Scalaradvectionequation标量平流方程

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1、LiteratureStudyLiteratureStudyJeroenWille20-03-2009/14:001StructureIntroductionScalaradvectionequationDiscontinuousGalerkinConclusionsandfurtherresearch20-03-2009/14:002IntroductionTwomodelsContinuousDiscontinuousFocusonnumericalmethods20-03-2009/14:003Scalaradvectione

2、quation1-dimensionalSUPGPerturbationVariablevelocity2-dimensionalSUPGPerturbation20-03-2009/14:004Scalaradvectionequation1DEquationWeakformulationImplicitEuler20-03-2009/14:005Scalaradvectionequation1Dresultscontinuous20-03-2009/14:006Scalaradvectionequation1Dresultsdi

3、scontinuous20-03-2009/14:007Scalaradvectionequation1DPerturbationPerturbationaddedtoequationNeumannboundaryconditionneededatoutflowboundaryExtratermtostiffnessmatrixExtratermtorighthandside20-03-2009/14:008Scalaradvectionequation1DPerturbationresults20-03-2009/14:009Sc

4、alaradvectionequation1DSUPGExtratermpaddedtotestfunctionpisconstantperelementpisdiscontinuousovertheelementsExtratermtomass-andstiffnessmatrix20-03-2009/14:0010Scalaradvectionequation1DSUPGresults20-03-2009/14:0011Scalaradvectionequation1Dvariablevelocityvnolongerfixed

5、,butv=v(x,t)definedbygradientofvequalszero,sovisconstantinspacePertimestep,extrasystemsolvedtodeterminep(1)20-03-2009/14:0012Scalaradvectionequation1Dvariablevelocityresults20-03-2009/14:0013Scalaradvectionequation2DEquationWeakformulation20-03-2009/14:0014Scalaradvect

6、ionequation2Dresultscontinuous20-03-2009/14:0015Scalaradvectionequation2Dresultsdiscontinuous20-03-2009/14:0016Scalaradvectionequation2DPerturbationPerturbationaddedtoequationNeumannboundaryconditionneededatoutflowboundaryExtratermtostiffnessmatrixExtratermtorighthands

7、ide20-03-2009/14:0017Scalaradvectionequation2DPerturbationresults20-03-2009/14:0018Scalaradvectionequation2DSUPGExtratermpaddedtotestfunctionpisconstantperelementpisdiscontinuousovertheelementsExtratermtomass-andstiffnessmatrix20-03-2009/14:0019Scalaradvectionequation2

8、DSUPGresults20-03-2009/14:0020DiscontinuousGalerkinApproximateupercellbylinearcombinationofpolynomialsUselegendre-pol