Volume 7 N°1 (2010)

Abstract: The purpose of this paper is to describe a new algorithm for the pure eulerian interface capturing method FVCF-NIP. In this method, the interface is sharp and piecewise linear. In a cell containing two materials, termed as mixed cell, each one is pure at both sides of the interface and no di-ffusion is allowed through it. A conservative scheme is written on each material volume using the condensate formalism which allows in particular sliding of materials on each others. However, material volumes in mixed cells can be tiny and therefore the condition on the time step can be too much restrictive. The conservative scheme is then written with a time step only calculated considering pure cells. In mixed cells, a control procedure is built to ensure a stable evolution in small materials volumes. This new algorithm enhances the robustness of the method and allows to simulate a wider range of flow regimes.

Paper presented by: J. Halama

This paper deals with the computation of two-phase flows in a porous medium, with two main objectives. First of all, we will present a new multi-dimensional well-balanced scheme, with its advantages and drawbacks. Furthermore, we will compare results of the porous model with approximations obtained with a full two-dimensional computation, where all obstacles have been taken into account in the computational domain. The two-phase flow model is hyperbolic, and the scheme takes its roots on a modified Rusanov scheme that integrates effects due to discontinuous porous profiles. The scheme perfectly maintains steady state profiles on any structured mesh.

Key words : Finite Volumes, Two-Fluid Model, Porous Medium

A new numerical method called Vofire is described here. It can be used for integrating transport equations approximated on general meshes in any dimension. The algorithm relies on a piecewise constant reconstruction of an unknown in each cell, where the reconstructed function varies only in the directions orthogonal to the velocity. This allows to design a non-dissipative and maximum preserving scheme for the transport of characteristic functions. It is then incorporated in a Lagrangian scheme with remeshing for the computation of multi-component compressible flows.

In this work, we propose a unified analysis framework encompassing a wide range of nonconforming discretizations of anisotropic heterogeneous diffusion operators on general meshes. The analysis relies on two discrete function analytic tools for piecewise polynomial spaces, namely a discrete Sobolev-Poincaré inequality and a discrete Rellich theorem. The convergence requirements are grouped into seven hypotheses, each of them characterizing one salient ingredient of the analysis. Finite volume schemes as well as the most common discontinuous Galerkin methods are shown to fit in the analysis. A new finite volume cell-centered method is also introduced.