求解一维理想磁流体方程的移动网格熵稳定格式

磁流体方程的数值求解在等离子体物理学、天体物理研究以及流动控制等领域具有重要意义，本文构造了用于求解理想磁流体动力学方程的基于移动网格的熵稳定格式，此方法将Roe型熵稳定格式与自适应移动网格算法结合，空间方向采用熵稳定格式对磁流体动力学方程进行离散，利用变分法构造网格演化方程并通过Gauss-Seidel迭代法对其迭代求解实现网格的自适应分布，在此基础上采用守恒型插值公式实现新旧节点上的量值传递，利用三阶强稳定Runge-Kutta方法将数值解推进到下一时间层。数值实验表明，该算法能有效捕捉解的结构(特别是激波和稀疏波),分辨率高，通用性好，具有强鲁棒性。

A moving-grid entropy stable scheme for the 1D ideal MHD equations

The numerical solution of the magnetohydrodynamics (MHD) equations is of great significance in the fields of plasma physics,astrophysics and flow control.In this paper,an entropy-stable scheme based on the moving grid is constructed for solving the ideal MHD equations.This method combines the Roe-type entropy-stable scheme with the adaptive moving-grid algorithm,where the entropy-stable scheme is used to discretize the MHD equations in space,and the grid evolution equation is constructed by the variational method and then solved iteratively by Gauss-Seidel method for the adaptive grid.Furthermore,the scheme uses the conservative interpolation formula for transmission between on the new nodes and the old ones,with the third-order strongly stable Runge-Kutta method in time step.Numerical experiments show that the algorithm can effectively capture the structure of the solutions (especially shock waves and rarefaction waves),and has high resolution,good versatility,and strong robustness.