Journal
SIAM JOURNAL ON APPLIED MATHEMATICS
Volume 70, Issue 6, Pages 1761-1787Publisher
SIAM PUBLICATIONS
DOI: 10.1137/070703272
Keywords
boundary layer; quasi-neutral limit; Euler-Poisson system; asymptotic preserving scheme; plasma
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We consider the two-fluid Euler-Poisson system modeling the expansion of a quasi-neutral plasma in the gap between two electrodes. The plasma is injected from the cathode using boundary conditions which are not at the quasi-neutral equilibrium. This generates a boundary layer at the cathode. We numerically show that classical schemes as well as the asymptotic preserving scheme developed in [P. Crispel, P. Degond, and M.-H. Vignal, J. Comput. Phys., 223 (2007), pp. 208-234] are unstable for general Roe type solvers when the mesh does not resolve the small scale of the Debye length. We formally derive a model describing the boundary layer. Analyzing this problem, we determine well-adapted boundary conditions. These well-adapted boundary conditions stabilize general solvers without resolving the Debye length.
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