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1、JOURNALOFCOMPUTATIONALPHYSICS143,381–402(1998)ARTICLENO.CP975856ASemi-implicitNumericalSchemeforReactingFlowI.StiffChemistryHabibN.Najm,¤;1PeterS.Wyckoff,¤andOmarM.Knioy¤SandiaNationalLaboratories,P.O.Box969,MS9051,Livermore,California94551,andyDepartmentofMechanicalEnginee
2、ring,JohnsHopkinsUniversity,Baltimore,Maryland21218-2686E-mail:hnnajm@ca.sandia.govReceivedMarch,21,1997;revisedAugust14,1997Anadditivesemi-implicitprojectionschemeforthesimulationofunsteadycom-bustionintwodimensionsisconstructed.Theschemereliesonazero-Machnumberformulation
3、ofthecompressibleconservationequationswithdetailedchemistry.Thegoverningequationsarediscretizedinspaceusingsecond-orderdifferencesandintegratedintimeusingasemi-implicitapproach.Timeintegrationoftheevo-lutionequationsforspeciesmassfraction,thermodynamicpressure,anddensityisp
4、erformedusingasemi-implicit,nonsplitschemethatcombinesasecond-orderpredictor–correctortreatmentofconvectionanddiffusionterms,andastiffintegra-torforthereactionsourceterms.Meanwhile,themomentumequationsareinte-gratedusingasecond-orderprojectionscheme.Theprojectionschemeisbas
5、edonapredictor–correctorapproachthatcouplestheevolutionofthevelocityandden-sityfieldsinordertostabilizecomputationsofreactingflowswithlargedensityvariations.ApressurePoissonequationisinvertedfollowingboththepredictorandcorrectorstepsusingafastsolver.Theadvantagesofthestiffint
6、egrationofreac-tionsourcetermsareanalyzedbycomparingtheperformanceoftheschemetothatofapredictor–correctorschemeinwhichreactionanddiffusionareintegratedinasimilarnonstifffashion.Thecomparisoninbasedonbothone-dimensional(1D)unsteadytestsofapremixedmethane–airflame,andunsteadyt
7、wo-dimensionaltestsofthesameflameinteractingwithacounterrotatingvortexpair.Inbothcases,theGRImech1.2reactionmechanismwith32speciesand177elementaryreactionsisused.Computedresultsshowthatthestiffreactionschemeenablesselectionoflargertimestepsandthusleadstosubstantialimprovemen
8、tintheperformanceofthecomputations.Forthepresentreactionmechanismandflameconditions
