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Analysis of an asymptotic preserving scheme for the Euler-Poisson system in the quasineutral limit

Publication ,  Journal Article
Degond, P; Liu, JG; Vignal, MH
Published in: SIAM Journal on Numerical Analysis
November 10, 2008

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.

Duke Scholars

Published In

SIAM Journal on Numerical Analysis

DOI

ISSN

0036-1429

Publication Date

November 10, 2008

Volume

46

Issue

3

Start / End Page

1298 / 1322

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
 

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Degond, P., Liu, J. G., & Vignal, M. H. (2008). Analysis of an asymptotic preserving scheme for the Euler-Poisson system in the quasineutral limit. SIAM Journal on Numerical Analysis, 46(3), 1298–1322. https://doi.org/10.1137/070690584
Degond, P., J. G. Liu, and M. H. Vignal. “Analysis of an asymptotic preserving scheme for the Euler-Poisson system in the quasineutral limit.” SIAM Journal on Numerical Analysis 46, no. 3 (November 10, 2008): 1298–1322. https://doi.org/10.1137/070690584.
Degond P, Liu JG, Vignal MH. Analysis of an asymptotic preserving scheme for the Euler-Poisson system in the quasineutral limit. SIAM Journal on Numerical Analysis. 2008 Nov 10;46(3):1298–322.
Degond, P., et al. “Analysis of an asymptotic preserving scheme for the Euler-Poisson system in the quasineutral limit.” SIAM Journal on Numerical Analysis, vol. 46, no. 3, Nov. 2008, pp. 1298–322. Scopus, doi:10.1137/070690584.
Degond P, Liu JG, Vignal MH. Analysis of an asymptotic preserving scheme for the Euler-Poisson system in the quasineutral limit. SIAM Journal on Numerical Analysis. 2008 Nov 10;46(3):1298–1322.

Published In

SIAM Journal on Numerical Analysis

DOI

ISSN

0036-1429

Publication Date

November 10, 2008

Volume

46

Issue

3

Start / End Page

1298 / 1322

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