您好,欢迎访问三七文档
NASAContractorReportICASEReportNo.94-4IC191594SJ_PARALLELIMPLICITUNSTRUCTUREDGRIDEULERSOLVERSV.VenkatakrishnanNASAContractNo.NASI-19480January1994InstituteforComputerApplicationsinScienceandEngineeringNASALangleyResearchCenterHampton,Virginia23681-0001OperatedbytheUniversitiesSpaceResearchAssociationNationalAeronauticsandSpaceAdministrationLangleyResearchCenterHampton,Virginia23681-0001et3,#N!o,Zi,,-,_1o')ILo..J_.wt/1,-.4.JN.Jo__.t.ut/)Q_4o_-O'w_._OZZ,.-mUN0000,#_0PARALLELIMPLICITUNSTRUCTUREDGRIDEULERSOLVERSV.Venkatakrishnan*InstituteforComputerApplicationsinScienceandEngineeringMS132C,NASALangleyResearchCenterHampton,VA23681-0001Abstractkmesh-vertexfinitevolumeschemeforsolvingtheEulerequationsontriangularunstructuredmeshesisimplementedonanMIMD(multipleinstruction/multipledatastream)parallelcomputer.Anexplicitfour-stageRunge-Kuttaschemeisusedtosolvetwo-dimensionalflowproblems.Afamilyofimplicitschemesisalsodevelopedtosolvetheseproblems,wherethelinearsystemthatarisesateachtimestepissolvedbyapreconditionedGMRESalgorithm.Twopartitioningstrategiesareemployed,onethatpartitionstrianglesandtheotherthatpartitionsvertices.Thechoiceofthepreconditionerinadistributedmemorysettingisdiscussed.Allthemethodsarecomparedbothintermsofelapsedtimesandconvergencerates.Itisshownthattheimplicitschemesofferadequateparallelismattheexpenseofminimalsequentialoverhead.Theuseofaglobalcoarsegridtofurtherminimizethisoverheadisalsoinvestigated.Theschemesareimplementedonadistributedmemoryparallelcomputer,theiPSC/860.*PartofthisworkwasdonewhiletheauthorwasemployedbyComputerSciencesCorporation,MoffettField,CAduringwhichtimetheworkwassupportedbytheNationalAeronauticsandSpaceAdministrationundertheNASAcontractNAS2-12961.ThisresearchwasalsosupportedundertheNASAcontractNo.NASl-19480whiletheauthorwasinresidenceattheInstituteforComputerApplicationsinScienceandEnginnering(ICASE),NASALangleyResearchCenter,Hampton,VA23681.21IntroductionTriangularmesheshavebecomequitepopularincomputationalfluiddynamics.Theyareidealforhandlingcomplexgeometriesandforadaptingtoflowfeatures,suchasshocksandboundarylayers.Considerableattentionhasbeenfocusedonimprovingthespatialoperator,whichhasevolvedtoaveryhighdegreeofsophisticationfortheEulerandNavier-Stokesequations[1,2].Distributedmemoryparallelcomputersseemtoofferanavenuefordoinglargeproblemsveryfastcluetotheirscalability.Forthegoalofsustainedhighperformanceonthesemachinestoberealized,manyfundamentalissuesneedtobeaddressed.Amongthesearescalablealgorithmsandsoftware.Explicitschemesusedincomputationalfluiddynamicsarecompletelyparallel.Theyonlyrequireasimpleupdateprocedurethatinvolveslocaldependencies.Onaparallelcomputer,suchschemestypicallyonlyrequirecommunicationtonearestneighbors.Implicitschemes,ontheoth'erhand,requirethesolutionofcoupledequationswhichinvolvesglobaldependencies.However,therearesomeapplications,suchascertainclassesofunsteadyflows,whereexplicitschemesarequiteuseful.Whensteadystatesolutionsaresought,explicitschemestypicallyrequirethousandsoftimestepstoconvergeandexhibitveryslowconvergencerates.Implicitschemesallowlargertimestepstobetakenandusuallyresultinbetterconvergencerates.Implicitschemeshavetobedesignedcarefullysincetheworkinvolvedateachtimestepcouldbesubstantial.VenkatakrishnanandMavriplis[3]developedandtestedafamilyofimplicitschemesontheCrayY-MPforsolvingthetwo-dimensionalcompressibleNavier-Stokesequationsonunstructuredmeshes.TheyconcludedthattheGeneralizedMinimalResidualtechniqueofSaadandSchultz[4]withincompleteLUpreconditioning(ILU(0))basedontheoriginalnonzeropattern(GMRES/ILU)wasbyfarthebestimplicitschemeoverawholerangeofflowconditionsandwasasefficientastheunstructuredmuitigridstrategyofMavriplisandJameson[2].Ondistributed-memoryparallelcomputers,thedesignofimplicitschemesismoredifficultsinceparallelismandloadbalanceduringtheimplicitphaseareadditionalconsiderations.Venkatakrishnanetal.[5]andDasetal.[6]haveshownthatitispossibletoobtainsupercom-puterperformancewhensolvingexplicitunstructuredgridproblemsontheiPSC/860.Bypayingcarefulattentiontothepartitioningofthemesh,communicationscheduleanddatastructures,theywereabletoshowthat2-3timesthespeedofaCrayY-MP/1couldbeobtainedwith128processorsoftheiPSC/860.Inthispaper,twodifferentwaysofpartitioningtheunstructuredmeshacrossprocessorsareexplored.Thedesignofimplicitschemessuitablefordistributed-memoryparallelcomputersisdiscussednext.TheissuesinimplementingtheGMRESalgorithmandthepreconditionersinparallelareaddressed.Finally,resultsforatypicalflowaroundamulti-elementairfoilarepresentedandtheperformancesoftheexplicitandimplicitschemesontheiPSC/860arecomparedusingthetwodifferentpartitioningstrategies.Theuseofacoarsegridtoimproveconvergenceisalsoinvestigatedwithoneoftheimplicitschemes.2GoverningEquationsandSpatialDiscretizationTheEulerequationsinintegralformforacontrolvolumeftwithboundary0_readd--tudv+F(u,n)dS=0.(1)f_Hereuisthesolutionvectorcomprisedoftheconservativevariablesdensity,thetwocomponentsofmomentumandtotalenergy.ThevectorF(u,n)representstheinviscidfluxve
本文标题:Parallel Implicit Unstructured Grid Euler Solvers,
链接地址:https://www.777doc.com/doc-3298360 .html