一种基于新型斜率限制器的理想磁流体方程的高分辨率熵相容格式

针对磁流体动力学方程, 通过分析数据重建所需的条件, 构造一种基于MUSCL(Monotone Upstream-Centred Scheme for Conservation Laws)型重建方法的斜率限制器, 获得了一种求解理想磁流体动力学方程的高分辨率熵相容格式。该格式在解的光滑区域具有高精度; 在解的间断区域可以合理地控制耗散, 可有效避免非物理现象的产生。采用熵稳定格式、熵相容格式和新的高分辨率熵相容格式对一维、二维理想磁流体动力学方程进行数值模拟。结果表明: 新格式能准确地捕捉解的结构, 且具有无振荡、高分辨、鲁棒等特性。

A High Resolution Entropy Consistent Scheme for Ideal Magnetohydrodynamics Equations with New Slope Limiter

A high resolution entropy consistent scheme for ideal MHD equations is presented. A slope limiter based on MUSCL-type data reconstruction method is constructed with analysis on conditions required for non-oscillation. The scheme has high accuracy in the smooth region of the solution. In the discontinuous region the numerical dissipation can be controlled reasonably and the non-physical phenomena can be avoided effectively. The entropy stable scheme, the entropy consistent scheme and the new high-resolution entropy consistent scheme are used to simulate one-dimensional and two-dimensional ideal MHD equations. It shows that the new scheme captures structure of the solution accurately, and has the characteristics of non-oscillation, high-resolution and robustness.