强磁场中Euler方程的一个渐近保持格式
An Asymptotic Preserving Scheme for the Euler equations in a strong magnetic field
摘要：
本文讨论带电粒子受洛伦兹力作用时的等温欧拉方程的数值逼近。当磁场较大时，得到了所谓的漂移流体近似。在这个极限中，相对于磁场方向的平行运动从垂直运动中分离出来，并且通过沿磁场线的零总力的约束隐含地给出。在本文中，我们提供了一个适定的椭圆方程的平行速度，这反过来又使我们能够构建一个渐近保持（AP）计划的欧拉-洛伦兹系统。这个方案产生了一个一致的近似欧拉-洛伦兹模型时，是有限的和一致的近似漂移极限时，是趋于0。最重要的是，它不需要对与较小的Δ k值相关的空间和时间步长进行任何约束。数值结果证实了该格式的AP性质及其渐近稳定性。
英文摘要：
This paper is concerned with the numerical approximation of the isothermal Euler equations for charged particles subject to the Lorentz force. When the magnetic field is large, the so-called drift-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 epsilon is finite and a consistent approximation of the drift limit when epsilon tends to 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.
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