1. Introduction

Here we present the finite volume diagrams SUSHI developed for the modeling of miscible two-phase (unsaturated) flows in porous media, miscible meaning here that the components can exist in several phases. These diagrams relate to the THM family of models. They are only intended for pure hydraulics (neither mechanical, nor thermal), i.e. if we use the classical nomenclature described in [R7.01.11] KIT_HH.

The finite volume schemes SUSHI (Scheme Using Stabilization and Hybrid Interfaces) were developed by Ophélie Angelini as part of her thesis [1] to deal in particular with the problems of steep fronts on any meshes. This schema is inspired by the Hybid Finite Volume (HVF) schema () introduced by R. Eymard et al. [4]. At the origin of this work, there was an abundance of literature indicating that these diagrams ensuring by definition a good representation of the flow were more adapted to this type of hyperbolic equations applied to highly heterogeneous domains. Implementing and disposing of such schemes therefore quickly seemed reasonable just to compare ourselves with members of the porous media flow community [2]. These schemes do not claim to replace finite elements but offer a robust alternative.

Here we will only briefly present the physical model of two-phase flows detailed in the documentation [R7.01.11].

This documentation therefore essentially presents the Finite Volumes spatial discretization schemes implemented on these models in Code_Aster. For more details, refer to Ophélie Angélini’s thesis [1]