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  

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

作　　者：沈亚玲 封建湖[1] 郑素佩[1] 李雅蓉 SHEN Yaling;FENG Jianhu;ZHENG Supei;LI Yarong(School of Science,Chang’an University,Xi’an,Shaanxi 710064,China)

机构地区：[1]长安大学理学院,陕西西安710064

出　　处：《计算物理》2022年第3期297-308,共12页Chinese Journal of Computational Physics

基　　金：国家自然科学基金(11971075)资助项目。

摘　　要：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 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.

关 键 词：磁流体方程 斜率限制器 高分辨率 

分 类 号：O241.82[理学—计算数学] O316.3[理学—数学]