Abstract
The present work is devoted to the simulation of a strongly magnetized plasma considered as a mixture of an ion fluid and an electron fluid. For the sake of simplicity, we assume that the model is isothermal and described by Euler equations coupled with a term representing the Lorentz force. Moreover we assume that both Euler systems are coupled through a quasi-neutrality constraint. The numerical method which is described in the present document is based on an Asymptotic-Preserving semi-discretization in time of a variant of this two-fluid Euler-Lorentz model with a small perturbation of the quasi-neutrality constraint. Firstly, we present the two-fluid model and the motivations for introducing a small perturbation into the quasi-neutrality equation, then we describe the time semi-discretization of the perturbed model and a fully-discrete finite volume scheme based on it. Finally, we present some numerical results which have been obtained with this method.
Highlights
The present work is devoted to the simulation of a strongly magnetized plasma considered as a mixture of an ion fluid and an electron fluid
We focus in this paper on a situation involving a strong Lorentz force and a low Mach number regime for both ion and electron fluids, i.e. we assume that pressure and Lorentz forces are of the same order as τ −1 where τ > 0 is the square of the ion Mach number and represents the ratio between the ion gyro-period and the characteristic time scale of the experiment
We studied the isothermal two-fluid Euler-Lorentz system coupled with a quasi-neutrality constraint in a low Mach number regime and a strong magnetic field
Summary
(2.14a) (2.14b) (2.14c) in which the parallel part of q0i and q0e are implicit. if we separate the parallel and perpendicular parts of (2.14b) for any α, we get. The semi-discretization we describe in the the lines is based on semi-implicit mass fluxes and fully implicit pressure and Lorentz forces This strategy is motivated by the fact that we want to preserve the balance between the pressure gradient and the Lorentz term, i.e. to insure that, at every time step tm, Tα ∇xnτ,m + qα nτ,m ∇xφτ,m − qτα,m × Bm = O(ǫα τ ) , ∀ α ∈ {i, e} ,. Where the notation θm stands for an approximation of the function θ = θ(x, t) at the time step t = tm This methodology differs from the AP semi-discretizations which were described in [5] and [16]: in these papers, the authors considered a fully explicit mass flux, a fully implicit Lorentz term and a semi-implicit pressure gradient, and this leads to a non-conservative discretization of the velocity equation.
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