Publications [#139009] of Jian-Guo Liu

Papers Accepted

1. P. Degond, J.-G. Liu and M.H. Vignal, Analysis of an asymptotic preserving scheme for the Euler-Poisson system in the quasineutral limit, SIAM J. Num. Anal. (2007)
   (last updated on 2007/12/07)

   Abstract:
   In a previous work, a new numerical discretization of the Euler-Poisson system has been proposed. This scheme is 'Asymptotic Preserving' in the quasineutral limit (i.e. when the Debye length epsilon tends to zero), which means that it becomes consistent with the limit model when epsilon tends to zero$. In the present work, we show that the stability domain of the present scheme is independent of epsilon. 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 with a space-centered one. The linearization is first performed about a zero mean velocity, and then about a non-zero 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 given.

   Keywords:
   stiffness • Debye length • electron plasma period • Burgers-Poisson • sheath problem • Klein-Gordon