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1、基于谱元法的热毛细流模拟及线性稳定性分析重庆大学博士学位论文学生姓名：尹林茂指导教师：曾忠教授专业：流体力学学科门类：工学重庆大学航空航天学院二O一六年四月Thermocapillary-FlowSimulationandLinearStabilityAnalysisbasedonSpectralElementMethodAThesisSubmittedtoChongqingUniversityinPartialFulfillmentoftheRequirementfortheDoctor’sDegreeofEngineeringByLinmaoYinSup
2、ervisedbyProf.ZengZhongSpecialty:FluidMechanicsCollegeofAerospaceEngineeringofChongqingUniversity,Chongqing,ChinaApril,2016重庆大学博士学位论文II英文摘要ABSTRACTThethermocapillaryflow,drivenbythenon-uniformsurfacetensionalongfreesurface,appearsofteninindustrialprocessing.Numericalsimulationonthe
3、rmocapillaryflow,couplingwiththedynamicdeformationoffreesurface,isalong-termchallengeincomputationalfluiddynamics.Meanwhile,theinvestigationonthermocapillaryflowanditsinstabilityisimportantinmanyengineeringapplication.Inthispaper,aGalerkinspectralelementmethod(GSEM)andlinearstabili
4、tyanalysisbasedonGSEMweredeveloped,andthenthermocapillaryflowanditsinstabilitywereinvestigated.Mymainworksaresummariedbrieflyas:①InaccordancewiththespectralapproximationtheoryoftheFourier/Legendreorthogonalfunctionsystems,theLegendre-LegendrespectralelementmethodandtheFourier-Legen
5、drespectralelementmethodforthePoisson-typeequationsweredeveloped,thenacomparisonofthecomputationalaccuracybetweenthetwospectralelementmethods(SEM)wasperformed.②InsolvingtheunsteadyNavier-Stokesequations,thetimesplittingmethod(TSM),includingtheclassicaltimesplittingmethod(CSM)andthe
6、normaltimesplittingmethod(NSM),iswidelyappliedinliterature.Inthispaper,animprovedTSM,so-calledthepresenttimesplittingmethod(PSM)wasproposed.Bymodifyingthepressureboundarycondition,theproposedPSMissuperiortoCSMinaccuracyandbetterthanNSMinstability.③InsolvingthesteadyNavier-Stokesequ
7、ations,thePN×PN-2methodwasmodifiedbyintroduingtheSIMPLEalgorithm,decouplingvelocityandpressureiniterationwasachieved,andthematrixdimensionincomputationwasreduced.Inaddition,theresultsindicatethatthePN×PN-2methodisbetterthanTSMinaccuracy,butitisworsethanTSMinthealgorithmstability.④T
8、heSEMincorporatingwiththed
