A 4th-Order WENO-Type Entropy Stable Scheme for Ideal Magnetohydrodynamic Equations

ZHANG Chengzhi; ZHENG Supei; CHEN Xue; ZHANG Rui

doi:10.21656/1000-0887.440178

Volume 44 Issue 11

Nov. 2023

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Article Navigation > Applied Mathematics and Mechanics > 2023 > 44(11): 1398-1412

ZHANG Chengzhi, ZHENG Supei, CHEN Xue, ZHANG Rui. A 4th-Order WENO-Type Entropy Stable Scheme for Ideal Magnetohydrodynamic Equations[J]. Applied Mathematics and Mechanics, 2023, 44(11): 1398-1412. doi: 10.21656/1000-0887.440178

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A 4th-Order WENO-Type Entropy Stable Scheme for Ideal Magnetohydrodynamic Equations

doi: 10.21656/1000-0887.440178

School of Sciences, Chang'an University, Xi'an 710064, P.R.China

Received Date: 2023-06-13
Rev Recd Date: 2023-08-02
Publish Date: 2023-11-01

Abstract

Abstract

A 4th-order entropy stable semi-discrete finite volume scheme was constructed for ideal magnetohydrodynamic equations. This scheme combines the high-order entropy conservative flux with the dissipation term reconstructed with the WENO scheme in the spatial direction. With a switching function added to the dissipation term, the numerical flux has lower dissipation and the WENO reconstruction satisfies the sign property. The source term used to control the divergence of the magnetic field is discretized with the center difference scheme to obtain high-order accuracy consistent with the entropy conservative flux. Several 1D and 2D cases show that, the scheme has no oscillation and strong robustness, and can accurately capture discontinuities.
- ideal magnetohydrodynamic equation,
- entropy stable scheme,
- WENO reconstruction,
- finite volume method

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References(21)

References

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