A strongly conservative finite element method for the coupling of darcy and stokes flow JCP 2010

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1、JournalofComputationalPhysics229(2010)5933–5943ContentslistsavailableatScienceDirectJournalofComputationalPhysicsjournalhomepage:www.elsevier.com/locate/jcpAstronglyconservativefiniteelementmethodforthecouplingofStokesandDarcyflowa,*,1b,2G.Kanschat,B.RivièreaDepartmentofMathematics,TexasA&MUnivers

2、ity,3368TAMU,CollegeStation,TX77843-3368,UnitedStatesbDepartmentofComputationalandAppliedMathematics,RiceUniversity,6100MainStreet,MS-134,Houston,TX77005-1892,UnitedStatesarticleinfoabstractArticlehistory:WeconsideramodelofcoupledfreeandporousmediaflowgovernedbyStokesandDarcyReceived12August2009e

3、quationswiththeBeavers–Joseph–Saffmaninterfacecondition.ThismodelisdiscretizedReceivedinrevisedform6April2010usingdivergence-conformingfiniteelementsforthevelocitiesinthewholedomain.Dis-Accepted13April2010continuousGalerkintechniquesandmixedmethodsareusedintheStokesandDarcysub-Availableonline27Ap

4、ril2010divdomains,respectively.ThisdiscretizationisstronglyconservativeinH(X)andweshowconvergence.NumericalresultsvalidateourfindingsandindicateoptimalconvergenceKeywords:orders.StokesflowÓ2010ElsevierInc.Allrightsreserved.DarcyflowBeavers–Joseph–SaffmanconditionFiniteelementmethodMixedfiniteelement

5、sDiscontinuousGalerkinMultiphysics1.IntroductionThecouplingofStokesandDarcyequationsarisesfromthemodelingofgroundwatercontaminationthroughstreamsandfiltrationproblems[25,19].Inthiswork,anewnumericalmethodisproposed,thatemploysdivergence-conformingvelocitydivspaces,i.e.spacesincludedinH(X).TheDarc

6、yflowisdiscretizedbyamixedfiniteelementmethodandtheStokesflowbyamixed(velocity–pressure)discontinuousGalerkin(DG)method.Thetwotypesofflowarecoupledbyappropriateinterfaceconditions,namelymassconservation,balanceofforcesacrosstheinterfaceandtheBeavers–Joseph–Saffmanlaw[6,30,20–22].divOneadvantageofour

7、approachisthatmassconservationinthesenseofH(X)isachieved.Inparticular,ifthereareno2sourcesorsinks,thedivergenceofthevelocityisanL(X)functionanditiszerointhatspace(see[12]).Thisimpliesthatthedivergenceofthevelocityispointwise