不连续伽列金方法简介

《不连续伽列金方法简介》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

1、不连续伽列金方法简介DiscontinuousGalerkinThediscontinuousGalerkin(DG)methodisoftenreferredtoasahybrid,ormixed,methodsinceitcombinesfeaturesofbothfiniteelementandfinitevolumemethods.Thesolutionisrepresentedwithineachelementasapolynomialapproximation(asinFEM),whiletheinterelementconvectiontermsare

2、resolvedwithupwindednumericalfluxformulas(asinFVM).Theoretically,solutionsmaybeobtainedtoanarbitrarilyhighorder-of-accuracy.WhilethediscontinuousGalerkinmethodwasdevelopedintheearly1970's,itwasnotusedforCFDsimulationsuntiltheearly1990'swhenitwasfirstusedtosolvetheEulerequationsbyCockbu

3、rnandShu.ThesolutionoftheNavier-StokesequationswiththeDGmethodwasfirstaccomplishedbyBassiandRebayin1997.AsthemethodgainedmoreattentionintheCFDresearchcommunity,furtheradvanceshavecomefairlyrapidly.ResearchersarenowusingtheDGmethodtoperformsimulationsofawidevarietyofflowregimes.Themetho

4、dhasbeenadaptedforusewithcompressibleandincompressible,steadyandunsteady,aswellaslaminarandturbulentconditions.Inadditiontobeingarbitrarilyhigher-orderaccurate,thediscontinuousGalerkinalsopermitstheformulationofverycompactnumericalschemes.Theisduetothefactthatthesolutionrepresentations

5、ineachelementarepurposefullykeptindependentofthesolutionsinothercells,withinter-elementcommunicationoccurringonlywithadjacentcells(elementssharingacommonface).Thischaracteristic,alongwithotherfavorablenumericalproperties,makesthismethodextremelyflexible(easilyhandlingawidevarietyofelem

6、enttypesandmeshtopologies)andalsoallowsanumberofadaptivetechniques(bothh-andp-refinement)andsolveraccelerationstrategiestobeimplementedinaratherstraightforwardmanner.DerivationforHyperbolicConservationLawsThediscontinuousGalerkinmethodisderivedfromthefiniteelementmethod,whichisitselfav

7、ariationalmethod.ToobtainthegoverningequationsfortheDGmethod,webeginwiththestrongformofthehyperbolicconservationlaws:Here,isanarrayofconservedquantities,andisanarrayoffluxvectorsdescribingthelocaltransportof.isanarrayofsourcetermswhichrepresentsthe(non-conservative)productionordestru