磁流体动力学程序中双极扩散的显式格式
An Explicit Scheme for Incorporating Ambipolar Diffusion in a Magnetohydrodynamics Code
摘要：
我们描述了一种方法，将双极扩散的强耦合近似到一个多维磁流体动力学代码的基础上的总变差递减计划。双极扩散项的贡献包括显式有限差分算子在一个完全不可分裂的方式，保持二阶精度。磁场的无发散条件在任何时候都是由磁通插值约束传输方案来保证的。超时间步长方法用于加速高分辨率计算和/或强双极扩散中的时间步长。我们进行了两个测试问题，稳态斜C型冲击和阿尔文波的衰减，证实了我们的数值方法的准确性和鲁棒性。从可压缩的MHD湍流与双极扩散的模拟结果表明，我们的方法的灵活性，以及它的能力，以遵循复杂的MHD流在双极扩散的存在。这些模拟结果表明，双极扩散的强度对MHD湍流的耗散率有很大的影响。
英文摘要：
We describe a method for incorporating ambipolar diffusion in the strong coupling approximation into a multidimensional magnetohydrodynamics code based on the total variation diminishing scheme. Contributions from ambipolar diffusion terms are included by explicit finite difference operators in a fully unsplit way, maintaining second order accuracy. The divergence-free condition of magnetic fields is exactly ensured at all times by a flux-interpolated constrained transport scheme. The super time stepping method is used to accelerate the timestep in high resolution calculations and/or in strong ambipolar diffusion. We perform two test problems, the steady-state oblique C-type shocks and the decay of Alfvén waves, confirming the accuracy and robustness of our numerical approach. Results from the simulations of the compressible MHD turbulence with ambipolar diffusion show the flexibility of our method as well as its ability to follow complex MHD flows in the presence of ambipolar diffusion. These simulations show that the dissipation rate of MHD turbulence is strongly affected by the strength of ambipolar diffusion.
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