	145	9	.	.	PUNCT
easat-7855	146	1	574	574	NUM
easat-7855	146	2	edelweiss	edelweiss	PROPN
easat-7855	146	3	applied	apply	VERB
easat-7855	146	4	science	science	NOUN
easat-7855	146	5	and	and	CCONJ
easat-7855	146	6	technology	technology	NOUN
easat-7855	146	7	issn	issn	PROPN
easat-7855	146	8	:	:	PUNCT
easat-7855	146	9	2576	2576	NUM
easat-7855	146	10	-	-	SYM
easat-7855	146	11	8484	8484	NUM
easat-7855	146	12	vol	vol	NOUN
easat-7855	146	13	.	.	PROPN
easat-7855	147	1	9	9	NUM
easat-7855	147	2	,	,	PUNCT
easat-7855	147	3	no	no	INTJ
easat-7855	147	4	.	.	NOUN
easat-7855	148	1	6	6	NUM
easat-7855	148	2	:	:	SYM
easat-7855	148	3	566	566	NUM
easat-7855	148	4	-	-	SYM
easat-7855	148	5	575	575	NUM
easat-7855	148	6	,	,	PUNCT
easat-7855	148	7	2025	2025	NUM
easat-7855	148	8	doi	doi	NOUN
easat-7855	148	9	:	:	PUNCT
easat-7855	148	10	10.55214/25768484.v9i6.7855	10.55214/25768484.v9i6.7855	NUM
easat-7855	148	11	©	©	PROPN
easat-7855	148	12	2025	2025	NUM
easat-7855	148	13	by	by	ADP
easat-7855	148	14	the	the	DET
easat-7855	148	15	author	author	NOUN
easat-7855	148	16	;	;	PUNCT
easat-7855	148	17	licensee	licensee	PROPN
easat-7855	148	18	learning	learn	VERB
easat-7855	148	19	gate	gate	PROPN
easat-7855	148	20	figure	figure	NOUN
easat-7855	148	21	6	6	NUM
easat-7855	148	22	shows	show	VERB
easat-7855	148	23	several	several	ADJ
easat-7855	148	24	subplots	subplot	NOUN
easat-7855	148	25	exhibiting	exhibit	VERB
easat-7855	148	26	the	the	DET
easat-7855	148	27	averages	average	NOUN
easat-7855	148	28	of	of	ADP
easat-7855	148	29	parts	part	NOUN
easat-7855	148	30	of	of	ADP
easat-7855	148	31	velocity	velocity	NOUN
easat-7855	148	32	and	and	CCONJ
easat-7855	148	33	pressure	pressure	NOUN
easat-7855	148	34	.	.	PUNCT
easat-7855	149	1	the	the	DET
easat-7855	149	2	initial	initial	ADJ
easat-7855	149	3	sidebar	sidebar	NOUN
easat-7855	149	4	exhibits	exhibit	VERB
easat-7855	149	5	the	the	DET
easat-7855	149	6	u	u	NOUN
easat-7855	149	7	part	part	NOUN
easat-7855	149	8	of	of	ADP
easat-7855	149	9	velocity	velocity	NOUN
easat-7855	149	10	(	(	PUNCT
easat-7855	149	11	horizontal	horizontal	ADJ
easat-7855	149	12	)	)	PUNCT
easat-7855	149	13	,	,	PUNCT
easat-7855	149	14	which	which	PRON
easat-7855	149	15	has	have	VERB
easat-7855	149	16	numbers	number	NOUN
easat-7855	149	17	near	near	ADP
easat-7855	149	18	zero	zero	NUM
easat-7855	149	19	.	.	PUNCT
easat-7855	150	1	the	the	DET
easat-7855	150	2	following	follow	VERB
easat-7855	150	3	plot	plot	NOUN
easat-7855	150	4	shows	show	VERB
easat-7855	150	5	the	the	DET
easat-7855	150	6	v	v	ADJ
easat-7855	150	7	part	part	NOUN
easat-7855	150	8	of	of	ADP
easat-7855	150	9	the	the	DET
easat-7855	150	10	velocity	velocity	NOUN
easat-7855	150	11	(	(	PUNCT
easat-7855	150	12	vertical	vertical	ADJ
easat-7855	150	13	)	)	PUNCT
easat-7855	150	14	,	,	PUNCT
easat-7855	150	15	it	it	PRON
easat-7855	150	16	is	be	AUX
easat-7855	150	17	scaled	scale	VERB
easat-7855	150	18	similarly	similarly	ADV
easat-7855	150	19	to	to	ADP
easat-7855	150	20	the	the	DET
easat-7855	150	21	u	u	NOUN
easat-7855	150	22	part	part	NOUN
easat-7855	150	23	.	.	PUNCT
easat-7855	151	1	the	the	DET
easat-7855	151	2	last	last	ADJ
easat-7855	151	3	plot	plot	NOUN
easat-7855	151	4	depicts	depict	VERB
easat-7855	151	5	a	a	DET
easat-7855	151	6	pressure	pressure	NOUN
easat-7855	151	7	gradient	gradient	NOUN
easat-7855	151	8	throughout	throughout	ADP
easat-7855	151	9	the	the	DET
easat-7855	151	10	area	area	NOUN
easat-7855	151	11	in	in	ADP
easat-7855	151	12	question	question	NOUN
easat-7855	151	13	,	,	PUNCT
easat-7855	151	14	with	with	ADP
easat-7855	151	15	levels	level	NOUN
easat-7855	151	16	approaching	approach	VERB
easat-7855	151	17	zero	zero	NUM
easat-7855	151	18	representing	represent	VERB
easat-7855	151	19	a	a	DET
easat-7855	151	20	stable	stable	ADJ
easat-7855	151	21	state	state	NOUN
easat-7855	151	22	in	in	ADP
easat-7855	151	23	the	the	DET
easat-7855	151	24	environment	environment	NOUN
easat-7855	151	25	being	be	AUX
easat-7855	151	26	mimicked	mimic	VERB
easat-7855	151	27	.	.	PUNCT
easat-7855	152	1	figure	figure	NOUN
easat-7855	152	2	6	6	NUM
easat-7855	152	3	.	.	PUNCT
easat-7855	152	4	velocity	velocity	NOUN
easat-7855	152	5	and	and	CCONJ
easat-7855	152	6	pressure	pressure	NOUN
easat-7855	152	7	distribution	distribution	NOUN
easat-7855	152	8	.	.	PUNCT
easat-7855	153	1	5	5	X
easat-7855	153	2	.	.	X
easat-7855	153	3	conclusion	conclusion	NOUN
easat-7855	153	4	the	the	DET
easat-7855	153	5	results	result	NOUN
easat-7855	153	6	show	show	VERB
easat-7855	153	7	that	that	SCONJ
easat-7855	153	8	the	the	DET
easat-7855	153	9	proposed	propose	VERB
easat-7855	153	10	approach	approach	NOUN
easat-7855	153	11	is	be	AUX
easat-7855	153	12	excellent	excellent	ADJ
easat-7855	153	13	at	at	ADP
easat-7855	153	14	modeling	model	VERB
easat-7855	153	15	difficult	difficult	ADJ
easat-7855	153	16	fluid	fluid	ADJ
easat-7855	153	17	circulation	circulation	NOUN
easat-7855	153	18	and	and	CCONJ
easat-7855	153	19	heat	heat	NOUN
easat-7855	153	20	transfer	transfer	NOUN
easat-7855	153	21	conditions	condition	NOUN
easat-7855	153	22	.	.	PUNCT
easat-7855	154	1	the	the	DET
easat-7855	154	2	merging	merging	NOUN
easat-7855	154	3	of	of	ADP
easat-7855	154	4	the	the	DET
easat-7855	154	5	navier	navier	NOUN
easat-7855	154	6	-	-	PUNCT
easat-7855	154	7	stokes	stokes	PROPN
easat-7855	154	8	solver	solver	NOUN
easat-7855	154	9	,	,	PUNCT
easat-7855	154	10	the	the	DET
easat-7855	154	11	poisson	poisson	NOUN
easat-7855	154	12	equation	equation	NOUN
easat-7855	154	13	solver	solver	ADV
easat-7855	154	14	,	,	PUNCT
easat-7855	154	15	and	and	CCONJ
easat-7855	154	16	the	the	DET
easat-7855	154	17	heat	heat	NOUN
easat-7855	154	18	equation	equation	NOUN
easat-7855	154	19	solver	solver	NOUN
easat-7855	154	20	give	give	VERB
easat-7855	154	21	an	an	DET
easat-7855	154	22	effective	effective	ADJ
easat-7855	154	23	means	mean	NOUN
easat-7855	154	24	for	for	ADP
easat-7855	154	25	technical	technical	ADJ
easat-7855	154	26	and	and	CCONJ
easat-7855	154	27	analytical	analytical	ADJ
easat-7855	154	28	modeling	modeling	NOUN
easat-7855	154	29	.	.	PUNCT
easat-7855	155	1	the	the	DET
easat-7855	155	2	framework	framework	NOUN
easat-7855	155	3	's	's	PART
easat-7855	155	4	detail	detail	NOUN
easat-7855	155	5	,	,	PUNCT
easat-7855	155	6	efficacy	efficacy	NOUN
easat-7855	155	7	,	,	PUNCT
easat-7855	155	8	and	and	CCONJ
easat-7855	155	9	universality	universality	NOUN
easat-7855	155	10	allow	allow	VERB
easat-7855	155	11	it	it	PRON
easat-7855	155	12	to	to	PART
easat-7855	155	13	be	be	AUX
easat-7855	155	14	suitable	suitable	ADJ
easat-7855	155	15	in	in	ADP
easat-7855	155	16	numerous	numerous	ADJ
easat-7855	155	17	usages	usage	NOUN
easat-7855	155	18	,	,	PUNCT
easat-7855	155	19	include	include	VERB
easat-7855	155	20	scientific	scientific	ADJ
easat-7855	155	21	analysis	analysis	NOUN
easat-7855	155	22	and	and	CCONJ
easat-7855	155	23	the	the	DET
easat-7855	155	24	design	design	NOUN
easat-7855	155	25	of	of	ADP
easat-7855	155	26	products	product	NOUN
easat-7855	155	27	.	.	PUNCT
easat-7855	156	1	the	the	DET
easat-7855	156	2	finished	finished	ADJ
easat-7855	156	3	product	product	NOUN
easat-7855	156	4	of	of	ADP
easat-7855	156	5	the	the	DET
easat-7855	156	6	results	result	NOUN
easat-7855	156	7	monitoring	monitoring	NOUN
easat-7855	156	8	and	and	CCONJ
easat-7855	156	9	evaluation	evaluation	NOUN
easat-7855	156	10	reveals	reveal	VERB
easat-7855	156	11	the	the	DET
easat-7855	156	12	technique	technique	NOUN
easat-7855	156	13	's	's	PART
easat-7855	156	14	stability	stability	NOUN
easat-7855	156	15	and	and	CCONJ
easat-7855	156	16	promise	promise	NOUN
easat-7855	156	17	for	for	ADP
easat-7855	156	18	future	future	ADJ
easat-7855	156	19	enhancement	enhancement	NOUN
easat-7855	156	20	.	.	PUNCT
easat-7855	157	1	the	the	DET
easat-7855	157	2	starting	starting	NOUN
easat-7855	157	3	point	point	NOUN
easat-7855	157	4	is	be	AUX
easat-7855	157	5	to	to	PART
easat-7855	157	6	determine	determine	VERB
easat-7855	157	7	the	the	DET
easat-7855	157	8	navierstokes	navierstoke	NOUN
easat-7855	157	9	equations	equation	NOUN
easat-7855	157	10	for	for	ADP
easat-7855	157	11	an	an	DET
easat-7855	157	12	invulnerable	invulnerable	NOUN
easat-7855	157	13	to	to	PART
easat-7855	157	14	channel	channel	VERB
easat-7855	157	15	using	use	VERB
easat-7855	157	16	ordinary	ordinary	ADJ
easat-7855	157	17	mathematical	mathematical	ADJ
easat-7855	157	18	strategies	strategy	NOUN
easat-7855	157	19	.	.	PUNCT
easat-7855	158	1	moreover	moreover	ADV
easat-7855	158	2	,	,	PUNCT
easat-7855	158	3	expanding	expand	VERB
easat-7855	158	4	capacity	capacity	NOUN
easat-7855	158	5	to	to	PART
easat-7855	158	6	permit	permit	VERB
easat-7855	158	7	bigger	big	ADJ
easat-7855	158	8	geometric	geometric	ADJ
easat-7855	158	9	complexity	complexity	NOUN
easat-7855	158	10	and	and	CCONJ
easat-7855	158	11	borders	border	NOUN
easat-7855	158	12	difficulties	difficulty	NOUN
easat-7855	158	13	,	,	PUNCT
easat-7855	158	14	alongside	alongside	ADP
easat-7855	158	15	features	feature	NOUN
easat-7855	158	16	including	include	VERB
easat-7855	158	17	actual	actual	ADJ
easat-7855	158	18	-	-	PUNCT
easat-7855	158	19	time	time	NOUN
easat-7855	158	20	information	information	NOUN
easat-7855	158	21	the	the	DET
easat-7855	158	22	production	production	NOUN
easat-7855	158	23	for	for	ADP
easat-7855	158	24	ongoing	ongoing	ADJ
easat-7855	158	25	training	training	NOUN
easat-7855	158	26	,	,	PUNCT
easat-7855	158	27	will	will	AUX
easat-7855	158	28	considerably	considerably	ADV
easat-7855	158	29	expand	expand	VERB
easat-7855	158	30	the	the	DET
easat-7855	158	31	range	range	NOUN
easat-7855	158	32	of	of	ADP
easat-7855	158	33	its	its	PRON
easat-7855	158	34	uses	use	NOUN
easat-7855	158	35	.	.	PUNCT
easat-7855	159	1	working	work	VERB
easat-7855	159	2	with	with	ADP
easat-7855	159	3	businesses	business	NOUN
easat-7855	159	4	in	in	ADP
easat-7855	159	5	applying	apply	VERB
easat-7855	159	6	computers	computer	NOUN
easat-7855	159	7	to	to	ADP
easat-7855	159	8	everyday	everyday	ADJ
easat-7855	159	9	challenges	challenge	NOUN
easat-7855	159	10	like	like	ADP
easat-7855	159	11	technology	technology	NOUN
easat-7855	159	12	may	may	AUX
easat-7855	159	13	offer	offer	VERB
easat-7855	159	14	useful	useful	ADJ
easat-7855	159	15	information	information	NOUN
easat-7855	159	16	and	and	CCONJ
easat-7855	159	17	propel	propel	VERB
easat-7855	159	18	research	research	NOUN
easat-7855	159	19	along	along	ADP
easat-7855	159	20	.	.	PUNCT
easat-7855	160	1	transparency	transparency	NOUN
easat-7855	160	2	:	:	PUNCT
easat-7855	160	3	the	the	DET
easat-7855	160	4	author	author	NOUN
easat-7855	160	5	confirms	confirm	VERB
easat-7855	160	6	that	that	SCONJ
easat-7855	160	7	the	the	DET
easat-7855	160	8	manuscript	manuscript	NOUN
easat-7855	160	9	is	be	AUX
easat-7855	160	10	an	an	DET
easat-7855	160	11	honest	honest	ADJ
easat-7855	160	12	,	,	PUNCT
easat-7855	160	13	accurate	accurate	ADJ
easat-7855	160	14	,	,	PUNCT
easat-7855	160	15	and	and	CCONJ
easat-7855	160	16	transparent	transparent	ADJ
easat-7855	160	17	account	account	NOUN
easat-7855	160	18	of	of	ADP
easat-7855	160	19	the	the	DET
easat-7855	160	20	study	study	NOUN
easat-7855	160	21	;	;	PUNCT
easat-7855	160	22	that	that	SCONJ
easat-7855	160	23	no	no	DET
easat-7855	160	24	vital	vital	ADJ
easat-7855	160	25	features	feature	NOUN
easat-7855	160	26	of	of	ADP
easat-7855	160	27	the	the	DET
easat-7855	160	28	study	study	NOUN
easat-7855	160	29	have	have	AUX
easat-7855	160	30	been	be	AUX
easat-7855	160	31	omitted	omit	VERB
easat-7855	160	32	;	;	PUNCT
easat-7855	160	33	and	and	CCONJ
easat-7855	160	34	that	that	SCONJ
easat-7855	160	35	any	any	DET
easat-7855	160	36	discrepancies	discrepancy	NOUN
easat-7855	160	37	from	from	ADP
easat-7855	160	38	the	the	DET
easat-7855	160	39	study	study	NOUN
easat-7855	160	40	as	as	SCONJ
easat-7855	160	41	planned	plan	VERB
easat-7855	160	42	have	have	AUX
easat-7855	160	43	been	be	AUX
easat-7855	160	44	explained	explain	VERB
easat-7855	160	45	.	.	PUNCT
easat-7855	161	1	this	this	DET
easat-7855	161	2	study	study	NOUN
easat-7855	161	3	followed	follow	VERB
easat-7855	161	4	all	all	DET
easat-7855	161	5	ethical	ethical	ADJ
easat-7855	161	6	practices	practice	NOUN
easat-7855	161	7	during	during	ADP
easat-7855	161	8	writing	writing	NOUN
easat-7855	161	9	.	.	PUNCT
easat-7855	162	1	acknowledgment	acknowledgment	NOUN
easat-7855	162	2	:	:	PUNCT
easat-7855	162	3	the	the	DET
easat-7855	162	4	authors	author	NOUN
easat-7855	162	5	would	would	AUX
easat-7855	162	6	like	like	VERB
easat-7855	162	7	to	to	PART
easat-7855	162	8	thank	thank	VERB
easat-7855	162	9	mustansiriyah	mustansiriyah	PROPN
easat-7855	162	10	university	university	PROPN
easat-7855	162	11	(	(	PUNCT
easat-7855	162	12	https://uomustansiriyah.edu.iq/	https://uomustansiriyah.edu.iq/	PROPN
easat-7855	162	13	)	)	PUNCT
easat-7855	162	14	in	in	ADP
easat-7855	162	15	baghdad	baghdad	PROPN
easat-7855	162	16	,	,	PUNCT
easat-7855	162	17	iraq	iraq	PROPN
easat-7855	162	18	,	,	PUNCT
easat-7855	162	19	for	for	ADP
easat-7855	162	20	its	its	PRON
easat-7855	162	21	support	support	NOUN
easat-7855	162	22	in	in	ADP
easat-7855	162	23	the	the	DET
easat-7855	162	24	present	present	ADJ
easat-7855	162	25	work	work	NOUN
easat-7855	162	26	.	.	PUNCT
easat-7855	163	1	575	575	NUM
easat-7855	163	2	edelweiss	edelweiss	PROPN
easat-7855	163	3	applied	apply	VERB
easat-7855	163	4	science	science	NOUN
easat-7855	163	5	and	and	CCONJ
easat-7855	163	6	technology	technology	NOUN
easat-7855	163	7	issn	issn	PROPN
easat-7855	163	8	:	:	PUNCT
easat-7855	163	9	2576	2576	NUM
easat-7855	163	10	-	-	SYM
easat-7855	163	11	8484	8484	NUM
easat-7855	163	12	vol	vol	NOUN
easat-7855	163	13	.	.	PROPN
easat-7855	164	1	9	9	NUM
easat-7855	164	2	,	,	PUNCT
easat-7855	164	3	no	no	INTJ
easat-7855	164	4	.	.	NOUN
easat-7855	165	1	6	6	NUM
easat-7855	165	2	:	:	SYM
easat-7855	165	3	566	566	NUM
easat-7855	165	4	-	-	SYM
easat-7855	165	5	575	575	NUM
easat-7855	165	6	,	,	PUNCT
easat-7855	165	7	2025	2025	NUM
easat-7855	165	8	doi	doi	NOUN
easat-7855	165	9	:	:	PUNCT
easat-7855	165	10	10.55214/25768484.v9i6.7855	10.55214/25768484.v9i6.7855	NUM
easat-7855	165	11	©	©	PROPN
easat-7855	165	12	2025	2025	NUM
easat-7855	165	13	by	by	ADP
easat-7855	165	14	the	the	DET
easat-7855	165	15	author	author	NOUN
easat-7855	165	16	;	;	PUNCT
easat-7855	165	17	licensee	licensee	PROPN
easat-7855	165	18	learning	learn	VERB
easat-7855	165	19	gate	gate	NOUN
easat-7855	165	20	copyright	copyright	NOUN
easat-7855	165	21	:	:	PUNCT
easat-7855	165	22	©	©	PROPN
easat-7855	165	23	2025	2025	NUM
easat-7855	165	24	by	by	ADP
easat-7855	165	25	the	the	DET
easat-7855	165	26	author	author	NOUN
easat-7855	165	27	.	.	PUNCT
easat-7855	166	1	this	this	DET
easat-7855	166	2	open	open	ADJ
easat-7855	166	3	-	-	PUNCT
easat-7855	166	4	access	access	NOUN
easat-7855	166	5	article	article	NOUN
easat-7855	166	6	is	be	AUX
easat-7855	166	7	distributed	distribute	VERB
easat-7855	166	8	under	under	ADP
easat-7855	166	9	the	the	DET
easat-7855	166	10	terms	term	NOUN
easat-7855	166	11	and	and	CCONJ
easat-7855	166	12	conditions	condition	NOUN
easat-7855	166	13	of	of	ADP
easat-7855	166	14	the	the	DET
easat-7855	166	15	creative	creative	ADJ
easat-7855	166	16	commons	common	NOUN
easat-7855	166	17	attribution	attribution	NOUN
easat-7855	166	18	(	(	PUNCT
easat-7855	166	19	cc	cc	NOUN
easat-7855	166	20	by	by	ADP
easat-7855	166	21	)	)	PUNCT
easat-7855	166	22	license	license	NOUN
easat-7855	166	23	(	(	PUNCT
easat-7855	166	24	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
easat-7855	166	25	)	)	PUNCT
easat-7855	166	26	.	.	PUNCT
easat-7855	167	1	references	reference	NOUN
easat-7855	167	2	[	[	X
easat-7855	167	3	1	1	X
easat-7855	167	4	]	]	PUNCT
easat-7855	167	5	j.	j.	PROPN
easat-7855	167	6	smith	smith	PROPN
easat-7855	167	7	and	and	CCONJ
easat-7855	167	8	a.	a.	NOUN
easat-7855	167	9	brown	brown	PROPN
easat-7855	167	10	,	,	PUNCT
easat-7855	167	11	"	"	PUNCT
easat-7855	167	12	numerical	numerical	ADJ
easat-7855	167	13	methods	method	NOUN
easat-7855	167	14	in	in	ADP
easat-7855	167	15	fluid	fluid	ADJ
easat-7855	167	16	dynamics	dynamic	NOUN
easat-7855	167	17	:	:	PUNCT
easat-7855	167	18	an	an	DET
easat-7855	167	19	overview	overview	NOUN
easat-7855	167	20	"	"	PUNCT
easat-7855	167	21	journal	journal	NOUN
easat-7855	167	22	of	of	ADP
easat-7855	167	23	computational	computational	ADJ
easat-7855	167	24	physics	physics	NOUN
easat-7855	167	25	,	,	PUNCT
easat-7855	167	26	vol	vol	NOUN
easat-7855	167	27	.	.	PROPN
easat-7855	167	28	450	450	NUM
easat-7855	167	29	,	,	PUNCT
easat-7855	167	30	p.	p.	NOUN
easat-7855	167	31	110708	110708	NUM
easat-7855	167	32	,	,	PUNCT
easat-7855	167	33	2022	2022	NUM
easat-7855	167	34	.	.	PUNCT
easat-7855	168	1	https://doi.org/10.1016/j.jcp.2021.110708	https://doi.org/10.1016/j.jcp.2021.110708	PUNCT
easat-7855	169	1	[	[	X
easat-7855	169	2	2	2	NUM
easat-7855	169	3	]	]	PUNCT
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easat-7855	169	14	for	for	ADP
easat-7855	169	15	fluid	fluid	ADJ
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easat-7855	169	17	simulation	simulation	NOUN
easat-7855	169	18	,	,	PUNCT
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easat-7855	169	21	&	&	CCONJ
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easat-7855	169	23	,	,	PUNCT
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easat-7855	169	25	.	.	PROPN
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easat-7855	169	30	,	,	PUNCT
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easat-7855	169	32	.	.	PUNCT
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easat-7855	170	4	]	]	PUNCT
easat-7855	170	5	p.	p.	PROPN
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easat-7855	170	7	and	and	CCONJ
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easat-7855	170	17	for	for	ADP
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easat-7855	170	19	geometries	geometry	NOUN
easat-7855	170	20	,	,	PUNCT
easat-7855	170	21	"	"	PUNCT
easat-7855	170	22	international	international	ADJ
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easat-7855	170	24	of	of	ADP
easat-7855	170	25	numerical	numerical	ADJ
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easat-7855	170	27	in	in	ADP
easat-7855	170	28	fluids	fluid	NOUN
easat-7855	170	29	,	,	PUNCT
easat-7855	170	30	vol	vol	NOUN
easat-7855	170	31	.	.	PROPN
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easat-7855	170	33	,	,	PUNCT
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easat-7855	170	35	.	.	NOUN
easat-7855	170	36	8	8	NUM
easat-7855	170	37	,	,	PUNCT
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easat-7855	170	39	.	.	PUNCT
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easat-7855	170	41	,	,	PUNCT
easat-7855	170	42	2021	2021	NUM
easat-7855	170	43	.	.	PUNCT
easat-7855	171	1	https://doi.org/10.1002/fld.5015	https://doi.org/10.1002/fld.5015	PROPN
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easat-7855	172	4	y.	y.	PROPN
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easat-7855	172	9	,	,	PUNCT
easat-7855	172	10	"	"	PUNCT
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easat-7855	172	12	fluid	fluid	ADJ
easat-7855	172	13	dynamics	dynamic	NOUN
easat-7855	172	14	simulations	simulation	NOUN
easat-7855	172	15	using	use	VERB
easat-7855	172	16	gpu	gpu	NOUN
easat-7855	172	17	and	and	CCONJ
easat-7855	172	18	pytorch	pytorch	NOUN
easat-7855	172	19	,	,	PUNCT
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easat-7855	172	21	journal	journal	NOUN
easat-7855	172	22	of	of	ADP
easat-7855	172	23	computational	computational	ADJ
easat-7855	172	24	science	science	NOUN
easat-7855	172	25	,	,	PUNCT
easat-7855	172	26	vol	vol	NOUN
easat-7855	172	27	.	.	PROPN
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easat-7855	172	29	,	,	PUNCT
easat-7855	172	30	p.	p.	NOUN
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easat-7855	172	32	,	,	PUNCT
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easat-7855	172	34	.	.	PUNCT
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easat-7855	173	3	5	5	X
easat-7855	173	4	]	]	PUNCT
easat-7855	173	5	m.	m.	NOUN
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easat-7855	173	7	and	and	CCONJ
easat-7855	173	8	t.	t.	PROPN
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easat-7855	173	10	,	,	PUNCT
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easat-7855	173	16	in	in	ADP
easat-7855	173	17	real	real	ADJ
easat-7855	173	18	-	-	PUNCT
easat-7855	173	19	time	time	NOUN
easat-7855	173	20	fluid	fluid	ADJ
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easat-7855	173	22	,	,	PUNCT
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easat-7855	173	28	,	,	PUNCT
easat-7855	173	29	vol	vol	NOUN
easat-7855	173	30	.	.	PROPN
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easat-7855	173	32	,	,	PUNCT
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easat-7855	173	35	,	,	PUNCT
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easat-7855	173	37	.	.	PUNCT
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easat-7855	175	1	[	[	X
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easat-7855	175	3	]	]	PUNCT
easat-7855	175	4	j.	j.	PROPN
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easat-7855	175	6	and	and	CCONJ
easat-7855	175	7	y.	y.	PROPN
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easat-7855	175	18	in	in	ADP
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easat-7855	175	21	,	,	PUNCT
easat-7855	175	22	"	"	PUNCT
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easat-7855	175	29	,	,	PUNCT
easat-7855	175	30	vol	vol	NOUN
easat-7855	175	31	.	.	PUNCT
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easat-7855	176	2	,	,	PUNCT
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easat-7855	176	5	,	,	PUNCT
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easat-7855	176	7	.	.	PUNCT
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easat-7855	177	9	,	,	PUNCT
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easat-7855	177	14	in	in	ADP
easat-7855	177	15	computational	computational	ADJ
easat-7855	177	16	fluid	fluid	ADJ
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easat-7855	177	18	,	,	PUNCT
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easat-7855	178	2	,	,	PUNCT
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easat-7855	178	9	,	,	PUNCT
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easat-7855	178	11	.	.	PUNCT
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easat-7855	180	9	,	,	PUNCT
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easat-7855	180	18	in	in	ADP
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easat-7855	180	31	.	.	PUNCT
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easat-7855	181	2	,	,	PUNCT
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easat-7855	181	4	.	.	PUNCT
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easat-7855	183	27	,	,	PUNCT
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easat-7855	183	29	.	.	PROPN
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easat-7855	183	31	,	,	PUNCT
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easat-7855	184	2	,	,	PUNCT
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easat-7855	184	4	.	.	PUNCT
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easat-7855	185	30	,	,	PUNCT
easat-7855	185	31	pp	pp	ADJ
easat-7855	185	32	.	.	PUNCT
easat-7855	186	1	86–97	86–97	NUM
easat-7855	186	2	,	,	PUNCT
easat-7855	186	3	2023	2023	NUM
easat-7855	186	4	.	.	PUNCT
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easat-7855	187	30	,	,	PUNCT
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easat-7855	187	36	.	.	NOUN
easat-7855	187	37	1	1	NUM
easat-7855	187	38	,	,	PUNCT
easat-7855	187	39	pp	pp	ADJ
easat-7855	187	40	.	.	PUNCT
easat-7855	187	41	11–14	11–14	NUM
easat-7855	187	42	,	,	PUNCT
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easat-7855	188	1	[	[	X
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easat-7855	188	41	30	30	NUM
easat-7855	188	42	,	,	PUNCT
easat-7855	188	43	no	no	INTJ
easat-7855	188	44	.	.	NOUN
easat-7855	188	45	11	11	NUM
easat-7855	188	46	,	,	PUNCT
easat-7855	188	47	pp	pp	ADJ
easat-7855	188	48	.	.	PUNCT
easat-7855	189	1	4711–4733	4711–4733	NUM
easat-7855	189	2	,	,	PUNCT
easat-7855	189	3	2020	2020	NUM
easat-7855	189	4	.	.	PUNCT
easat-7855	190	1	[	[	X
easat-7855	190	2	13	13	NUM
easat-7855	190	3	]	]	PUNCT
easat-7855	190	4	m.	m.	NOUN
easat-7855	190	5	mkhatshwa	mkhatshwa	PROPN
easat-7855	190	6	,	,	PUNCT
easat-7855	190	7	s.	s.	PROPN
easat-7855	190	8	motsa	motsa	PROPN
easat-7855	190	9	,	,	PUNCT
easat-7855	190	10	and	and	CCONJ
easat-7855	190	11	p.	p.	PROPN
easat-7855	190	12	sibanda	sibanda	NOUN
easat-7855	190	13	,	,	PUNCT
easat-7855	190	14	"	"	PUNCT
easat-7855	190	15	overlapping	overlap	VERB
easat-7855	190	16	multi	multi	ADJ
easat-7855	190	17	-	-	ADJ
easat-7855	190	18	domain	domain	ADJ
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easat-7855	190	23	systems	system	NOUN
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easat-7855	190	26	pdes	pde	NOUN
easat-7855	190	27	with	with	ADP
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easat-7855	190	30	applications	application	NOUN
easat-7855	190	31	,	,	PUNCT
easat-7855	190	32	"	"	PUNCT
easat-7855	190	33	in	in	ADP
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easat-7855	190	35	in	in	ADP
easat-7855	190	36	fluid	fluid	ADJ
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easat-7855	190	41	of	of	ADP
easat-7855	190	42	icafd	icafd	NOUN
easat-7855	190	43	2018	2018	NUM
easat-7855	190	44	,	,	PUNCT
easat-7855	190	45	singapore	singapore	PROPN
easat-7855	190	46	,	,	PUNCT
easat-7855	190	47	springer	springer	NOUN
easat-7855	190	48	,	,	PUNCT
easat-7855	190	49	2021	2021	NUM
easat-7855	190	50	.	.	PUNCT
easat-7855	191	1	[	[	X
easat-7855	191	2	14	14	NUM
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easat-7855	191	4	b.	b.	PROPN
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easat-7855	191	6	,	,	PUNCT
easat-7855	191	7	s.	s.	PROPN
easat-7855	191	8	qadeer	qadeer	PROPN
easat-7855	191	9	,	,	PUNCT
easat-7855	191	10	and	and	CCONJ
easat-7855	191	11	p.	p.	NOUN
easat-7855	191	12	stinis	stinis	NOUN
easat-7855	191	13	,	,	PUNCT
easat-7855	191	14	"	"	PUNCT
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easat-7855	191	18	-	-	PUNCT
easat-7855	191	19	based	base	VERB
easat-7855	191	20	spectral	spectral	ADJ
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easat-7855	191	22	for	for	ADP
easat-7855	191	23	partial	partial	ADJ
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easat-7855	191	26	,	,	PUNCT
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easat-7855	191	32	.	.	PROPN
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easat-7855	191	38	,	,	PUNCT
easat-7855	191	39	p.	p.	NOUN
easat-7855	191	40	1739	1739	NUM
easat-7855	191	41	,	,	PUNCT
easat-7855	191	42	2023	2023	NUM
easat-7855	191	43	.	.	PUNCT
easat-7855	191	44	https://doi.org/10.1038/s41598-022-26602-3	https://doi.org/10.1038/s41598-022-26602-3	NUM
easat-7855	192	1	[	[	X
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easat-7855	192	7	s.	s.	PROPN
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easat-7855	192	9	,	,	PUNCT
easat-7855	192	10	and	and	CCONJ
easat-7855	192	11	w.	w.	PROPN
easat-7855	192	12	ying	ying	PROPN
easat-7855	192	13	,	,	PUNCT
easat-7855	192	14	"	"	PUNCT
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easat-7855	192	19	for	for	ADP
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easat-7855	192	21	partial	partial	ADJ
easat-7855	192	22	differential	differential	NOUN
easat-7855	192	23	equations	equation	NOUN
easat-7855	192	24	,	,	PUNCT
easat-7855	192	25	"	"	PUNCT
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easat-7855	192	29	,	,	PUNCT
easat-7855	192	30	2024	2024	NUM
easat-7855	192	31	.	.	PUNCT
easat-7855	193	1	https://doi.org/10.48550/arxiv.2407.03347	https://doi.org/10.48550/arxiv.2407.03347	PROPN
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easat-7855	193	4	]	]	PUNCT
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easat-7855	193	8	and	and	CCONJ
easat-7855	193	9	n.	n.	NOUN
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easat-7855	193	11	,	,	PUNCT
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easat-7855	193	15	for	for	ADP
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easat-7855	193	24	equations	equation	NOUN
easat-7855	193	25	,	,	PUNCT
easat-7855	193	26	"	"	PUNCT
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easat-7855	193	28	journal	journal	NOUN
easat-7855	193	29	of	of	ADP
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easat-7855	193	31	and	and	CCONJ
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easat-7855	193	36	.	.	PROPN
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easat-7855	194	2	,	,	PUNCT
easat-7855	194	3	no	no	INTJ
easat-7855	194	4	.	.	NOUN
easat-7855	194	5	1	1	NUM
easat-7855	194	6	,	,	PUNCT
easat-7855	194	7	pp	pp	ADJ
easat-7855	194	8	.	.	PUNCT
easat-7855	195	1	54–58	54–58	NUM
easat-7855	195	2	,	,	PUNCT
easat-7855	195	3	2024	2024	NUM
easat-7855	195	4	.	.	PUNCT
easat-7855	196	1	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
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easat-7855	196	5	https://doi.org/10.1016/j.jocs.2021.101393	https://doi.org/10.1016/j.jocs.2021.101393	PROPN
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