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We propose an original scheme for the time discretization of a triphasic CahnHilliard/Navier-Stokes model. This scheme allows an uncoupled resolution of the discrete CahnHilliard and Navier-Stokes system, is unconditionally stable and preserves, at the discrete level, the main properties of the continuous model. The existence of discrete solutions is proved… (More)

In this article, we investigate numerical schemes for solving a three component CahnHilliard model. The space discretization is performed by using a Galerkin formulation and the finite element method. Concerning the time discretization, the main difficulty is to write a scheme ensuring, at the discrete level, the decrease of the free energy and thus the… (More)

The aim of this paper is to describe some numerical aspects linked to incompressible three-phase flow simulations, thanks to Cahn-Hilliard type model. The numerical capture of transfer phenomenon in the neighborhood of the interface require a mesh thickness which become crippling in the case where it is applied to the whole computational domain. This… (More)

- Florent Berthelin, Thierry Goudon, Sébastian Minjeaud
- Math. Comput.
- 2015

We introduce a new scheme of finite volume type for barotropic Euler equations. The numerical unknowns, namely densities and velocities, are defined on staggered grids. The numerical fluxes are defined by using the framework of kinetic schemes. We can consider general (convex) pressure laws. We justify that the density remains non negative and the total… (More)

In this paper, we investigate numerical schemes for solving a three component CahnHilliard model. The space discretization is performed by using a Galerkin formulation and the finite element method. For the time discretization, the main difficulty is to write a scheme ensuring, at the discrete level, the decrease of the energy. We study three different… (More)

This work is concerned with the consistency study of a 1D (staggered kinetic) finite volume scheme for barotropic Euler models. We prove a Lax-Wendroff-like statement: the limit of a converging (and uniformly bounded) sequence of stepwise constant functions defined from the scheme is a weak entropic-solution of the system of conservation laws.

- Florent Berthelin, Thierry Goudon, Sébastian Minjeaud
- J. Sci. Comput.
- 2016

We propose a numerical scheme for the simulation of fluid-particles flows with two incompressible phases. The numerical strategy is based on a finite volume discretization on staggered grids, with a flavor of kinetic schemes in the definition of the numerical fluxes. We particularly pay attention to the difficulties related to the volume conservation… (More)

- Sébastian Minjeaud, Richard Pasquetti
- J. Comput. Physics
- 2015

In the recent paper [2], a penalty method is proposed to address the so-called Bohm boundary conditions which are generally imposed to model the limiters, i.e. the walls that intercept in a tokamak the magnetic field lines. This approach is validated by considering a simple one-dimensional hyperbolic system, that constitutes a minimal transport model for… (More)

- Sébastian Minjeaud
- J. Comput. Physics
- 2013

In this article, we propose to study two issues associated with the use of the incremental projection method for solving the incompressible Navier-Stokes equation. The first one is the combination of this time splitting algorithm with an adaptive local refinement method. The second one is the reduction of spurious velocities due to the right-hand side of… (More)