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

Authors:
P. Degond;H. Liu;D. Savelief;M. -H. Vignal
Affiliations:
Institut de Mathé/matiques de Toulouse, Université/ Paul Sabatier, Toulouse cedex, France 31062 and Institut de Mathé/matiques de Toulouse, Université/ de Toulouse/ UPS, INSA, UT1, ...;Department of Mathematics, Iowa State University, Ames, USA 50011;Institut de Mathé/matiques de Toulouse, Université/ de Toulouse/ UPS, INSA, UT1, UTM and CNRS, Toulouse, France 31062;Institut de Mathé/matiques de Toulouse, Université/ de Toulouse/ UPS, INSA, UT1, UTM and CNRS, Toulouse, France 31062
Venue:
Journal of Scientific Computing
Year:
2012

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Abstract

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.