双流体等离子体方程的熵稳定数值格式
Entropy Stable Numerical Schemes for Two-Fluid Plasma Equations
AI总结：
针对双流体等离子体方程，结合熵守恒通量和数值扩散算子设计熵稳定有限差分格式，并利用IMEX-RK时间推进方法处理刚性源项，仅需求解局部线性方程。
摘要：
双流体理想等离子体方程是理想MHD方程的推广形式，其中电子和离子被视为不同的组分。由于其非线性特性以及刚性源项的存在（特别是高荷质比和低拉莫尔半径情况），设计高效的数值格式变得复杂。本文通过结合熵守恒通量和合适的数值扩散算子，为双流体方程设计了熵稳定有限差分格式。此外，为了克服刚性源项带来的时间步长限制，我们基于隐式-显式（IMEX）-龙格库塔（RK）格式设计了时间推进方法。我们利用双流体等离子体方程的特殊结构，使得每个时间步只需在每个网格单元内求解局部线性方程。通过基准数值实验展示了这些格式的鲁棒性和精度。
英文摘要：
Two-fluid ideal plasma equations are a generalized form of the ideal MHD equations in which electrons and ions are considered as separate species. The design of efficient numerical schemes for the these equations is complicated on account of their non-linear nature and the presence of stiff source terms, especially for high charge to mass ratios and for low Larmor radii. In this article, we design entropy stable finite difference schemes for the two-fluid equations by combining entropy conservative fluxes and suitable numerical diffusion operators. Furthermore, to overcome the time step restrictions imposed by the stiff source terms, we devise time-stepping routines based on implicit-explicit (IMEX)-Runge Kutta (RK) schemes. The special structure of the two-fluid plasma equations is exploited by us to design IMEX schemes in which only local (in each cell) linear equations need to be solved at each time step. Benchmark numerical experiments are presented to illustrate the robustness and accuracy of these schemes.
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