Numerical approximation of the Euler–Maxwell model in the quasineutral limit

We derive and analyze an Asymptotic-Preserving scheme for the Euler–Maxwell system in the quasi-neutral limit. We prove that the linear stability condition on the time-step is independent of the scaled Debye length λ when λ → 0. Numerical validation performed on Riemann initial data and for a model plasma opening switch device show that the AP-scheme is convergent to the Euler–Maxwell solution when Δ x/ λ → 0 where Δ x is the spatial discretization. But, when λ/Δ x → 0, the AP-scheme is consistent with the quasi-neutral Euler–Maxwell system. The scheme is also perfectly consistent with the Gauss equation. The possibility of using large time and space steps leads to several orders of magnitude reductions in computer time and storage.