科研之友
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摘要
We present a numerical scheme for the approximation of the system of partial differential equations of the Peaceman model for the miscible displacement of one fluid by another in a two dimensional porous medium. In this scheme, the velocity-pressure equations are treated by a mixed finite element discretization using the Raviart-Thomas element, and the concentration equation is approximated by a finite volume discretization using the Upstream scheme, knowing that the Raviart-Thomas element gives good approximations for fluids velocities and that the Upstream scheme is well suited for convection dominated equations. We prove a maximum principle for our approximate concentration more precisely 0 <= c(h)(x, t) <= 1 a.e. in Omega(T) as long as some grid conditions are satisfied - at the difference of Chainais and Droniou [6] who have only observed that their approximate concentration remains in [0; 1] (and such is the case for other proposed numerical methods; e. g., [22, 21]). Moreover our grid conditions are satisfied even with very large time steps and spatial steps. Finally we prove the consistency of the proposed scheme and thus are assured of convergence. A numerical test is reported.
- 出版日期2012-11-24
