ANALYSIS OF AN ASYMPTOTIC PRESERVING SCHEME FORTHE EULER–POISSON SYSTEM IN THE QUASINEUTRAL LIMIT

摘要

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. Thisscheme is "asymptotic preserving" in the quasineutral limit (i.e., when the Debye length e tends tozero), which means that it becomes consistent with the limit model when e 0. In the presentwork, we show that the stability domain of the present scheme is independent of E. This stabilityanalysis is performed on the Fourier transformed (with respect to the space variable) linearizedsystem. 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 linearizationis first performed about a zero mean velocity and then about a nonzero mean velocity. At the variousstages of the analysis, our scheme is compared with more classical schemes and its improved stabilityproperty is outlined. The analysis of a fully discrete (in space and time) version of the scheme is alsogiven. Finally, some considerations about a model nonlinear problem, the Burgers—Poisson problem,are also discussed.