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Mesh adaptation for two-phase flow

S. El Hassouni, Z. Mghazli

Abstract


The aim of this work is to develop and analyze an a posteriori residual estimation of the Darcy’s equation. We consider the case of variable permeability and non homogeneous Dirichlet condition. The velocity and pressure equations are solved by a mixed finite element method which can be interpreted as a finite volume scheme. Then we present an adaptive numerical technique based on these estimators for two-phase flow. To validate these estimators, the problem is solved with PauMarr (Afif and Amaziane, 2008) to obtain a saturation and then by FreeFEM++ (Hecht, Le Hyaric, Oht-suka and Pironneau, 2007) to obtain the Darcy velocity and the pressure.

Keywords


mixed finite element method, a posteriori error estimate, mesh adaptation, two-phase flow.

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