Energy stable discretization for two-phase porous media flows

Clément Cancès (1) , Flore Nabet (2)

1 RAPSODI - Reliable numerical approximations of dissipative systems
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

We propose a P1 finite-element scheme with mass-lumping for a model of two incompressible and immiscible phases in a porous media flow. We prove the dissipation of the free energy and the existence of a solution to the nonlinear scheme. We also present numerical simulations to illustrate the behavior of the scheme.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Clément Cancès, Flore Nabet. Energy stable discretization for two-phase porous media flows. Finite Volumes for Complex Applications IX, Jun 2020, Bergen, Norway. ⟨hal-02442233v2⟩