歐拉方程基于徑向基函數(shù)的高分辨率格式研究.pdf

1、南京航空航天大學(xué)碩士學(xué)位論文歐拉方程基于徑向基函數(shù)的高分辨率格式研究姓名：時桂芝申請學(xué)位級別：碩士專業(yè)：計算數(shù)學(xué)指導(dǎo)教師：王春武20070301歐拉方程基于徑向基函數(shù)的高分辨率格式研究iiAbstractTheresearchonnumericalmethodfhyperbolicconservationlawsisoneoftheimptantdirectionsincomputationalmathematics.manyfinit

2、edifferenceschemeshavebeenwidelyusedtosolvehyperbolicconservationlaws.Intraditionalfinitedifferenceschemespolynomialinterpolationdivideddifferenceshavebeentakentoapproximatethederivatives.Howeverwiththeincreasingoftheder

3、ofinterpolationpolynomialsseriousoscillationwilloccurthenumericalerrsinstabilitiescanbeincurred.Inthispaperweuseradialbasisfunctiontoconstructdifferencescheme.Firstlytheradialbasisfunction(RBF)isusedtoapproximatethederiv

4、ativesdiscretizeEulerequationsweobtaintheschemeone.Secondlybyingthestencilselfadaptivelywithessentiallynonoscillaty(ENO)ideasRBFisappliedtocomputethevaluesofvariablesfurtherthenumericalfluxesatthecellboundarywecanobtaina

5、highresolutionschemewhichiscalledschemetwo.AstheRBFinterpolationismestabletheobtainedschemewillbemestable.RBFinterpolationonlydependonthedistanceofthemeshnodesitcanbeusedtodealwithscatteredmeshnodes.Theaboveobtainedschem

6、esareemployedtosimulatethescalarequationonedimensionalEulerequationsitisfoundthatschemetwowksbetterthanschemeone.SchemetwoisextendedftwodimensionalEulerequationnumericalresultscomparewellwiththetheeticalsolutionshowitsca