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A new MMOCAA-MFE method for compressible miscible displacement in porous media. (English) Zbl 1302.76109

Summary: Combining the modified method of characteristics with adjusted advection (MMOCAA) with a splitting positive definite mixed finite element (MFE) scheme, we establish a new mixed finite element procedure for solving compressible miscible displacement in porous media. This procedure can preserve the mass conservation globally, the coefficient matrix of the mixed system is symmetric positive definite and the flux equation is separated from the pressure equation. We analyse the convergence and give an optimal \(L^2\)-norm error estimate. Finally we present some numerical results to confirm our theoretical analysis.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
76S05 Flows in porous media; filtration; seepage
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