Math @ Duke

Publications [#246946] of JianGuo Liu
Papers Published
 Degond, P; Liu, JG; Vignal, MH, Analysis of an asymptotic preserving scheme for the EulerPoisson system in the quasineutral limit,
SIAM Journal on Numerical Analysis, vol. 46 no. 3
(2008),
pp. 12981322, ISSN 00361429 [doi]
(last updated on 2018/07/21)
Abstract: In a previous work [P. Crispel, P. Degond, and M.H. Vignal, J. Comput. Phys., 223 (2007), pp. 208234], a new numerical discretization of the EulerPoisson 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 spacedecentered scheme is used (which brings in some numerical dissipation) rather than a spacecentered 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 BurgersPoisson problem, are also discussed. © 2008 Society for Industrial and Applied Mathematics.
Keywords: stiffness • Debye length • electron plasma period • BurgersPoisson • sheath problem • KleinGordon


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