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

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 ass...

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Bibliographic Details
Published in:Journal of scientific computing 2012-04, Vol.51 (1), p.59-86
Main Authors: Degond, P., Liu, H., Savelief, D., Vignal, M.-H.
Format: Article
Language:English
Subjects:
Algorithms
Analysis of PDEs
Compressibility
Computational Mathematics and Numerical Analysis
Electron density
Gas dynamics
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical models
Mathematics
Mathematics and Statistics
Plasma physics
Poisson equation
Theoretical
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Summary: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.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-011-9495-1