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1、AHIGHRESOLUTIONFINITEVOLUMEMETHODFORSOLVINGSHALLOWWATEREQUATIONSABSTRACT: Ahigh-resolutionfinitevolumenumericalmethodforsolvingtheshallowwaterequationsisdevelopedinthispaper.InordertoextendfinitedifferenceTVDschemetofinitevolumemethod,anewgeometryandtopologyofcontro
2、lbodiesisdefinedconsideringthecorrespondingtherelationshipsbetweennodesandelements.ThissolverisimplementedonarbitraryquadrilateralmeshesandthEirsatelliteelements,andbasedonasecond-orderhybridtypeTVDschemeinspacediscretizationandatwo-stepRunge-Kuttamethodintimediscre
3、tization.Thenitisusedtodealwithtwotypicaldam-breakproblemsandverysatisfactoryresultsareobtainedcomparingwithothernumericalsolutions.Itcanbeconsideredasanefficientimplementforthecomputationofshallowwaterproblems,especiallyconcerningthosehavingdiscontinuities,subcriti
4、calandsupercriticalflowsandwithcomplexgeometries.KEYWORDS: shallowwaterequations,finitevolume,TVDscheme,dam-breakbores1. INTRODUCTIONItisnecessarytoconductfluidflowanalysesinmanyareas,suchasinenvironmentalandhydraulicengineering.Numericalmethodbecomesgraduallythemo
5、stimportantapproach.Thecomputationforgeneralshallowwaterflowproblemsaresuccessful,butthestudiesofcomplexproblems,suchashavingdiscontinuities,freesurfaceandirregularboundariesarestillunderdevelopment.Theanalysisofdam-breakflowsisaveryimportantsubjectbothinscienceande
6、ngineering.Forthecomplexboundaries,thetraditionalmethodhasusuallyinvolvedakindofbody-fittedcoordinatetransformationsystem,whilstthismaymaketheoriginalequationsbecomemorecomplicatedandsometimesthetransformationwouldbedifficult.Itisnaturallydesirabletohandlearbitraryc
7、omplexgeometriesoneverycontrolelementwithouthavingtousecoordinatetransformations.Forthenumericalapproach,thegeneralmethodscanbelistedascharacteristics,implicitandapproximateRiemannsolver,etc.TheTVDfinitedifferenceschemeisplayingapeculiarroleinsuchstudies,butitisvery
8、littleinfinitevolumediscretization.ThetraditionalTVDschemeshavedifferentfeaturesintheaspectsofconstructiveformandnumericalperformance.Some
