Li-1990-International_Journal_for_Numerical_Methods_in_Engineering

《Li-1990-International_Journal_for_Numerical_Methods_in_Engineering》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、INTERNATIONALJOURNALFORNUMERICALMETHODSINENGINEERING,VOL.29,1343-1358(1990)LEAST-SQUARESCHARACTERISTICSANDFINITEELEMENTSFORADVECTION-DISPERSIONSIMULATIONc.w.LIDepartmentofCivilandStructuralEngineering,HongKongPolytechnic.HungHorn,Kowloon,HongKongSUMMARYThemethodofcharacteristicsiscombinedwiththe

2、methodofleast-squarestosolvetheadvectionequationwithinthefiniteelementframework.Fouriermodeanalysisshowsthatthenumericalschemeisstableandaccurateevenwhenalinearbasisfunctionisused.However,inpracticalapplication,theinvolvementofusingnumericalquadratureinthismethodcanproducenumericalinstability,de

3、pendingonthevalueoftheCourantnumberused.ItisfoundthatusingC1continuousHermitiancubicbasisfunctionsintheschemereducesthedegreeofinstabilitysignificantlyandproduceshighaccuracy.Whenbeingusedinasplit-operatorapproach,thismethodcombinesnaturallywiththestandardfiniteelementmethodandresultsinahighlyac

4、curateschemeforadvectiondispersionsimulation.INTRODUCTIONThedifficultyinthenumericalapproximationoftheadvection-dispersionequationliesonthefactthattheequationcanbenearlyhyperbolic(advectiondominated).CentraldifferenceschemesandGalerkinfiniteelementschemesareunabletoapproximatethesolutionaccurate

5、lywhenthesituationisadvectiondominatedandthesolutionconsistsofsharpgradients.Theyusuallyproducesolutionswithnodetonodeoscillations,indicatingthattheshortestresolvablewavecannotbepropagated.Mostremedialworksaredoneinthelineofthoughttoeliminatesuchshortwaveoscillationsbyintroducingdampingtothesche

6、me,andretaintheaccuracyforlongerwaves.Takingintoaccountthedirectionalnatureoftheadvectionprocess,variousasymmetricweightingfunctionsareemployedinthefiniteelementformulation(upwindingtechnique).Whilemanyschemesaresuccessfulinsolvingthesteadystateformoftheadvection4ispersionequation,'-'mostofthemp

7、aythecostofsmearingthesolutionprofileintransientproblems(e.g.HuyakornandNilkuha,6ShapiroandPinder'),withtheexceptionofthestreamlineupwind/PetrovGalerkinscheme.*Theseindicatethatthetemporaldiscretizationerrorissignificantintr