Speaker
Description
In this talk, we introduce an enhanced discretization method for incompressible two-phase Darcy flows in heterogeneous porous media with discontinuous capillary pressures. The model is expressed in the total-velocity formulation, leading to a coupled system consisting of a degenerate parabolic equation for the non-wetting phase saturation and a pressure equation governing the total velocity.
Our approach combines a positive Vertex Approximate Gradient (VAG) scheme for flux discretization with a hybrid upwinding strategy for the phase mobilities. This ensures a discrete maximum principle, guaranteeing that the saturation remains within its physical range. Furthermore, suitable energy estimates are derived from key flux approximations, which enable us to prove the existence of discrete solutions and establish the stability of the scheme.
Comprehensive numerical experiments on challenging heterogeneous test cases demonstrate the robustness of the method in terms of accuracy and nonlinear convergence. Comparisons with the classical phase-potential upwinding technique and with an earlier hybrid upwinding strategy highlight significant improvements in stability and performance. These results indicate that the proposed scheme provides a reliable and efficient tool for simulating multiphase flow in complex porous media.
| Country | France |
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