A Finite Volume Scheme for Darcy-Brinkman’s Model of Two-Phase Flows in Porous Media
In this paper, we are interested in the displacement of two incompressible phases in a Darcy-Brinkman flow in a porous media. The equations are obtained by the conservation of the mass and by considering the Brinkman regularization velocity of each phase. This model is treated in its general form with the whole nonlinear terms. This paper deals with construction and convergence analysis of a finite volume scheme together with a phase-by-phase upstream according to the total velocity. Finally, numerical tests illustrate the behavior of the solutions of this proposed scheme.
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