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

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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.

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Authors and Affiliations

  1. Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118 route de Narbonne, 31062, Toulouse cedex, France

    P. Degond

  2. Institut de Mathématiques de Toulouse, Université de Toulouse; UPS, INSA, UT1, UTM and CNRS, 31062, Toulouse, France

    P. Degond, D. Savelief & M.-H. Vignal

  3. Department of Mathematics, Iowa State University, Ames, IA, 50011, USA

    H. Liu

Authors
  1. P. Degond
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  2. H. Liu
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  3. D. Savelief
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  4. M.-H. Vignal
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Correspondence to P. Degond.

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Degond, P., Liu, H., Savelief, D. et al. Numerical Approximation of the Euler-Poisson-Boltzmann Model in the Quasineutral Limit. J Sci Comput 51, 59–86 (2012). https://doi.org/10.1007/s10915-011-9495-1

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  • DOI: https://doi.org/10.1007/s10915-011-9495-1

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