求解理想磁流体方程的四阶WENO型熵稳定格式

张成治; 郑素佩; 陈雪; 张蕊

doi:10.21656/1000-0887.440178

求解理想磁流体方程的四阶WENO型熵稳定格式

doi: 10.21656/1000-0887.440178

长安大学理学院，西安 710064

基金项目:

国家自然科学基金项目 11971075

详细信息

作者简介:
张成治(1999—)，男，硕士生(E-mail: zhangchengzhi2021@163.com)

通讯作者:
郑素佩(1978—)，女，副教授，博士，硕士生导师(通讯作者. E-mail: zsp2008@chd.edu.cn)

中图分类号: O241
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- 文章访问数: 467
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- 被引次数: 0
出版历程
- 收稿日期: 2023-06-13
- 修回日期: 2023-08-02
- 刊出日期: 2023-11-01

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

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

摘要

摘要: 构造了一种用于求解理想磁流体方程的四阶熵稳定半离散有限体积格式.该格式空间方向上将高阶熵守恒通量与采用WENO重构的耗散项结合，得到高阶熵稳定通量.通过在耗散项中添加开关函数，使得数值通量具有更低的耗散并且高阶WENO重构满足符号性质.对用来控制磁场散度的源项采用中心格式离散，最终得到与熵守恒通量一致的高阶精度.几个一维、二维算例表明该格式无振荡，鲁棒性强，可以精确捕捉间断.
- 理想磁流体方程 /
- 熵稳定格式 /
- WENO重构 /
- 有限体积法
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

HTML全文

图 1 Ryu-Jones Riemman问题

Figure 1. The Ryu-Jones Riemman problem

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图 2 ES-WENO格式在T=0和T=0.4对应的开关函数值

Figure 2. The switch function values corresponding to the ES-WENO scheme at T=0 and T=0.4

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图 3 Torrilhon Riemman问题

Figure 3. The Torrilhon Riemman problem

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图 4 二维Orszag-Tang漩涡问题

Figure 4. The 2D Orszag-Tang vortex problem

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图 5 总熵随时间变化图

Figure 5. The changes of the total entropy with time

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图 6 第一转子问题

Figure 6. The 1st rotor problem

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图 7 云-激波相互作用

Figure 7. Cloud-shock interactions

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表 1 T=5时不同网格数下B₁的L¹, L^∞误差以及对应的收敛阶

Table 1. L¹, L^∞ errors in B₁ at T=5 and corresponding convergence rates for different mesh numbers

N	L¹ error	order	L^∞ error	order
16	9.165E-4		1.477E-3
32	2.838E-5	5.013	4.514E-5	5.032
64	2.100E-6	3.756	3.325E-6	3.763
128	1.320E-7	3.992	2.076E-7	4.001
256	8.337E-9	3.985	1.312E-8	3.984

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