Analysis of an asymptotic preserving scheme for the Euler-Poisson system in the quasineutral limit. (English) Zbl 1173.82032
The stability property of a recently proposed numerical scheme for the Euler-Poisson system P. Crispel, P. Degond and M.-H. Vignal [J. Comput. Phys. 223, No. 1, 208–234 (2007; Zbl 1163.76062)] is analyzed. The linearized Euler-Poisson system is considered about both zero and nonzero velocities and after a Fourier transform in space, the time discretization is applied under scrutiny. The influence of a space-decentered discretization is mimicked by adding viscosity terms in both the mass and momentum conservation equations. It is shown that the resulting scheme is uniformly stable with respect to the Debye parameter. By contrast, other schemes lose the uniform stability property. Elements of a nonlinear stability analysis have been given by considering a model Burgers-Poisson problem.
Reviewer: Iván Abonyi (Budapest)
MSC:
82D10 | Statistical mechanics of plasmas |
76W05 | Magnetohydrodynamics and electrohydrodynamics |
76X05 | Ionized gas flow in electromagnetic fields; plasmic flow |
76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
76N20 | Boundary-layer theory for compressible fluids and gas dynamics |
76L05 | Shock waves and blast waves in fluid mechanics |
35Q05 | Euler-Poisson-Darboux equations |