High resolution rotated flux scheme for two-dimensional magnetohydrodynamics equations(二维磁流体方程的高分辨率旋转通量格式)

Abstract

The rotated flux method could be used to effectively eliminate the shock instability of the approximate Riemann solver and suppress the generation of non-physical phenomenon if the equations to be solved meet the rotational invariance. For the 2D ideal magnetohydrodynamics (MHD) and shallow water magnetohydrodynamics (SWMHD) equations, the rotation-like matrix of flux function was constructed, and the corresponding rotational invariance theorem was given with proof, which was then used to deal with the governing equations applying quasi-1D method to derive the semi-discrete rotated flux scheme. Combining entropy stable flux and anti-diffusive flux by a flux limiter, a new flux that can adaptively adjust the dissipation term was obtained. Numerical experiments show that the new scheme can accurately capture the structure of solution, has high resolution, strong robustness and can be easily extended to higher dimensions.(若待解方程满足旋转不变性，则可通过旋转通量法有效消除近似Riemann求解器的激波不稳定现象，抑制非物理现象的产生。针对二维理想磁流体（MHD）方程和浅水波磁流体（SWMHD）方程，构造了通量函数的类旋转矩阵，给出了方程的旋转不变性证明；根据该性质对控制方程做类一维处理，推导了方程的半离散旋转通量格式；利用通量限制器，将熵稳定通量和反扩散通量进行加权组合，得到能够自适应调整耗散量的高分辨率旋转通量格式。数值实验表明，此格式能精确捕捉解的结构，分辨率高、鲁棒性强，且易向高维推广。)

Keywords

• ideal magnetohydrodynamics equations(理想磁流体方程)
• shallow water magnetohydrodynamics equations(浅水波磁流体方程)
• rotational invariance(旋转不变性)
• high resolution entropy stable flux(高分辨率熵稳定通量)