Analysis of immersed boudary method for stokes flow.pdf

《Analysis of immersed boudary method for stokes flow.pdf》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、AnalysisoftheImmersedBoundaryMethodforStokesFlowbyThomasT.BringleyAdissertationsubmittedinpartialfulfillmentoftherequirementsforthedegreeofDoctorofPhilosophyDepartmentofMathematicsNewYorkUniversityMay,2008CharlesS.Peskin—Advisor°cThomasT.BringleyAllRightsReserved,2008AbstractTheimmersedboundarymet

2、hodisanumericalschemefordynamicalsimulationsofsolidorelasticbodiesimmersedinasurroundingfluid.ThemethodwasoriginallyintroducedbyPeskintomodeltheflowofbloodinthehumanheart.Ithassinceproventobeageneralandrobustmethodfordiverseflowproblemsarisinginbiologyandengineering.Recently,theimmersedboundarymetho

3、dhasbeenappliedtobiologicalproblemsatthemicro-scaleorsmaller,includingswimmingmicroorganismsandbiomolecu-larmotors.Atthesescales,theStokesequationsgovernthedynamicsofthesurroundingfluid,anditisparticularlyimportanttorepresentaccuratelythehydrodynamicinteractionsthatgovernthemotionofimmersedbodies.

4、Inthisthesis,weconstructanewversionoftheimmersedboundarymethodforStokesflow.Ouranalysisofthisnewmethodshedslightonseveralfundamentalquestionsabouttheimmersedboundarymethod.Inthenewmethod,thestructuresareimmersedinaninfinitethree-dimensionalfluid;noartificialboundariesarenecessary.Althoughwestartfroma

5、discreterep-resentationofthefluidonaninfinitegrid,weareabletoeliminatethefluidvariablesandreducethedynamicstothatofafinitecollectionofLagrangianpoints.Asymptoticmethodsreducethecomputationalcostandrevealthemagnitudesofthenumericalerrors,aswellasthedependenceoftheseer-rorsontheapproximatedeltafunction

6、usedtoregularizesingularsources.ivWediscussthepropertiesandtheconstructionofthesedeltafunctions.Wethenstudyrepresentationsofsimplerigidbodies:spheresandcylinders,bysimplest-possibleconfigurationsofLagrangianpoints,anisolatedpointforasphereandalineararrayofpointsforacylinder.Weusenumericalexperi-me

7、ntationtofindhowthephysicalparametersoftheseimmersedbodiesarerelatedtothenumericalparametersofthemethod.Wefindthattheerrorsinourmethodaresmallifparametersarechosenappropriately,andwegiverecipesforparameterchoicesthatshou