The Stationary Boltzmann equation for a two component gas in the slab with different molecular masses

The stationary Boltzmann equation for hard and soft forces in the context of a two component gas is considered in the slab when the molecular masses of the 2 component are different. An $L^{1}$ existence theorem is proved when one component satisfies a given indata profile and the other component satisfies diffuse reflection at the boundaries. Weak $L^{1}$ compactness is extracted from the control of the entropy production term

Asymptotic-Preserving scheme for a bi-fluid Euler-Lorentz model

The present work is devoted to the simulation of a strongly magnetized plasma considered as a mixture of an ion fluid and an electron fluid. For the sake of simplicity, we assume that the model is isothermal and described by Euler equations coupled with a term representing the Lorentz force. Moreover we assume that both Euler systems are coupled through a quasi-neutrality constraint. The numerical method which is described in the present document is based on an Asymptotic-Preserving semi-discretization in time of a variant of this two-fluid Euler-Lorentz model with a small perturbation of the quasi-neutrality constraint. Firstly, we present the two-fluid model and the motivations for introducing a small perturbation into the quasi-neutrality equation, then we describe the time semi-discretization of the perturbed model and a fully-discrete finite volume scheme based on it. Finally, we present some numerical results which have been obtained with this method

Dissipative hydrodynamic models for the diffusion of impurities in a gas.

Recently linear dissipative models of the Boltzmann equation have been introduced. In this work, we consider the problem of constructiing suitable hydrodynamic approximations for such models where the mean velocity and the temperature of inelastic particles appear as independent variables

Degenerate anisotropic elliptic problems and magnetized plasma simulations.

International audienceThis paper is devoted to the numerical approximation of a degen- erate anisotropic elliptic problem. The numerical method is designed for arbitrary space-dependent anisotropy directions and does not re- quire any specially adapted coordinate system. It is also designed to be equally accurate in the strongly and the mildly anisotropic cases. The method is applied to the Euler-Lorentz system, in the drift-fluid limit. This system provides a model for magnetized plasmas

Derivation of BGK models for mixtures

International audienceThis paper is devoted to the construction of a BGK operator for gas mixtures. The construction is based as in ([12], [13]) on the introduction of relaxation coefficients and a principle of minimization of the entropy under constraints of moments. These free parameters are com pared with the free parameters introduced in the Thermodynamics of Irr eversible Processes approach of the Navier-Stokes system. At the end t he BGK model is proved to satisfy Fick and Newton law

Numerical resolution of an anisotropic non-linear diffusion problem

International audienceThis paper is devoted to the numerical resolution of an anisotropic non-linear diffusion problem involving a small parameter ε, defined as the anisotropy strength reciprocal. In this work, the anisotropy is carried by a variable vector function b. The equation being supplemented with Neumann boundary conditions, the limit ε → 0 is demonstrated to be a singular perturbation of the original diffusion equation. To address efficiently this problem, an Asymptotic-Preserving scheme is derived. This numerical method does not require the use of coordinates adapted to the anisotropy direction and exhibits an accuracy as well as a computational cost independent of the anisotropy strength

Asymptotic-preserving well-balanced scheme for the electronic M1 model in the diffusive limit: particular cases.

This work is devoted to the derivation of an asymptotic-preserving scheme for the electronic M1 model in the diffusive regime. The case without electric field and the homogeneous case are studied. The derivation of the scheme is based on an approximate Riemann solver where the intermediate states are chosen consistent with the integral form of the approximate Riemann solver. This choice can be modified to enable the derivation of a numerical scheme which also satisfies the admissible conditions and is well-suited for capturing steady states. Moreover, it enjoys asymptotic-preserving properties and handles the diffusive limit recovering the correct diffusion equation. Numerical tests cases are presented, in each case, the asymptotic-preserving scheme is compared to the classical HLL [43] scheme usually used for the electronic M1 model. It is shown that the new scheme gives comparable results with respect to the HLL scheme in the classical regime. On the contrary, in the diffusive regime, the asymptotic-preserving scheme coincides with the expected diffusion equation, while the HLL scheme suffers from a severe lack of accuracy because of its unphysical numerical viscosity