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

doi:10.19596/j.cnki.1001-246x.8405

摘要/Abstract

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。

关键词: 磁流体方程, 斜率限制器, 高分辨率

Abstract:

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.

Key words: magnetohydrodynamics equations, slope limiter, high-resolution

沈亚玲, 封建湖, 郑素佩, 李雅蓉. 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[J]. 计算物理, 2022, 39(3): 297-308.

Yaling SHEN, Jianhu FENG, Supei ZHENG, Yarong LI. A High Resolution Entropy Consistent Scheme for Ideal Magnetohydrodynamics Equations with New Slope Limiter[J]. Chinese Journal of Computational Physics, 2022, 39(3): 297-308.

图/表 7

图1 Brio-Wu激波管问题的计算结果(a)密度；(b)速度w；(c)压力；(d)总熵随时间的变化

Fig.1 Numerical results of Brio-Wu shock tube problem (a) density; (b) speed w; (c) pressure; and (d) total entropy as functions of time

图2 Ryu and Jones黎曼问题的计算结果(a)密度；(b)速度w；(c)压力；(d)总熵随时间的变化

Fig.2 Numerical results of Ryu and Jones Riemann problem (a) density; (b) speed w; (c) pressure; and (d) total entropy as functions of time

图3 Dai-Woodward激波管问题的计算结果(a)密度；(b)速度u；(c)速度v；(d)压力

Fig.3 Numerical results of Dai-Woodward shock tube problem (a) density; (b) speed u; (c) speed v; (d) pressure

图4 First Rotor问题的熵稳定格式计算结果(a)密度；(b)压力；(c)马赫数；(d)磁场强度

Fig.4 Numerical results of entropy stable scheme for First Rotor problem (a) density; (b) pressure; (c) Mach number; (d) magnetic field intensity

图5 First Rotor问题的高分辨率熵相容格式计算结果(a)密度；(b)压力；(c)马赫数；(d)磁场强度

Fig.5 Numerical results of high resolution entropy consistent scheme for First Rotor problem (a) density; (b) pressure; (c) Mach number; (d) magnetic field intensity

图6 爆炸波问题的熵稳定格式计算结果(a)密度；(b)压力

Fig.6 Numerical results of entropy stable scheme for blast wave problem (a) density; (b) pressure

图7 爆炸波问题的高分辨率熵相容格式计算结果(a)密度；(b)压力

Fig.7 Numerical results of high resolution entropy consistent scheme for blast wave problem (a) density; (b) pressure

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