资源描述：
《removing the stiffness of elastic force from the immersed boundary method for the 2d stokesnew》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。
1、RemovingtheStiffnessofElasticForcefromtheImmersedBoundaryMethodforthe2DStokesEquationsThomasY.Hou∗ZuoqiangShi†June16,2007AbstractTheImmersedBoundarymethodhasevolvedintooneofthemostusefulcomputa-tionalmethodsinstudyingfluidstructureinteraction.Ontheotherhand,theImmersedBound
2、arymethodisalsoknowntosufferfromaseveretimestepstabilityrestrictionwhenusinganexplicittimediscretization.Inthispaper,weproposeseveralefficientsemi-implicitschemestoremovethisstiffnessfromtheImmersedBoundarymethodforthetwo-dimensionalStokesflow.First,weobtainanovelunconditional
3、lystablesemi-implicitdiscretizationfortheimmersedboundaryproblem.Usingthisunconditionallystabledis-cretizationasabuildingblock,wederiveseveralefficientsemi-implicitschemesfortheimmersedboundaryproblembyapplyingtheSmallScaleDecompositiontothisuncondi-tionallystablediscretiza
4、tion.Ourstabilityanalysisandextensivenumericalexperimentsshowthatoursemi-implicitschemesoffermuchbetterstabilitypropertythantheexplicitscheme.Unlikeotherimplicitorsemi-implicitschemesproposedintheliterature,oursemi-implicitschemescanbesolvedexplicitlyinthespectralspace.Thu
5、sthecomputationalcostofoursemi-implicitschemesiscomparabletothatofanexplicitscheme,butwithamuchbetterstabilityproperty.1IntroductionarXiv:0801.2398v2[cs.CE]18Jan2008TheImmersedBoundarymethodwasoriginallyintroducedbyPeskininthe1970’stomodeltheflowaroundheartvalves.Nowithase
6、volvedintoageneralusefulmethodinstudyingthemotionofoneormoremassless,elasticsurfaceimmersedinanincompressible,viscousfluid,particularlyinbiofluiddynamicsproblemswherecomplexgeometriesandimmersedelasticmembranesarepresent.Themethodhasbeensuccessfullyappliedtoavarietyofproble
7、msincludingbloodflowintheheart[25,16,17,18,26,19,20],vibrationsofthecochlearbasilarmembrane[2,8],plateletaggregationduringclotting[7,34],aquaticlocomotion[5,6,11,35,3],flowwithsuspendedparticles[5,31],andinsetflight[21,22],Wereferto[27]foranextensivelistofapplications.TheImm
8、ersedBoundarymethodemploysauniformEuleriangridovertheentiredomaintodescribethevelocityfieldofthefl
