求解理想磁流体方程的四阶WENO型熵稳定格式  

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

作　　者：张成治 郑素佩[1] 陈雪 张蕊 ZHANG Chengzhi;ZHENG Supei;CHEN Xue;ZHANG Rui(School of Sciences,Chang’an University,Xi’an 710064,P.R.China)

机构地区：[1]长安大学理学院,西安710064

出　　处：《应用数学和力学》2023年第11期1398-1412,共15页Applied Mathematics and Mechanics

基　　金：国家自然科学基金项目(11971075)。

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.A 4th-order entropy stable semi-discrete finite volume scheme was constructed for ideal magneto-hydrodynamic 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 dissi-pation 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.

关 键 词：理想磁流体方程 熵稳定格式 WENO重构 有限体积法 

分 类 号：O241[理学—计算数学]