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Numerical approximation of the Euler-Maxwell model in the quasineutral limit. (English) Zbl 1244.82009
An asymptotic-preserving (AP) scheme is proposed and analysed for the Euler-Maxwell (EM) system of a one-fluid plasma model. First the ions are supposed to be immobile and to form a fixed neutralizing background. Then the model is extended to a two-fluid one, where both ions and electrons are mobile. The analysis involves a proof of AP character and its linear stability is independent of the scaled Debye parameter (D) when D tends to zero. The numerical simulations involve comparison between AP scheme to a classical scheme in one-, and two-fluid configuration for the Riemann problem (of the formation of a shock) and the plasma opening switch device. The numerical convergence study shows that both the classical and AP schemes are convergent to EM solution with resolved time and space description.
In the case of under-resolved time and space discretization the AP scheme is consistent with the quasi-neutral EM system. The proposed spatial discretization allows for a perfect consistency with Gauss equation.

MSC:
82B10 Quantum equilibrium statistical mechanics (general)
76W05 Magnetohydrodynamics and electrohydrodynamics
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