论文标题
自由流保持有限差异方案，用于曲线网眼上理想的磁流失动力学
Free-stream preserving finite difference schemes for ideal magnetohydrodynamics on curvilinear meshes
论文作者
论文摘要
在本文中，为理想的磁水动力学（MHD）方程开发了高阶自由流的有限差加权（WENO）方案。在受约束的运输框架下，引入了汉密尔顿 - 雅各布（H-J）方程来进化的磁电势以控制发散误差。在这项工作中，我们将WENO方案的替代公式[10]用于非线性双曲保护定律，并设计了一种解决磁力势的新方法。理论推导和数值结果表明，该方案可以保留MHD方程的自由流解决方案，并比对于此类问题的标准有限差异方案更有效地减少错误。
In this paper, a high order free-stream preserving finite difference weighted essentially non-oscillatory (WENO) scheme is developed for the ideal magnetohydrodynamic (MHD) equations on curvilinear meshes. Under the constrained transport framework, magnetic potential evolved by a Hamilton-Jacobi (H-J) equation is introduced to control the divergence error. In this work, we use the alternative formulation of WENO scheme [10] for the nonlinear hyperbolic conservation law, and design a novel method to solve the magnetic potential. Theoretical derivation and numerical results show that the scheme can preserve free-stream solutions of MHD equations, and reduce error more effectively than the standard finite difference WENO schemes for such problems.
