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空间科学学报 2003
ACLASSOFTWO-STEPTVDMACCORMACKTYPENUMERICALSCHEMEFORMHDEQUATIONS, PP. 401-412 Keywords: TwostepTVDMacCormackscheme,MHDnumericalsimulation Abstract: Inthispaper,anewnumericalschemeofTotalVariationDiminishing(TVD)MacCormacktypeforMagnetoHydroDynamic(MHD)equationsisproposedbytakingintoaccountofthecharacteristicssuchasconvergence,stability,resolution.ThisnewschemeisestablishedbysolvingtheMHDequationswithaTVDmodifiedMacCormackschemeforthepurposeofdevelopingaschemeofquickconvergenceaswellasofTVDproperty.Toshowthevalidation,simplicityandpracticabilityoftheschemeformodellingMHDproblems,aself-similarCauchyproblemwiththediscontinuousinitialdataconsistingofconstantstates,andthecollisionoftwofastMHDshocks,andtwo-dimensionalOrszagandTang'sMHDvortexproblemarediscussedwiththenumericalresultsconformingtotheexistingresultsobtainedbytheRoetypeTVD,thehigh-orderGodunovscheme,andWeightedEssentiallyNon-Oscillatory(WENO)scheme.Thenumericaltestsshowthatthistwo-stepTVDMacCormacknumericalschemeforMHDsystemisofrobustoperationinthepresenceofverystrongwaves,thinshockfronts,thincontactandslipsurfacediscontinuities.
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