简介：Anewmethodwasproposedforconstructingtotalvariationdiminishing(TVD)upwindschemesinconservationforms.Twolimiterswereusedtopreventnon-physicaloscillationsacrossdiscontinuity.BothlimiterscanensurethenonlinearcompactschemesTVDproperty.TwocompactTVD(CTVD)schemesweretested,oneisthird-orderaccuracy,andtheotherisfifth-order.Theperformanceofthenumericalalgorithmswasassessedbyone-dimensionalcomplexwavesandRiemannproblems,aswellasatwo-dimensionalshock-vortexinteractionandashock-boundaryflowinteraction.Numericalresultsshowtheirhigh-orderaccuracyandhighresolution,andlowoscillationsacrossdiscontinuities.更多还原

简介：Aclassofthree-levelexplicitdifferenceschemesforthedispersiveequationu1=auxxxareestablishedTheseschemeshavehigherstabilityandinvolvefourmeshpointsatthemiddlelevel.TheirlocaltruncationerrorsareO（τ+h）andstabilityconditionsarefrom|R|≤0.25to|R|≤10,where|R|=|a|τ/h3,whichismuchbetterthan|R|≤0.25.

简介：Inthepresentpaper,aclassofexplicitforwardtime-differenceschemesareestablishedfromageometricviewwithstrictanalyticaldeductions.Thisclassincludestheschemeswithaconstanttimeintervalandwithadjustabletimein-tervals,whichisprovedtobeeffectiveandremarkablytime-savinginnumericaltestsandapplications.

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简介：Afinitedifferencemethodispresentedtosimulatetransversevibrationsofanaxiallymovingstring.Bydiscretizingthegoverningequationandtheequationofstress-strainrelationatdifferentfrictionalknots,twolinearsparsefinitedifferenceequationsystemsareobtained.Thetwoexplicitdifferenceschemescanbecalculatedalternatively,whichmakethecomputationmuchmoreefficient.Thenumericalmethodmakesthenonlinearmodeleasiertodealwithandoftruncationerrors,O(Δt~2+Δx~2).Italsoshowsquitegoodstabilityforsmallinitialvalues.Numericalexamplesarepresentedtodemonstratetheefficiencyandthestabilityofthealgorithm,anddynamicanalysisofaviscoelasticstringisgivenbyusingthenumericalresults.

简介：BytheaidofanideaoftheweightedENOschemes,someweight-typehigh-resolutiondifferenceschemeswithdifferentordersofaccuracyarepresentedinthispaperbyusingsuitableweightsinsteadoftheminmodfunctionsappearinginvariousTVDschemes.Numericalcomparisonsbetweentheweightedschemesandthenon-weightedschemeshavebeendoneforscalarequation,one-dimensionalEulerequations,two-dimensionalNavier-StokesequationsandparabolizedNavier-Stokesequations.

简介：ThenumericalsolutionsofstandingwavesforEulerequationswiththenonlinearfreesurfaceboundaryconditioninatwo-dimensional(2D)tankarestudied.Theirregulartankismappedontoafixedsquaredomainthroughpropermappingfunctions.Astaggeredmeshsystemisemployedina2Dtanktocalculatetheelevationofthetransientfluid.Atime-independentfinitedifferencemethod,whichisdevelopedbyBang-fuhChen,isusedtosolvetheEulerequationsforincompressibleandinviscidfluids.Thenumericalresultsagreewellwiththeanalyticsolutionsandpreviouslypublishedresults.Thesloshingprofilesofsurgeandheavemotionwithinitialstandingwavesarepresented.Theresultsshowveryclearnonlinearandbeatingphenomena.

简介：Inthispaper,weproposeanovelincompressiblefinite-differencelatticeBoltzmannEquation(FDLBE).Becausesourcetermsthatreflecttheinteractionbetweenphasescanbeaccuratelydescribed,thenewmodelissuitableforsimulatingtwo-waycouplingincompressiblemultiphaseflow.The2-Dparticle-ladenflowoverabackward-facingstepischosenasatestcasetovalidatethepresentmethod.Favorableresultsareobtainedandthepresentschemeisshowntohavegoodprospectsinpracticalapplications.

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