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《Li-1990-International_Journal_for_Numerical_Methods_in_Engineering》由會(huì)員上傳分享，免費(fèi)在線閱讀，更多相關(guān)內(nèi)容在學(xué)術(shù)論文-天天文庫(kù)。
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
