Numerical approximation for a degenerate parabolic-elliptic system modeling flows in porous media

Electronic Journal of Differential Equations

卷:2012

关键词: Mixed finite element methods;    finite volume methods;    porous media;   

DOI  :  

来源: DOAJ

【 摘 要 】

We present a numerical scheme for the approximation of the systemof partial differential equations of the Peaceman model for themiscible displacement of one fluid by another in a two dimensionalporous medium. In this scheme, the velocity-pressure equations aretreated by a mixed finite element discretization using theRaviart-Thomas element, and the concentration equation isapproximated by a finite volume discretization using the Upstream scheme,knowing that the Raviart-Thomas element gives good approximationsfor fluids velocities and that the Upstream scheme is well suitedfor convection dominated equations. We prove a maximum principlefor our approximate concentration more precisely$ 0leq c_h(x,t)leq 1$ a.e. in $Omega_T $ as long as somegrid conditions are satisfied - at the difference ofChainais and Droniou [6]who have only observed that theirapproximate concentration remains in $[0;1]$ (and such is the casefor other proposed numerical methods; e.g., [21,22].Moreover our grid conditions are satisfied even with very largetime steps and spatial steps. Finally we prove the consistencyof the proposed scheme and thus are assured of convergence.A numerical test is reported.

【 授权许可】

Unknown