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 ε tends to zero), which means that it becomes consistent with the limit model when ε → 0. In the present work, we show that the stability domain of the present scheme is independent of ε. 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. © 2008 Society for Industrial and Applied Mathematics.
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- Numerical & Computational Mathematics
- 4903 Numerical and computational mathematics
- 4901 Applied mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics
Citation
Published In
DOI
ISSN
Publication Date
Volume
Issue
Start / End Page
Related Subject Headings
- Numerical & Computational Mathematics
- 4903 Numerical and computational mathematics
- 4901 Applied mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics