An Asymptotic Preserving scheme for the Euler equations in a strong magnetic field

JOURNAL OF COMPUTATIONAL PHYSICS

卷:228

Article

Degond, P.^2,3  Deluzet, F.^2,3  Sangam, A.^1,2,3  Vignal, M. -H.^2,3 

[1] Univ Nice, Lab Jean Alexandre Dieudonne, CNRS, Lab Jean Alexandre Dieudonne,UMR 6621, F-06108 Nice, France

[2] Univ Toulouse, INSA, UPS,Inst Math Toulouse, UT1,UTM, F-31062 Toulouse, France

[3] CNRS, Inst Math Toulouse, UMR 5219, F-31062 Toulouse, France

关键词: Plasmas;    Euler equations;    Lorentz force;    Large magnetic field;    Drift-fluid limit;    Asymptotic-Preserving scheme;   

DOI  :  10.1016/j.jcp.2008.12.040

来源: Elsevier

【 摘 要 】

This paper is concerned with the numerical approximation of the isothermal Euler equations for charged particles subject to the Lorentz force (the 'Euler-Lorentz' system). When the magnetic field is large, or equivalently, when the parameter F representing the non-dimensional ion cyclotron frequency tends to zero, the so-called drift-fluid (or gyro-fluid) approximation is obtained. In this limit, the parallel motion relative to the magnetic field direction splits from perpendicular motion and is given implicitly by the constraint of zero total force along the magnetic field lines. In this paper, we provide a well-posed elliptic equation for the parallel velocity which in turn allows us to construct an Asymptotic-Preserving (AP) scheme for the Euler-Lorentz system. This scheme gives rise to both a consistent approximation of the Euler-Lorentz model when E is finite and a consistent approximation of the drift limit when epsilon -> 0. Above all, it does not require any constraint on the space and time-steps related to the small value of epsilon. Numerical results are presented, which confirm the AP character of the scheme and its Asymptotic Stability. (C) 2009 Elsevier Inc. All rights reserved.

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