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一类强耦合的奇异摄动对流扩散方程组的移动网格方法（英文）.docx

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一类强耦合的奇异摄动对流扩散方程组的移动网格方法（英文） Movingmeshmethodsforstronglycoupledsingularperturbationconvection-diffusionequations Introduction: Awiderangeofmathematicalmodelsinscienceandengineeringinvolvethestudyofconvection-diffusionprocesses.Thesemodelsarehighlyrelevanttonumerousapplications,includingatmosphericsciences,combustion,andporousmedia.Inthiscontext,movingmeshmethodshaveproventobeaneffectivetoolthatcanbeusedtosimulatethedynamicsofconvection-diffusionprocessesatlowcomputationalcost.Inthispaper,wepresentanewmovingmeshmethodthatistailoredtosolveaclassofstronglycoupledsingularperturbationconvection-diffusionequations. Methodology: Theproposedmethodisbasedonamovingmeshapproachthatusesapartialdifferentialequationtodescribetheevolutionofacomputationalgrid.Specifically,weuseanequidistributionprinciplethatensuresthatthecomputationalgridisuniformlydistributedoverthespatialdomain.Briefly,themethodconsistsofthreemainsteps:1)constructtheinitialgrid,2)solvethedifferentialequationsonthegrid,and3)movethegridbasedontheequidistributionprinciple. Forthenumericalsolutionoftheconvection-diffusionequations,weuseafinitedifferenceapproachthatapproximatesthepartialderivativesusingaweighteddifferenceformula.Theresultingsystemofalgebraicequationsissolvedusinganiterativemethod. Results: Weapplytheproposedmethodtoatestproblem,whichconsistsofacoupledsystemofsingularlyperturbedconvection-diffusionequations.Theproblemissimulatedusingauniformgridandamovingmesh.Ournumericalresultsconfirmthatthemovingmeshapproachyieldsamoreaccurateandefficientsolutionthanthefixedgridmethod,asitadaptstothespatialvariationofthesolution.Moreover,thecomputationalcostofthemovingmeshmethodissignificantlylowerthanthatoftheuniformgridmethod. Discussion: Theproposedmethodisveryeffectiveforsimulatingstronglycoupledsingularperturbationconvection-diffusionproblems.Theequidistributionprincipleensuresthatthecomputationalgridadaptstothesolution,leadingtogreateraccuracyandefficiency.Althoughourresultsshowthatthemethodisveryeffective,ith