Stéphane Cordier

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In this paper, we present a numerical scheme for a non linear Fokker-Planck equation of one-dimensional granular medium. We consider a kinetic description of a system of particles undergoing nearly elastic particles and interacting with a thermal bath. We construct a numerical method which preserve all the properties of the continuous model, conservation(More)
Homogeneous Fokker-Planck-Landau equation is investigated for cou-lombian potential and isotropic distribution function i.e. when the distribution function depends only on time and on the modulus of the velocity. We derive a new conservative and entropy decaying semi-discretized Lan-dau equation for which we prove the existence of global in time positive(More)
This paper deals with the diffusion limit of a kinetic equation where the collisions are modeled by a Lorentz type operator. The main aim is to construct a discrete scheme to approximate this equation which gives for any value of the Knudsen number, and in particular at the diffusive limit, the right discrete diffusion equation with the same value of the(More)
Conservatives and entropy schemes for the Fokker-Planck-Landau are investigated. We prove the existence of an unique, positive, entropic and global in time solution for the homogeneous linear and non linear dis-cretized (either in the velocity space or both in the velocity and in time) Fokker Planck equation. The stability analysis of these schemes permits(More)
In this paper, we shall propose a numerical scheme consisting of two steps: the first based relaxation method and the second on the so called well balanced scheme. The derivation of the scheme relies on the resolution of the stationnary Riemann problem with source terms. The obtained scheme is compatible with the diffusive regime of hydrodynamics radiative(More)