A Massively Parallel Hybrid Finite Volume/Finite Element Scheme for Computational Fluid Dynamics

In this paper, we propose a novel family of semi-implicit hybrid finite volume/finite element schemes for computational fluid dynamics (CFD), in particular for the approximate solution of the incompressible and compressible Navier-Stokes equations, as well as for the shallow water equations on stagg...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Mathematics (Basel) Ročník 9; číslo 18; s. 2316
Hlavní autoři: Río-Martín, Laura, Busto, Saray, Dumbser, Michael
Médium: Journal Article
Jazyk:angličtina
Vydáno: Basel MDPI AG 01.09.2021
Témata:
ADER methodology
Algorithms
Applied mathematics
Asymptotic methods
Compressible flow
Computational fluid dynamics
Computer simulation
Conjugate gradient method
Degrees of freedom
Direct numerical simulation
Discretization
Distributed memory
Domain decomposition methods
Finite element method
Finite volume method
finite volume scheme
Fluid dynamics
Fluid flow
Food science
Free convection
High Mach number
incompressible and compressible Navier-Stokes equations
Incompressible flow
Mach number
Mathematical models
Matrices (mathematics)
Message passing
Navier-Stokes equations
Parallel processing
Partial differential equations
semi-implicit scheme on staggered unstructured meshes
shallow water equations
Shock waves
Simulation
Supercomputers
Turbulent flow
Variables
ISSN:2227-7390, 2227-7390
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Abstract In this paper, we propose a novel family of semi-implicit hybrid finite volume/finite element schemes for computational fluid dynamics (CFD), in particular for the approximate solution of the incompressible and compressible Navier-Stokes equations, as well as for the shallow water equations on staggered unstructured meshes in two and three space dimensions. The key features of the method are the use of an edge-based/face-based staggered dual mesh for the discretization of the nonlinear convective terms at the aid of explicit high resolution Godunov-type finite volume schemes, while pressure terms are discretized implicitly using classical continuous Lagrange finite elements on the primal simplex mesh. The resulting pressure system is symmetric positive definite and can thus be very efficiently solved at the aid of classical Krylov subspace methods, such as a matrix-free conjugate gradient method. For the compressible Navier-Stokes equations, the schemes are by construction asymptotic preserving in the low Mach number limit of the equations, hence a consistent hybrid FV/FE method for the incompressible equations is retrieved. All parts of the algorithm can be efficiently parallelized, i.e., the explicit finite volume step as well as the matrix-vector product in the implicit pressure solver. Concerning parallel implementation, we employ the Message-Passing Interface (MPI) standard in combination with spatial domain decomposition based on the free software package METIS. To show the versatility of the proposed schemes, we present a wide range of applications, starting from environmental and geophysical flows, such as dambreak problems and natural convection, over direct numerical simulations of turbulent incompressible flows to high Mach number compressible flows with shock waves. An excellent agreement with exact analytical, numerical or experimental reference solutions is achieved in all cases. Most of the simulations are run with millions of degrees of freedom on thousands of CPU cores. We show strong scaling results for the hybrid FV/FE scheme applied to the 3D incompressible Navier-Stokes equations, using millions of degrees of freedom and up to 4096 CPU cores. The largest simulation shown in this paper is the well-known 3D Taylor-Green vortex benchmark run on 671 million tetrahedral elements on 32,768 CPU cores, showing clearly the suitability of the presented algorithm for the solution of large CFD problems on modern massively parallel distributed memory supercomputers.
AbstractList In this paper, we propose a novel family of semi-implicit hybrid finite volume/finite element schemes for computational fluid dynamics (CFD), in particular for the approximate solution of the incompressible and compressible Navier-Stokes equations, as well as for the shallow water equations on staggered unstructured meshes in two and three space dimensions. The key features of the method are the use of an edge-based/face-based staggered dual mesh for the discretization of the nonlinear convective terms at the aid of explicit high resolution Godunov-type finite volume schemes, while pressure terms are discretized implicitly using classical continuous Lagrange finite elements on the primal simplex mesh. The resulting pressure system is symmetric positive definite and can thus be very efficiently solved at the aid of classical Krylov subspace methods, such as a matrix-free conjugate gradient method. For the compressible Navier-Stokes equations, the schemes are by construction asymptotic preserving in the low Mach number limit of the equations, hence a consistent hybrid FV/FE method for the incompressible equations is retrieved. All parts of the algorithm can be efficiently parallelized, i.e., the explicit finite volume step as well as the matrix-vector product in the implicit pressure solver. Concerning parallel implementation, we employ the Message-Passing Interface (MPI) standard in combination with spatial domain decomposition based on the free software package METIS. To show the versatility of the proposed schemes, we present a wide range of applications, starting from environmental and geophysical flows, such as dambreak problems and natural convection, over direct numerical simulations of turbulent incompressible flows to high Mach number compressible flows with shock waves. An excellent agreement with exact analytical, numerical or experimental reference solutions is achieved in all cases. Most of the simulations are run with millions of degrees of freedom on thousands of CPU cores. We show strong scaling results for the hybrid FV/FE scheme applied to the 3D incompressible Navier-Stokes equations, using millions of degrees of freedom and up to 4096 CPU cores. The largest simulation shown in this paper is the well-known 3D Taylor-Green vortex benchmark run on 671 million tetrahedral elements on 32,768 CPU cores, showing clearly the suitability of the presented algorithm for the solution of large CFD problems on modern massively parallel distributed memory supercomputers.
Author Busto, Saray
Dumbser, Michael
Río-Martín, Laura
Author_xml – sequence: 1
  givenname: Laura
  orcidid: 0000-0002-7812-3161
  surname: Río-Martín
  fullname: Río-Martín, Laura
– sequence: 2
  givenname: Saray
  orcidid: 0000-0002-6509-4269
  surname: Busto
  fullname: Busto, Saray
– sequence: 3
  givenname: Michael
  orcidid: 0000-0002-8201-8372
  surname: Dumbser
  fullname: Dumbser, Michael
BookMark eNptUU1r3DAQFSWFpmlO-QOCHssmkixL8jFss00goYV-XJWxPGq0yNZWkgv77-N2Ewilc5mZx3uP-XhLjqY0ISFnnJ03TccuRqgPHTei4eoVORZC6JVe8KMX9RtyWsqWLdHxxsjumNxf0jsoJfzGuKdfIEOMGOn1vs9hoJswhYr0R4rziBdP3VXEEadKv7qHpaA-ZbpO426uUEOaINJNnBftx_0EY3DlHXntIRY8fcon5Pvm6tv6enX7-dPN-vJ25Rol66pplfJaDxqY7jji0DnWtj0DwMFLpsBgD4OHHoXrmRIKG-M6P2gvzcCwb07IzcF3SLC1uxxGyHubINi_QMo_LeQaXETbam6cEdwbPkgu217yVmvvmAcuWuMXr_cHr11Ov2Ys1W7TnJfdihWtVlIqbvjC4geWy6mUjN66cDhCzRCi5cz--Yt98ZdF8-EfzfOk_2M_Aq75kSw
CitedBy_id crossref_primary_10_1002_fld_5143
crossref_primary_10_1002_fld_5122
crossref_primary_10_1063_5_0167927
crossref_primary_10_1063_5_0216276
crossref_primary_10_1016_j_jcp_2023_112493
crossref_primary_10_1007_s11069_024_06557_6
crossref_primary_10_3390_math9222972
crossref_primary_10_1007_s42967_023_00290_w
crossref_primary_10_1016_j_amc_2022_127457
crossref_primary_10_1016_j_amc_2023_128426
crossref_primary_10_1007_s10915_024_02770_4
crossref_primary_10_1016_j_apnum_2024_01_014
crossref_primary_10_1016_j_jcp_2023_112521
crossref_primary_10_1016_j_amc_2022_127539
Cites_doi 10.1080/00221689509498555
10.1080/00423114.2016.1156134
10.1007/978-3-322-89564-6
10.1007/s10915-018-0731-9
10.1007/978-1-4612-3172-1
10.2514/6.1989-366
10.1016/j.compfluid.2009.03.008
10.1016/j.cpc.2020.107251
10.1007/s00161-014-0401-6
10.1137/0910004
10.1016/j.jcp.2020.109866
10.1016/j.applthermaleng.2017.11.086
10.1016/j.jcp.2009.01.025
10.1007/978-3-642-12971-1
10.1002/fld.1650010406
10.1017/S0022112083001159
10.1016/j.camwa.2017.03.021
10.1016/j.apnum.2016.07.014
10.1016/j.compfluid.2007.02.008
10.1017/CBO9780511791253
10.1093/mnras/sty542
10.1016/0021-9991(81)90128-5
10.1006/jcph.1998.6127
10.3389/fphy.2020.00032
10.6028/jres.049.044
10.1016/0045-7825(86)90110-6
10.1016/j.jcp.2014.06.059
10.1016/j.compfluid.2012.08.023
10.1016/j.compfluid.2009.07.003
10.1063/1.1699639
10.1002/cpa.3160050303
10.1007/978-3-642-60543-7_12
10.1109/ACCESS.2020.2966032
10.1137/050628052
10.1016/0041-5553(62)90062-9
10.1006/jcph.1999.6414
10.1016/j.cma.2005.10.010
10.1016/0045-7930(73)90027-3
10.1016/0021-9991(78)90023-2
10.1016/j.amc.2021.126117
10.1007/s10915-021-01600-1
10.1007/s10915-021-01429-8
10.1016/j.jcp.2018.08.003
10.1016/j.jcp.2004.10.013
10.1007/978-1-4612-0713-9
10.1002/fld.1650150602
10.1007/s00466-009-0436-x
10.1016/j.jcp.2017.01.020
10.1016/j.cma.2009.03.001
10.1137/0725032
10.1137/0719018
10.1002/(SICI)1097-0363(20000215)32:3<331::AID-FLD941>3.0.CO;2-C
10.1007/BF02812178
10.1007/978-1-4615-0663-8
10.1016/j.compfluid.2019.104399
10.1016/j.jcp.2014.02.034
10.1016/j.jcp.2012.10.038
10.1016/j.cma.2014.10.041
10.1017/S0022112010003599
10.1016/S0167-6105(02)00351-3
10.1088/1361-6544/aa712d
10.1063/1.1761178
10.1137/0907059
10.1016/j.camwa.2019.06.019
10.1016/j.jcp.2013.09.029
10.1002/fld.4681
10.1016/0045-7930(94)90004-3
10.1007/BF01448839
10.1007/BF01385799
10.1016/j.jcp.2016.02.015
10.1016/0021-9991(90)90091-E
10.1002/fld.1032
10.1111/sapm.12238
10.1007/b79761
10.1137/17M1111036
10.1016/j.cma.2009.10.016
10.1016/j.jcp.2020.109743
10.1002/fld.1650041102
10.3390/axioms7030063
10.1016/j.compfluid.2004.06.005
10.1016/j.jcp.2004.01.023
10.1016/j.camwa.2016.03.016
10.1016/j.cma.2013.01.006
10.4208/cicp.181012.010313a
10.1016/j.compfluid.2008.11.012
10.1006/jpdc.1997.1404
10.1016/j.jcp.2004.12.024
10.1137/100799071
10.1016/j.jcp.2017.03.030
10.1016/0377-0427(95)00227-8
10.1016/j.jcp.2017.10.004
10.1090/S0025-5718-1982-0645656-0
10.1016/j.jcp.2016.05.009
ContentType Journal Article
Copyright 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Copyright_xml – notice: 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
DBID AAYXX
CITATION
3V.
7SC
7TB
7XB
8AL
8FD
8FE
8FG
8FK
ABJCF
ABUWG
AFKRA
ARAPS
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
FR3
GNUQQ
HCIFZ
JQ2
K7-
KR7
L6V
L7M
L~C
L~D
M0N
M7S
P62
PHGZM
PHGZT
PIMPY
PKEHL
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
PTHSS
Q9U
DOA
DOI 10.3390/math9182316
DatabaseName CrossRef
ProQuest Central (Corporate)
Computer and Information Systems Abstracts
Mechanical & Transportation Engineering Abstracts
ProQuest Central (purchase pre-March 2016)
Computing Database (Alumni Edition)
Technology Research Database
ProQuest SciTech Collection
ProQuest Technology Collection
ProQuest Central (Alumni) (purchase pre-March 2016)
Materials Science & Engineering Collection
ProQuest Central (Alumni)
ProQuest Central UK/Ireland
Advanced Technologies & Computer Science Collection
ProQuest Central Essentials
ProQuest Central
ProQuest Technology Collection
ProQuest One Community College
ProQuest Central Korea
Engineering Research Database
ProQuest Central Student
SciTech Premium Collection
ProQuest Computer Science Collection
Computer Science Database
Civil Engineering Abstracts
ProQuest Engineering Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
Computing Database
Engineering Database
ProQuest Advanced Technologies & Aerospace Collection
ProQuest Central Premium
ProQuest One Academic
Publicly Available Content Database
ProQuest One Academic Middle East (New)
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Applied & Life Sciences
ProQuest One Academic (retired)
ProQuest One Academic UKI Edition
ProQuest Central China
Engineering Collection
ProQuest Central Basic
DOAJ Directory of Open Access Journals
DatabaseTitle CrossRef
Publicly Available Content Database
Computer Science Database
ProQuest Central Student
Technology Collection
Technology Research Database
Computer and Information Systems Abstracts – Academic
ProQuest One Academic Middle East (New)
Mechanical & Transportation Engineering Abstracts
ProQuest Advanced Technologies & Aerospace Collection
ProQuest Central Essentials
ProQuest Computer Science Collection
Computer and Information Systems Abstracts
ProQuest Central (Alumni Edition)
SciTech Premium Collection
ProQuest One Community College
ProQuest Central China
ProQuest Central
ProQuest One Applied & Life Sciences
ProQuest Engineering Collection
ProQuest Central Korea
ProQuest Central (New)
Advanced Technologies Database with Aerospace
Engineering Collection
Advanced Technologies & Aerospace Collection
Civil Engineering Abstracts
ProQuest Computing
Engineering Database
ProQuest Central Basic
ProQuest Computing (Alumni Edition)
ProQuest One Academic Eastern Edition
ProQuest Technology Collection
ProQuest SciTech Collection
Computer and Information Systems Abstracts Professional
ProQuest One Academic UKI Edition
Materials Science & Engineering Collection
Engineering Research Database
ProQuest One Academic
ProQuest One Academic (New)
ProQuest Central (Alumni)
DatabaseTitleList
Publicly Available Content Database
CrossRef
Database_xml – sequence: 1
  dbid: DOA
  name: DOAJ Directory of Open Access Journals
  url: https://www.doaj.org/
  sourceTypes: Open Website
– sequence: 2
  dbid: PIMPY
  name: Publicly Available Content Database
  url: http://search.proquest.com/publiccontent
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISSN 2227-7390
ExternalDocumentID oai_doaj_org_article_5718c821f81d4145b41577fc0fa1258f
10_3390_math9182316
GroupedDBID -~X
5VS
85S
8FE
8FG
AADQD
AAFWJ
AAYXX
ABDBF
ABJCF
ABPPZ
ABUWG
ACIPV
ACIWK
ADBBV
AFFHD
AFKRA
AFPKN
AFZYC
ALMA_UNASSIGNED_HOLDINGS
AMVHM
ARAPS
AZQEC
BCNDV
BENPR
BGLVJ
BPHCQ
CCPQU
CITATION
DWQXO
GNUQQ
GROUPED_DOAJ
HCIFZ
IAO
ITC
K6V
K7-
KQ8
L6V
M7S
MODMG
M~E
OK1
PHGZM
PHGZT
PIMPY
PQGLB
PQQKQ
PROAC
PTHSS
RNS
3V.
7SC
7TB
7XB
8AL
8FD
8FK
FR3
JQ2
KR7
L7M
L~C
L~D
M0N
P62
PKEHL
PQEST
PQUKI
PRINS
Q9U
ID FETCH-LOGICAL-c364t-3566f77d7a0791eed9c055b0aaedf406a8ebadfabe2cb0626e38c9fd7f48d0eb3
IEDL.DBID K7-
ISICitedReferencesCount 17
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000699776200001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 2227-7390
IngestDate Fri Oct 03 12:43:29 EDT 2025
Fri Jul 25 11:58:04 EDT 2025
Sat Nov 29 07:18:07 EST 2025
Tue Nov 18 21:44:49 EST 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 18
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c364t-3566f77d7a0791eed9c055b0aaedf406a8ebadfabe2cb0626e38c9fd7f48d0eb3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0002-7812-3161
0000-0002-8201-8372
0000-0002-6509-4269
OpenAccessLink https://www.proquest.com/docview/2576446181?pq-origsite=%requestingapplication%
PQID 2576446181
PQPubID 2032364
ParticipantIDs doaj_primary_oai_doaj_org_article_5718c821f81d4145b41577fc0fa1258f
proquest_journals_2576446181
crossref_citationtrail_10_3390_math9182316
crossref_primary_10_3390_math9182316
PublicationCentury 2000
PublicationDate 2021-09-01
PublicationDateYYYYMMDD 2021-09-01
PublicationDate_xml – month: 09
  year: 2021
  text: 2021-09-01
  day: 01
PublicationDecade 2020
PublicationPlace Basel
PublicationPlace_xml – name: Basel
PublicationTitle Mathematics (Basel)
PublicationYear 2021
Publisher MDPI AG
Publisher_xml – name: MDPI AG
References Dassi (ref_72) 2017; 74
(ref_83) 2006; 44
ref_91
ref_90
ref_12
ref_11
ref_10
Riemann (ref_27) 1860; 8
Dumbser (ref_100) 2010; 39
Heywood (ref_18) 1988; 25
Richtmyer (ref_2) 1950; 21
Toro (ref_35) 2009; 228
Rusanov (ref_78) 1962; 1
Russo (ref_71) 2016; 72
Casulli (ref_39) 1984; 4
Boscheri (ref_115) 2014; 275
Taylor (ref_13) 1973; 1
ref_25
ref_24
ref_23
Fambri (ref_46) 2016; 110
ref_22
Dumbser (ref_65) 2017; 39
Bonaventura (ref_43) 2000; 158
(ref_16) 1991; 59
ref_26
(ref_33) 1994; 23
Tinoco (ref_54) 1991; 16
ref_79
Song (ref_57) 2016; 54
ref_77
ref_75
ref_74
Toro (ref_32) 2012; 70
Fraccarollo (ref_102) 1995; 33
Ferrari (ref_103) 2010; 663
Fambri (ref_70) 2018; 477
Albensoeder (ref_94) 2005; 206
Dolejsi (ref_51) 2004; 198
Brachet (ref_93) 1983; 130
Dolejsi (ref_52) 2008; 4
ref_82
ref_81
Yi (ref_98) 2018; 374
Harlow (ref_36) 1965; 8
ref_80
ref_89
ref_88
Johnson (ref_55) 2005; 34
(ref_34) 1999; 148
(ref_38) 1986; 7
Fokkema (ref_62) 1996; 71
Saavedra (ref_28) 2014; 271
ref_50
Busto (ref_29) 2018; 353
Favrie (ref_111) 2017; 30
Sod (ref_101) 1978; 27
Guermond (ref_53) 2006; 195
Casulli (ref_40) 1990; 86
Huang (ref_64) 2020; 8
Roe (ref_20) 1981; 43
Gaburro (ref_76) 2018; 477
Peshkov (ref_108) 2016; 28
Dumbser (ref_107) 2019; 89
Fortin (ref_15) 1981; 1
ref_69
ref_68
Dumbser (ref_86) 2016; 314
(ref_99) 2008; 37
Yelash (ref_96) 2014; 268
Hestenes (ref_60) 1952; 49
Boscheri (ref_114) 2013; 14
Badia (ref_92) 2015; 285
Dumbser (ref_85) 2009; 38
Tavelli (ref_47) 2016; 319
Weinzierl (ref_67) 2011; 33
Ferrari (ref_106) 2009; 38
Osher (ref_21) 1982; 38
Dumbser (ref_87) 2010; 199
Courant (ref_1) 1928; 100
Ritz (ref_4) 1909; 135
Karypis (ref_59) 1998; 48
Park (ref_45) 2005; 49
Heywood (ref_17) 1982; 19
Lu (ref_63) 2017; 53
Castro (ref_84) 2009; 198
Behrens (ref_95) 2013; 235
Bispen (ref_97) 2017; 335
ref_31
ref_110
ref_30
ref_113
Casulli (ref_42) 2000; 32
ref_112
ref_37
Zhang (ref_58) 2018; 130
Dumbser (ref_104) 2013; 257
ref_105
Dassi (ref_73) 2020; 79
ref_109
Boscarino (ref_49) 2018; 77
Courant (ref_3) 1952; 5
Godunov (ref_19) 1959; 47
Bungartz (ref_66) 2010; 46
Hughes (ref_14) 1986; 54
ref_9
ref_8
Shirai (ref_56) 2003; 91
Sonneveld (ref_61) 1989; 10
ref_5
ref_7
Casulli (ref_41) 1992; 15
Tavelli (ref_48) 2017; 341
ref_6
Rosatti (ref_44) 2005; 204
References_xml – volume: 33
  start-page: 843
  year: 1995
  ident: ref_102
  article-title: Experimental and numerical assessment of the shallow water model for two-dimensional dam-break type problems
  publication-title: J. Hydraul. Res.
  doi: 10.1080/00221689509498555
– ident: ref_9
– volume: 54
  start-page: 723
  year: 2016
  ident: ref_57
  article-title: Nonlinear analysis of wind-induced vibration of high-speed railway catenary and its influence on pantograph–catenary interaction
  publication-title: Veh. Syst. Dyn.
  doi: 10.1080/00423114.2016.1156134
– ident: ref_10
  doi: 10.1007/978-3-322-89564-6
– volume: 77
  start-page: 850
  year: 2018
  ident: ref_49
  article-title: All Mach number second order semi-implicit scheme for the Euler equations of gasdynamics
  publication-title: J. Sci. Comput.
  doi: 10.1007/s10915-018-0731-9
– ident: ref_11
  doi: 10.1007/978-1-4612-3172-1
– ident: ref_82
  doi: 10.2514/6.1989-366
– volume: 38
  start-page: 1731
  year: 2009
  ident: ref_85
  article-title: ADER schemes on unstructured meshes for nonconservative hyperbolic systems: Applications to geophysical flows
  publication-title: Comput. Fluids
  doi: 10.1016/j.compfluid.2009.03.008
– ident: ref_69
  doi: 10.1016/j.cpc.2020.107251
– volume: 28
  start-page: 85
  year: 2016
  ident: ref_108
  article-title: A hyperbolic model for viscous Newtonian flows
  publication-title: Contin. Mech. Thermodyn.
  doi: 10.1007/s00161-014-0401-6
– volume: 10
  start-page: 36
  year: 1989
  ident: ref_61
  article-title: CGS, a fast Lanczos-type solver for nonsymmetric linear systems
  publication-title: SIAM J. Sci. Stat. Comput.
  doi: 10.1137/0910004
– ident: ref_109
  doi: 10.1016/j.jcp.2020.109866
– volume: 130
  start-page: 1328
  year: 2018
  ident: ref_58
  article-title: Full vehicle CFD investigations on the influence of front-end configuration on radiator performance and cooling drag
  publication-title: Appl. Therm. Eng.
  doi: 10.1016/j.applthermaleng.2017.11.086
– volume: 228
  start-page: 3368
  year: 2009
  ident: ref_35
  article-title: FORCE schemes on unstructured meshes I: Conservative hyperbolic systems
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2009.01.025
– ident: ref_91
  doi: 10.1007/978-3-642-12971-1
– volume: 47
  start-page: 357
  year: 1959
  ident: ref_19
  article-title: A finite difference method for the computation of discontinuous solutions of the equations of fluid dynamics
  publication-title: Mat. Sb.
– volume: 1
  start-page: 347
  year: 1981
  ident: ref_15
  article-title: Old and new finite elements for incompressible flows
  publication-title: Int. J. Numer. Methods Fluids
  doi: 10.1002/fld.1650010406
– volume: 130
  start-page: 411
  year: 1983
  ident: ref_93
  article-title: Small-scale structure of the Taylor-Green vortex
  publication-title: J. Fluid Mech.
  doi: 10.1017/S0022112083001159
– volume: 74
  start-page: 1110
  year: 2017
  ident: ref_72
  article-title: High-order Virtual Element Method on polyhedral meshes
  publication-title: Comput. Math. Appl.
  doi: 10.1016/j.camwa.2017.03.021
– volume: 110
  start-page: 41
  year: 2016
  ident: ref_46
  article-title: Spectral semi-implicit and space-time discontinuous Galerkin methods for the incompressible Navier-Stokes equations on staggered Cartesian grids
  publication-title: Appl. Numer. Math.
  doi: 10.1016/j.apnum.2016.07.014
– volume: 37
  start-page: 450
  year: 2008
  ident: ref_99
  article-title: High order numerical simulation of aeolian tones
  publication-title: Comput. Fluids
  doi: 10.1016/j.compfluid.2007.02.008
– ident: ref_24
  doi: 10.1017/CBO9780511791253
– volume: 477
  start-page: 2251
  year: 2018
  ident: ref_76
  article-title: Well-balanced Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming meshes for the Euler equations of gas dynamics with gravity
  publication-title: Mon. Not. R. Astron. Soc.
  doi: 10.1093/mnras/sty542
– volume: 43
  start-page: 357
  year: 1981
  ident: ref_20
  article-title: Approximate Riemann Solvers, Parameter vectors, and Difference schemes
  publication-title: J. Comput. Phys.
  doi: 10.1016/0021-9991(81)90128-5
– volume: 8
  start-page: 43
  year: 1860
  ident: ref_27
  article-title: Über die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite
  publication-title: Abh. K. Ges. Wiss. Gött.
– volume: 148
  start-page: 497
  year: 1999
  ident: ref_34
  article-title: Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry
  publication-title: J. Comput. Phys.
  doi: 10.1006/jcph.1998.6127
– ident: ref_110
  doi: 10.3389/fphy.2020.00032
– volume: 49
  start-page: 409
  year: 1952
  ident: ref_60
  article-title: Methods of conjugate gradients for solving linear systems
  publication-title: J. Res. Natl. Bur. Stand.
  doi: 10.6028/jres.049.044
– volume: 54
  start-page: 341
  year: 1986
  ident: ref_14
  article-title: A new finite element formulation for computational fluid dynamics: II. Beyond SUPG
  publication-title: Comput. Methods Appl. Mech. Eng.
  doi: 10.1016/0045-7825(86)90110-6
– volume: 275
  start-page: 484
  year: 2014
  ident: ref_115
  article-title: A direct Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic systems in 3D
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2014.06.059
– volume: 70
  start-page: 1
  year: 2012
  ident: ref_32
  article-title: Flux splitting schemes for the Euler equations
  publication-title: Comput. Fluids
  doi: 10.1016/j.compfluid.2012.08.023
– volume: 39
  start-page: 60
  year: 2010
  ident: ref_100
  article-title: Arbitrary high order PNPM schemes on unstructured meshes for the compressible Navier-Stokes equations
  publication-title: Comput. Fluids
  doi: 10.1016/j.compfluid.2009.07.003
– volume: 21
  start-page: 232
  year: 1950
  ident: ref_2
  article-title: A method for the calculation of hydrodynamics shocks
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.1699639
– volume: 5
  start-page: 243
  year: 1952
  ident: ref_3
  article-title: On the solution of nonlinear hyperbolic differential equations by finite differences
  publication-title: Comm. Pure Appl. Math.
  doi: 10.1002/cpa.3160050303
– ident: ref_80
  doi: 10.1007/978-3-642-60543-7_12
– volume: 8
  start-page: 12438
  year: 2020
  ident: ref_64
  article-title: A Novel Perturbed Matrix Inversion Based Method for the Acceleration of Finite Element Analysis in Crack-Scanning Eddy Current NDT
  publication-title: IEEE Access
  doi: 10.1109/ACCESS.2020.2966032
– ident: ref_6
– ident: ref_75
– volume: 44
  start-page: 300
  year: 2006
  ident: ref_83
  article-title: Numerical methods for nonconservative hyperbolic systems: A theoretical framework
  publication-title: SIAM J. Numer. Anal.
  doi: 10.1137/050628052
– ident: ref_25
– ident: ref_81
– volume: 1
  start-page: 304
  year: 1962
  ident: ref_78
  article-title: The calculation of the interaction of non-stationary shock waves and obstacles
  publication-title: USSR Comput. Math. Math. Phys.
  doi: 10.1016/0041-5553(62)90062-9
– volume: 158
  start-page: 186
  year: 2000
  ident: ref_43
  article-title: A Semi-implicit Semi-Lagrangian Scheme Using the Height Coordinate for a Nonhydrostatic and Fully Elastic Model of Atmospheric Flows
  publication-title: J. Comput. Phys.
  doi: 10.1006/jcph.1999.6414
– volume: 195
  start-page: 6011
  year: 2006
  ident: ref_53
  article-title: An overview of projection methods for incompressible flows
  publication-title: Comput. Methods Appl. Mech. Eng.
  doi: 10.1016/j.cma.2005.10.010
– volume: 1
  start-page: 73
  year: 1973
  ident: ref_13
  article-title: A numerical solution of the Navier-Stokes equations using the finite element technique
  publication-title: Comput. Fluids
  doi: 10.1016/0045-7930(73)90027-3
– volume: 27
  start-page: 1
  year: 1978
  ident: ref_101
  article-title: A survey of several finite difference methods for systems of non-linear hyperbolic conservation laws
  publication-title: J. Comput. Phys.
  doi: 10.1016/0021-9991(78)90023-2
– ident: ref_74
  doi: 10.1016/j.amc.2021.126117
– ident: ref_77
  doi: 10.1007/s10915-021-01600-1
– ident: ref_89
– ident: ref_113
  doi: 10.1007/s10915-021-01429-8
– ident: ref_88
  doi: 10.1016/j.amc.2021.126117
– volume: 135
  start-page: 1
  year: 1909
  ident: ref_4
  article-title: Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik
  publication-title: J. Die Reine Angew. Math.
– volume: 374
  start-page: 873
  year: 2018
  ident: ref_98
  article-title: Time Integration of Unsteady Nonhydrostatic Equations with Dual Time Stepping and Multigrid Methods
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2018.08.003
– ident: ref_5
– volume: 204
  start-page: 353
  year: 2005
  ident: ref_44
  article-title: Semi-implicit, semi-Lagrangian modelling for environmental problems on staggered Cartesian grids with cut cells
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2004.10.013
– ident: ref_22
  doi: 10.1007/978-1-4612-0713-9
– volume: 15
  start-page: 629
  year: 1992
  ident: ref_41
  article-title: Semi-implicit finite difference methods for three–dimensional shallow water flow
  publication-title: Int. J. Numer. Methods Fluids
  doi: 10.1002/fld.1650150602
– ident: ref_26
– volume: 46
  start-page: 103
  year: 2010
  ident: ref_66
  article-title: The PDE framework Peano applied to fluid dynamics: An efficient implementation of a parallel multiscale fluid dynamics solver on octree-like adaptive Cartesian grids
  publication-title: Comput. Mech.
  doi: 10.1007/s00466-009-0436-x
– volume: 335
  start-page: 222
  year: 2017
  ident: ref_97
  article-title: Asymptotic preserving IMEX finite volume schemes for low Mach number Euler equations with gravitation
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2017.01.020
– volume: 198
  start-page: 2520
  year: 2009
  ident: ref_84
  article-title: Two-dimensional sediment transport models in shallow water equations. A second order finite volume approach on unstructured meshes
  publication-title: Comput. Methods Appl. Mech. Eng.
  doi: 10.1016/j.cma.2009.03.001
– volume: 25
  start-page: 489
  year: 1988
  ident: ref_18
  article-title: Finite element approximation of the nonstationary Navier-Stokes Problem. III. Smoothing property and higher order error estimates for spatial discretization
  publication-title: SIAM J. Numer. Anal.
  doi: 10.1137/0725032
– ident: ref_90
– volume: 19
  start-page: 275
  year: 1982
  ident: ref_17
  article-title: Finite element approximation of the nonstationary Navier-Stokes Problem. I. Regularity of solutions and second order error estimates for spatial discretization
  publication-title: SIAM J. Numer. Anal.
  doi: 10.1137/0719018
– volume: 32
  start-page: 331
  year: 2000
  ident: ref_42
  article-title: An unstructured grid, three-dimensional model based on the shallow water equations
  publication-title: Int. J. Numer. Methods Fluids
  doi: 10.1002/(SICI)1097-0363(20000215)32:3<331::AID-FLD941>3.0.CO;2-C
– volume: 16
  start-page: 141
  year: 1991
  ident: ref_54
  article-title: CFD codes and applications at Boeing
  publication-title: Sadhana
  doi: 10.1007/BF02812178
– ident: ref_79
  doi: 10.1007/978-1-4615-0663-8
– ident: ref_50
  doi: 10.1016/j.compfluid.2019.104399
– volume: 53
  start-page: 1
  year: 2017
  ident: ref_63
  article-title: Acceleration of Frequency Sweeping in Eddy-Current Computation
  publication-title: IEEE Trans. Magn.
– volume: 268
  start-page: 106
  year: 2014
  ident: ref_96
  article-title: Adaptive discontinuous evolution Galerkin method for dry atmospheric flow
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2014.02.034
– volume: 235
  start-page: 371
  year: 2013
  ident: ref_95
  article-title: Comparison between adaptive and uniform discontinuous Galerkin simulations in dry 2D bubble experiments
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2012.10.038
– volume: 285
  start-page: 32
  year: 2015
  ident: ref_92
  article-title: Assessment of variational multiscale models for the large eddy simulation of turbulent incompressible flows
  publication-title: Comput. Methods Appl. Mech. Eng.
  doi: 10.1016/j.cma.2014.10.041
– volume: 663
  start-page: 456
  year: 2010
  ident: ref_103
  article-title: Three-dimensional flow evolution after a dambreak
  publication-title: J. Fluid Mech.
  doi: 10.1017/S0022112010003599
– ident: ref_8
– volume: 91
  start-page: 279
  year: 2003
  ident: ref_56
  article-title: Aerodynamic simulation by CFD on flat box girder of super-long-span suspension bridge
  publication-title: J. Wind. Eng. Ind. Aerodyn.
  doi: 10.1016/S0167-6105(02)00351-3
– volume: 30
  start-page: 2718
  year: 2017
  ident: ref_111
  article-title: A rapid numerical method for solving Serre-Green-Naghdi equations describing long free surface gravity waves
  publication-title: Nonlinearity
  doi: 10.1088/1361-6544/aa712d
– volume: 8
  start-page: 2182
  year: 1965
  ident: ref_36
  article-title: Numerical calculation of time-dependent viscous incompressible flow of fluid with a free surface
  publication-title: Phys. Fluids
  doi: 10.1063/1.1761178
– volume: 7
  start-page: 870
  year: 1986
  ident: ref_38
  article-title: A second-order accurate pressure correction method for viscous incompressible flow
  publication-title: SIAM J. Sci. Stat. Comput.
  doi: 10.1137/0907059
– volume: 79
  start-page: 1936
  year: 2020
  ident: ref_73
  article-title: A C1 Virtual Element Method on polyhedral meshes
  publication-title: Comput. Math. Appl.
  doi: 10.1016/j.camwa.2019.06.019
– volume: 271
  start-page: 360
  year: 2014
  ident: ref_28
  article-title: A projection hybrid finite volume/element method for low-Mach number flows
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2013.09.029
– volume: 89
  start-page: 16
  year: 2019
  ident: ref_107
  article-title: A divergence-free semi-implicit finite volume scheme for ideal, viscous and resistive magnetohydrodynamics
  publication-title: Int. J. Numer. Methods Fluids
  doi: 10.1002/fld.4681
– volume: 23
  start-page: 1049
  year: 1994
  ident: ref_33
  article-title: Upwind Methods for Hyperbolic Conservation Laws with Source Terms
  publication-title: Comput. Fluids
  doi: 10.1016/0045-7930(94)90004-3
– volume: 100
  start-page: 32
  year: 1928
  ident: ref_1
  article-title: Über die partiellen Differenzengleichungen der mathematischen Physik
  publication-title: Math. Ann.
  doi: 10.1007/BF01448839
– volume: 59
  start-page: 615
  year: 1991
  ident: ref_16
  article-title: Finite element approximation of incompressible Navier-Stokes equations with slip boundary condition II
  publication-title: Numer. Math.
  doi: 10.1007/BF01385799
– volume: 314
  start-page: 824
  year: 2016
  ident: ref_86
  article-title: High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: Viscous heat-conducting fluids and elastic solids
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2016.02.015
– volume: 86
  start-page: 56
  year: 1990
  ident: ref_40
  article-title: Semi-implicit finite difference methods for the two–dimensional shallow water equations
  publication-title: J. Comput. Phys.
  doi: 10.1016/0021-9991(90)90091-E
– ident: ref_7
– volume: 49
  start-page: 905
  year: 2005
  ident: ref_45
  article-title: Multiple pressure variables methods for fluid flow at all Mach numbers
  publication-title: Int. J. Numer. Methods Fluids
  doi: 10.1002/fld.1032
– ident: ref_112
  doi: 10.1111/sapm.12238
– ident: ref_23
  doi: 10.1007/b79761
– volume: 39
  start-page: A2564
  year: 2017
  ident: ref_65
  article-title: Central weighted ENO schemes for hyperbolic conservation laws on fixed and moving unstructured meshes
  publication-title: SIAM J. Sci. Comput.
  doi: 10.1137/17M1111036
– volume: 477
  start-page: 4543
  year: 2018
  ident: ref_70
  article-title: ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics
  publication-title: Mon. Not. R. Astron. Soc. (MNRAS)
– volume: 199
  start-page: 625
  year: 2010
  ident: ref_87
  article-title: FORCE schemes on unstructured meshes II: Non-conservative hyperbolic systems
  publication-title: Comput. Methods Appl. Mech. Eng.
  doi: 10.1016/j.cma.2009.10.016
– ident: ref_30
  doi: 10.1016/j.jcp.2020.109743
– ident: ref_37
– volume: 4
  start-page: 1001
  year: 1984
  ident: ref_39
  article-title: Pressure method for the numerical solution of transient, compressible fluid flows
  publication-title: Int. J. Numer. Methods Fluids
  doi: 10.1002/fld.1650041102
– ident: ref_68
  doi: 10.3390/axioms7030063
– volume: 4
  start-page: 231
  year: 2008
  ident: ref_52
  article-title: Semi-implicit interior penalty discontinuous Galerkin methods for viscous compressible flows
  publication-title: Comm. Comput. Phys.
– volume: 34
  start-page: 1115
  year: 2005
  ident: ref_55
  article-title: Thirty years of development and application of CFD at Boeing Commercial Airplanes, Seattle
  publication-title: Comput. Fluids
  doi: 10.1016/j.compfluid.2004.06.005
– volume: 198
  start-page: 727
  year: 2004
  ident: ref_51
  article-title: A semi-implicit discontinuous Galerkin finite element method for the numerical solution of inviscid compressible flow
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2004.01.023
– volume: 72
  start-page: 1968
  year: 2016
  ident: ref_71
  article-title: On the choice of the internal degrees of freedom for the nodal Virtual Element Method in two dimensions
  publication-title: Comput. Math. Appl.
  doi: 10.1016/j.camwa.2016.03.016
– volume: 257
  start-page: 47
  year: 2013
  ident: ref_104
  article-title: A diffuse interface method for complex three–dimensional free surface flows
  publication-title: Comput. Methods Appl. Mech. Eng.
  doi: 10.1016/j.cma.2013.01.006
– ident: ref_31
  doi: 10.1016/j.amc.2021.126117
– volume: 14
  start-page: 1174
  year: 2013
  ident: ref_114
  article-title: Arbitrary–Lagrangian–Eulerian One–Step WENO Finite Volume Schemes on Unstructured Triangular Meshes
  publication-title: Commun. Comput. Phys.
  doi: 10.4208/cicp.181012.010313a
– volume: 38
  start-page: 1203
  year: 2009
  ident: ref_106
  article-title: A new 3D parallel SPH scheme for free surface flows
  publication-title: Comput. Fluids
  doi: 10.1016/j.compfluid.2008.11.012
– volume: 48
  start-page: 96
  year: 1998
  ident: ref_59
  article-title: Multilevel k-way Partitioning Scheme for Irregular Graphs
  publication-title: J. Parallel Distrib. Comput.
  doi: 10.1006/jpdc.1997.1404
– ident: ref_12
– volume: 206
  start-page: 536
  year: 2005
  ident: ref_94
  article-title: Accurate three-dimensional lid-driven cavity flow
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2004.12.024
– volume: 33
  start-page: 2732
  year: 2011
  ident: ref_67
  article-title: Peano-A traversal and storage scheme for octree-like adaptive Cartesian multiscale grids
  publication-title: SIAM J. Sci. Comput.
  doi: 10.1137/100799071
– volume: 341
  start-page: 341
  year: 2017
  ident: ref_48
  article-title: A pressure-based semi-implicit space-time discontinuous Galerkin method on staggered unstructured meshes for the solution of the compressible Navier-Stokes equations at all Mach numbers
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2017.03.030
– volume: 71
  start-page: 125
  year: 1996
  ident: ref_62
  article-title: Generalized conjugate gradient squared
  publication-title: J. Comput. Appl. Math.
  doi: 10.1016/0377-0427(95)00227-8
– volume: 353
  start-page: 169
  year: 2018
  ident: ref_29
  article-title: A projection hybrid high order finite volume/finite element method for incompressible turbulent flows
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2017.10.004
– ident: ref_105
– volume: 38
  start-page: 339
  year: 1982
  ident: ref_21
  article-title: Upwind Difference Schemes for Hyperbolic Conservation Laws
  publication-title: Math. Comput.
  doi: 10.1090/S0025-5718-1982-0645656-0
– volume: 319
  start-page: 294
  year: 2016
  ident: ref_47
  article-title: A staggered space-time discontinuous Galerkin method for the three-dimensional incompressible Navier-Stokes equations on unstructured tetrahedral meshes
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2016.05.009
SSID ssj0000913849
Score 2.2931771
Snippet In this paper, we propose a novel family of semi-implicit hybrid finite volume/finite element schemes for computational fluid dynamics (CFD), in particular for...
SourceID doaj
proquest
crossref
SourceType Open Website
Aggregation Database
Enrichment Source
Index Database
StartPage 2316
SubjectTerms ADER methodology
Algorithms
Applied mathematics
Asymptotic methods
Compressible flow
Computational fluid dynamics
Computer simulation
Conjugate gradient method
Degrees of freedom
Direct numerical simulation
Discretization
Distributed memory
Domain decomposition methods
Finite element method
Finite volume method
finite volume scheme
Fluid dynamics
Fluid flow
Food science
Free convection
High Mach number
incompressible and compressible Navier-Stokes equations
Incompressible flow
Mach number
Mathematical models
Matrices (mathematics)
Message passing
Navier-Stokes equations
Parallel processing
Partial differential equations
semi-implicit scheme on staggered unstructured meshes
shallow water equations
Shock waves
Simulation
Supercomputers
Turbulent flow
Variables
SummonAdditionalLinks – databaseName: DOAJ Directory of Open Access Journals
  dbid: DOA
  link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LS8NAEF6keNCD-MRqlT30JIQm2U1291i1oZeWgg96i_vIYiFW6UPov3c2m5aKghePCRsSZpL5vi-ZzIdQm6RGOJocyDgGgRIbHqjQ0MB54vBEJqlQpjKbYMMhH4_FaMvqy_WE-fHAPnAg2COueRxZIFY0ookCxGHM6tBKwGZuXfUF1rMlpqoaLCLCqfA_5BHQ9R3gf68ich-90m8QVE3q_1GIK3TJDtFBTQtx11_OEdoppsdof7CZqTo_QS9dPACmC9WpXOGRnDkTlBL3V-6XK5xNHHfEz1Wt6dRbPd8ajh8gMW8FBnqKvYlD_QIQZ-USjr33pvTzU_SU9R7v-kHtjxBoktJFQICKWcYMkyETEYCd0GGSqFDKwlgAaskLJY2Vqoi1CkG5FIRrYQ2zlJsQVPQZakzfp8U5wsCzDGFEU2MoYLZWXBHDY-pMbIwOSRPdrEOW63p4uPOwKHMQES6--VZ8m6i9WfzhZ2b8vuzWxX6zxA26rnZA-vM6_flf6W-i1jpzef30zXMnokDmAnm5-I9zXKK92HWyVJ1lLdRYzJbFFdrVn4vJfHZd3XhfJrXc4w
  priority: 102
  providerName: Directory of Open Access Journals
Title A Massively Parallel Hybrid Finite Volume/Finite Element Scheme for Computational Fluid Dynamics
URI https://www.proquest.com/docview/2576446181
https://doaj.org/article/5718c821f81d4145b41577fc0fa1258f
Volume 9
WOSCitedRecordID wos000699776200001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVAON
  databaseName: DOAJ Directory of Open Access Journals
  customDbUrl:
  eissn: 2227-7390
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000913849
  issn: 2227-7390
  databaseCode: DOA
  dateStart: 20130101
  isFulltext: true
  titleUrlDefault: https://www.doaj.org/
  providerName: Directory of Open Access Journals
– providerCode: PRVHPJ
  databaseName: ROAD: Directory of Open Access Scholarly Resources
  customDbUrl:
  eissn: 2227-7390
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000913849
  issn: 2227-7390
  databaseCode: M~E
  dateStart: 20130101
  isFulltext: true
  titleUrlDefault: https://road.issn.org
  providerName: ISSN International Centre
– providerCode: PRVPQU
  databaseName: Computer Science Database
  customDbUrl:
  eissn: 2227-7390
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000913849
  issn: 2227-7390
  databaseCode: K7-
  dateStart: 20130301
  isFulltext: true
  titleUrlDefault: http://search.proquest.com/compscijour
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Engineering Database
  customDbUrl:
  eissn: 2227-7390
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000913849
  issn: 2227-7390
  databaseCode: M7S
  dateStart: 20130301
  isFulltext: true
  titleUrlDefault: http://search.proquest.com
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Proquest Central (CZ)
  customDbUrl:
  eissn: 2227-7390
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000913849
  issn: 2227-7390
  databaseCode: BENPR
  dateStart: 20130301
  isFulltext: true
  titleUrlDefault: https://www.proquest.com/central
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Publicly Available Content Database
  customDbUrl:
  eissn: 2227-7390
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000913849
  issn: 2227-7390
  databaseCode: PIMPY
  dateStart: 20130301
  isFulltext: true
  titleUrlDefault: http://search.proquest.com/publiccontent
  providerName: ProQuest
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3db9MwED_BxgN7YHxqhVH5YU9IUZPYqZ0ntLFWQ6hVxACNp-CPeEzq2q3pkPbC386d4xYQiBdeIiV2FCtn3_3ufL4fwAEfupJgcqLzHB2U3KnEpE4kxImjCl0MS-MC2YScTtXZWVnFgFsb0yrXOjEoarewFCMfEDBG1wUN0uur64RYo2h3NVJo3IXtDL9F8_ydTDYxFqp5qUTZHcvj6N0PEAV-LTPa-hr-ZohCvf4_1HGwMePd_x3dQ3gQ0SU77KbDI7jTzB_DzmRTmrV9Al8O2QQBMyq52S2r9JK4VGbs5JZObrHxBUFQ9imorEG8G3UZ5uwU5XvZMES5rOOCiHFENp7d4LvHHbd9-xQ-jkcf3pwkkWYhsXwoVglHROeldFKnsszQZpY2LQqTat04j_Zeq8Zo57VpcmtSdIAarmzpnfRCuRSd8WewNV_Mmz1gCNccl9wK5wSafmuU4U7lgrhwnE15D16t_3ltYw1yosKY1eiLkIDqXwTUg4NN56uu9Mbfux2R8DZdqF52eLBYntdx-dUFmmCr8swjPBeZKAziFim9Tb1GhKd8D_bXcq3jIm7rn0J9_u_mF3A_p1SXkHq2D1ur5U3zEu7Zb6uLdtmH7aPRtHrfD-5-P8zQPqWYntL1-wjbq7eT6vMP1Z3yIw
linkProvider ProQuest
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Nb9NAEB2VgkQ58F01UGAP5YJkZeNdx-sDQoU2StUmqtSCenP3k1ZKk5KkoPyp_sbOrO0AAnHrgaPtdSLbz2_erGfnAWyJritIJic6TTFBSZ1KDHcyIU8clemsWxgXzSby4VCdnBSHK3DdrIWhssqGEyNRu4mlOfI2CWNMXTAgfbj8lpBrFH1dbSw0Kljs-8UPTNlm7_d28Pm-TdPe7vGnflK7CiRWdOU8EShgQp67XPO86GCIKCzPMsO19i5geNPKG-2CNj61hqPe90LZIrg8SOU45p74u3fgriT2j6WCR8s5HeqxqWRRLQMUouBtVJ1nRYc-tXV_C3zRH-AP-o8xrffof7sbj-FhrZ7ZdgX3J7Dix0_hwWDZenb2DE632QATAiTx0YId6il5xYxYf0Er01jvnCQ2-xIpuV1v7VYV9OwI8XvhGap4Vnld1POkrDe6wnN3FmN9gX_xHD7fyiWuw-p4MvYbwFCOOpELK52TKG2sUUY4lUry-nGWixa8a55xaese62T1MSox1yJAlL8AogVby8GXVWuRvw_7SGBZDqF-4HHHZPq1rOmlzFBiWJV2AqYfsiMzg7osz4PlQaOCVaEFmw2OypqkZuVPEL349-E3cL9_PDgoD_aG-y9hLaWynlhmtwmr8-mVfwX37Pf5-Wz6Or4PDE5vG3I3Sc5NQA
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1bb9MwFD4aG0LwwB1RGOCH8YIU1bWT2n5AaKONNo1VFTftLfMVJnXtaDtQ_xq_juPEKSAQb3vgMYmTKPHnc75jH58PYIf3nYo0OdOMYYDCnMwMdXkWNXFkoYu-Mq4WmxCjkTw-VuMN-N7uhYlpla1NrA21m9k4R96NxBhDF3RI3ZDSIsaD8tX5lywqSMWV1lZOo4HIoV99w_Bt8fJggH39nLFy-P71fpYUBjLL-_ky40hmghBOaCpUD92FsrQoDNXau4CuTktvtAvaeGYNRe7vubQqOBFy6SjGofjcK7AlkGTg6NraG47Gb9czPLHipsxVsymQc0W7yEE_q15ceOv_5gZrtYA_nEHt4cpb__O_uQ03E68mu81AuAMbfnoXbhyti9Iu7sHJLjnCUAHN-2RFxnoeVWQmZH8V96yR8jSSb_KxNtbddDRscuvJO0T2mSfI70mjgpFmUEk5ucB7B6upPsNX3IcPl_KJD2BzOpv6h0CQqDouuM2dy5H0WCMNd5LlUQXIWco78KLt78qm6utRBGRSYRQWwVH9Ao4O7KwbnzdFR_7ebC8CZ90kVgqvT8zmn6pkeKoCyYeVrBcwMMl7eWGQsQkRLA0aua0MHdhuMVUl87WofgLq0b8vP4NriLTqzcHo8DFcZzHfp86_24bN5fzCP4Gr9uvydDF_mgYHgZPLxtwP6tFXUQ
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+Massively+Parallel+Hybrid+Finite+Volume%2FFinite+Element+Scheme+for+Computational+Fluid+Dynamics&rft.jtitle=Mathematics+%28Basel%29&rft.au=R%C3%ADo-Mart%C3%ADn%2C+Laura&rft.au=Busto%2C+Saray&rft.au=Dumbser%2C+Michael&rft.date=2021-09-01&rft.pub=MDPI+AG&rft.eissn=2227-7390&rft.volume=9&rft.issue=18&rft.spage=2316&rft_id=info:doi/10.3390%2Fmath9182316&rft.externalDBID=HAS_PDF_LINK
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2227-7390&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2227-7390&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2227-7390&client=summon