非線性對流擴散問題的迎風(fēng)型有限元法及其在油藏數(shù)值模擬中的應(yīng)用.pdf

1、南開大學(xué)博士學(xué)位論文非線性對流擴散問題的迎風(fēng)型有限元法及其在油藏數(shù)值模擬中的應(yīng)用姓名：哈什姆A.卡什庫申請學(xué)位級別：博士專業(yè)：計算數(shù)學(xué)指導(dǎo)教師：胡健偉2002.4.1AbstractTheinvestigationoftheconvection—diffusionproblemshasbeentheobjectofanin，creasinginterestofanumberofspecialityaswellasmathematicia

2、nsSpecialattentionispaidparticularlytoproblemwithconvectiondominatingoverdiffusionInthisdissertationwefirstconsideredupwindfiniteelementschemefornonlinearconvectiontermwhicharediscretizedusinganapproximationofpartialupwi

3、ndtypefortheresultingboundaryintegralonthecircumcentricfinitevolumemeshdualtoatriangulargridofweaklyacutetype，whereasthediffusiontermisapproximatedbystandardGalerkinfiniteelementmethodandweprovealemmatothemaximumprincipl

4、ewithconditionsmoreweakthanIkeda，Slemma(seef20J)andthenprovethemaximumprincipleandconvergenceoftheschemeInthesecondpartweappliedupwindfiniteelementschemeforreservoirsimulationThemiscibledisplace—mentofoneincompressiblean

5、dcompressiblefluidbyanotherinaporousmediumisgovernedbyasystemoftwoequations，oneforthepressureandtheotherfortheconcentrationofonefluidsThepressureandtheDarcyvelocityareapproximatedsimultaneouslybymixedfiniteelementmethodi

6、nordertobetterapproximatethetotalDarcyvelocitywhichcouplestheconcentrationequationwithpressureequation，andtheconcentrationequationisapproximatedbyacombinationofaGalerkinfiniteelementmethodandupwindfiniteelementmethodUnde

7、rtheassumptionthattheexactsolutionpossessessomeregularitypropertiesandthetriangulationsareotaweaklyacutetype，thediscretemassconservationlawandconvergenceoftheap—proximatedsolutionareprovedTheimmiscibledisplacementofonein