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

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

Abstract

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

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.

Figures/Tables 7

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

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

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

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

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

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

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

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