Marie-Hélène Vignal

Analysis of an Asymptotic Preserving Scheme for the Euler-Poisson System in the Quasineutral Limit

In a previous work [P. Crispel, P. Degond, and M.-H. Vignal, J. Comput. Phys., 223 (2007), pp. 208-234], a new numerical discretization of the Euler-Poisson system was proposed. This scheme is “asymptotic preserving” in the quasineutral limit (i.e., when the Debye length

Numerical and theoretical study of a Dual Mesh Method using finite volume schemes for two phase flow problems in porous media

\varepsilon

A PLASMA EXPANSION MODEL BASED ON THE FULL EULER–POISSON SYSTEM

tends to zero), which means that it becomes consistent with the limit model when

Numerical Approximation of the Euler-Poisson-Boltzmann Model in the Quasineutral Limit

\varepsilon \to 0

Plasma Expansion in Vacuum: Modeling the Breakdown of Quasi Neutrality

. In the present work, we show that the stability domain of the present scheme is independent of

A one-dimensional model of plasma expansion

\varepsilon

A boundary layer problem for an asymptotic preserving scheme in the quasi-neutral limit for the Euler-Poisson system

. This stability analysis is performed on the Fourier transformed (with respect to the space variable) linearized system. We show that the stability property is more robust when a space-decentered scheme is used (which brings in some numerical dissipation) rather than a space-centered scheme. The linearization is first performed about a zero mean velocity and then about a nonzero mean velocity. At the various stages of the analysis, our scheme is compared with more classical schemes and its improved stability property is outlined. The analysis of a fully discrete (in space and time) version of the scheme is also given. Finally, some considerations about a model nonlinear problem, the Burgers-Poisson problem, are also discussed.

Study of a New Asymptotic Preserving Scheme for the Euler System in the Low Mach Number Limit

Summary. In this paper we are interested in two phase flow problems in porous media. We use a Dual Mesh Method to discretize this problem with finite volume schemes. In a simplified case (elliptic - hyperbolic system) we prove the convergence of approximate solutions to the exact solutions. We use the Dual Mesh Method in physically complex problems (heterogeneous cases with non constant total mobility). We validate numerically the Dual Mesh Method on practical examples by computing error estimates for different test-cases.

Study of a Finite Volume Scheme for the Drift-Diffusion System. Asymptotic Behavior in the Quasi-Neutral Limit

In this paper, we consider a quasi-neutral plasma expanding in the vacuum gap separating two electrodes. During the expansion, some particles are emitted from the plasma-vacuum interface and form a beam in the vacuum. Starting from the two-fluid full Euler–Poisson model, we derive an asymptotic model. This asymptotic model consists of a quasi-neutral model in the plasma region, a Child–Langmuir law in the beam region and connection relations at the plasma-beam interface. For this model, we propose a numerical scheme which accounts for the motion of the plasma-beam interface and is much more efficient than the resolution of the original two-fluid Euler–Poisson problem. We demonstrate the efficiency of the model by means of numerical simulations for two different one-dimensional test cases.

Diffusion Limits of Kinetic Models

This paper analyzes various schemes for the Euler-Poisson-Boltzmann (EPB) model of plasma physics. This model consists of the pressureless gas dynamics equations coupled with the Poisson equation and where the Boltzmann relation relates the potential to the electron density. If the quasi-neutral assumption is made, the Poisson equation is replaced by the constraint of zero local charge and the model reduces to the Isothermal Compressible Euler (ICE) model. We compare a numerical strategy based on the EPB model to a strategy using a reformulation (called REPB formulation). The REPB scheme captures the quasi-neutral limit more accurately.