求解理想磁流体方程的高分辨率熵稳定格式

High resolution entropy stable scheme for ideal MHD equations

针对磁流体力学方程,提出一种基于限制器机制的熵稳定格式.新格式的构造方法与TVD格式类似,利用通量限制函数将高阶熵守恒格式与一阶熵稳定格式结合.得到的新格式保有熵守恒格式和熵稳定格式的优点,可以准确地捕捉激波,同时在解的间断区域避免非物理现象的产生、在解的光滑区域具有高精度,从而达到高分辨率的效果.将所得格式的数值结果与熵守恒格式和熵稳定格式的数值结果进行对比,结果表明,新构造的格式具有高分辨率和基本无振荡等良好的特性.

A new high resolution entropy stable scheme based on the limiter mechanism is proposed for the ideal magnetohydrodynamics(MHD)equations.The construction technique of the new scheme is similar to that of the TVD schemes.A higher order entropy conservative scheme and a first order entropy stable scheme are combined with a flux limiter function.The new high resolution entropy scheme preserves advantages of the entropy conservative scheme and the entropy stable scheme,capturing shocks accurately while avoiding non-physical phenomena in the regions of the discontinuous solutions and having higher accuracy in the regions of the smooth solutions,thus achieves high resolution.The numerical results such as density,velocity and pressure are presented and compared with that of entropy conservative scheme and entropy stable scheme.Several numerical experiments demonstrate the high resolution property of the new scheme.