1、南開(kāi)大學(xué)博士學(xué)位論文非線性對(duì)流擴(kuò)散問(wèn)題的迎風(fēng)型有限元法及其在油藏?cái)?shù)值模擬中的應(yīng)用姓名：哈什姆A.卡什庫(kù)申請(qǐng)學(xué)位級(jí)別：博士專業(yè)：計(jì)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