一种求解有交界面椭圆型方程间断条件捕捉格式

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7vj4vW77S*7[?pg2011–4–20AJumpConditionCapturingSchemeforEllipticInterfaceProblemsCandidateYuanyuanZhouSupervisorProfessorYunqingHuangandAssociateProfessorJianjunXuCollegeSchoolofM

3、athematicsandComputationalScienceProgramComputationalMathematicsSpecializationTheoryandapplicationsofnumericalmethodsforPDEsDegreeMasterofScienceUniversityXiangtanUniversityDateApril20th,2011+99℄#W5w4?W

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13、A&C8k^~obWS)9xoHzÆ-a>xni>IAbstractTheimmersedinterfacemethodisgeneraltechniqueforsolvingdifferentialequationswithinterfaceproblemsandnowitisappliedinvariousaspectsoffluiddynamics.Interfaceproblemsusuallyleadtodifferenti

14、alequationswhosesolutionsanditsderivativeshavediscontinuitiesornon-smoothnessacrosssomeinterface.Manydifferentialequationnumericalmethodsdonotworkefficientlyforinterfaceproblems.Inthispapertheimmersedinterfacemethodforsolvingellipticinterfaceprob-lemsin2Disextendedtothe

15、situationwheninterfaceandjumpsareimplicitlyprovidedbyfunctionsonthegridpointsinaneighborhoodoftheinterface.Theresultingschemeisparticularlysuitableforinterfacecapturingmethodssuchasthelevelsetmethod.Formulationsoftheoriginalimmersedinterfacemethodaremod-ifiedforthisim

16、plicitsetting,includingtheinterfacejumprelations,thealgebraicequationsfordeterminingthecoefficientsofthefinitedifferenceschemeatirregul