Study of a numerical scheme for miscible two-phase flow in porous media

Robert Eymard (1) , V Schleper (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 Institut für Angewandte Analysis und Numerische Simulation, Universität Stuttgart, Germany

We study the convergence of a finite volume scheme for a model of miscible two-phase flow in porous media. In this model, one phase can dissolve into the other one. The convergence of the scheme is proved thanks to an estimate on the two pressures, which allows to prove some estimates on the discrete time derivative of some nonlinear functions of the unknowns. Monotony arguments allow to show some properties on the limits of these functions. A key point in the scheme is to use particular averaging formula for the dissolution function arising in the space term.

Mots clés: Two-phase flow in porous medium; dissolution; finite volume methods; convergence study

Domaines: Analyse numérique [math.NA]

Robert Eymard, V Schleper. Study of a numerical scheme for miscible two-phase flow in porous media. Numerical Methods for Partial Differential Equations, 2013, pp.30(3):723-748, 2014. ⟨10.1002/num.21823⟩. ⟨hal-00741425v4⟩