Convergence of a Vertex centred Discretization of Two-Phase Darcy flows on General Meshes

Konstantin Brenner (1, 2) , Roland Masson (1, 2)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 COFFEE - COmplex Flows For Energy and Environment

This article analyses the convergence of the Vertex Approximate Gradient (VAG) scheme recently introduced for the discretization of multiphase Darcy flows on general polyhedral meshes. The convergence of the scheme to a weak solution is shown in the particular case of an incompressible immiscible two phase Darcy flow model with capillary diffusion using a global pressure formulation. A remarkable property in practice is that the convergence is proven whatever the distribution of the volumes at the cell centres and at the vertices used in the control volume discretization of the saturation equation. The numerical experiments carried out for various families of 2D and 3D meshes confirm this result on a one dimensional Buckley Leverett solution.

Mots clés: porous media; two-phase flows; finite volume; convergence analysis; finite element

Domaines: Analyse numérique [math.NA]

Konstantin Brenner, Roland Masson. Convergence of a Vertex centred Discretization of Two-Phase Darcy flows on General Meshes. International Journal on Finite Volumes, 2013, 10, pp.1-37. ⟨hal-00755072v2⟩