二维磁流体方程的高分辨率旋转通量格式OACSTPCD

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.