Numerical approximation of the Euler-Poisson-Boltzmann model in the quasineutral limit

Pierre Degond (1) , Hailiang Liu (2) , Dominique Savelief (1) , Marie-Hélène Vignal (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 Department of Mathematics, Iowa State University

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.

Domaines: Equations aux dérivées partielles [math.AP]

Pierre Degond, Hailiang Liu, Dominique Savelief, Marie-Hélène Vignal. Numerical approximation of the Euler-Poisson-Boltzmann model in the quasineutral limit. Journal of Scientific Computing, 2012, 51 (1), pp.59-86. ⟨10.1007/s10915-011-9495-1⟩. ⟨hal-00529593⟩