An adaptive moving mesh method for two-dimensional ideal magnetohydrodynamics
An adaptive moving mesh method for two-dimensional ideal magnetohydrodynamics
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DOI：
10.1016/j.jcp.2006.05.031
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
Jian-jun Han;Huazhong Tang
中科院分区：
文献类型：
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作者：
Jian-jun Han;Huazhong Tang
本文提出了一种二维理想磁流体力学（MHD）自适应移动网格算法，该算法利用交错约束输运技术来保持磁场无发散。该算法由两个独立的部分组成：MHD进化和网格重分配。第一部分是固定四边形网格上的高分辨率、无发散、冲击捕获方案，第二部分是迭代过程。在每次迭代中，首先重新分配网格点，然后使用保守插值公式计算重新映射的新网格上的质量、动量和总能量的单元平均值；将磁势以非保守的方式重新映射到新网格上，并重建为新网格上的无散度磁场。数值算例表明，该方法能达到较高的数值精度，并能在理想MHD问题中跟踪和解析强激波，同时保持磁场的无散度特性。数值算例包括光滑alfvsamn波问题、二维和2.5D激波管问题、双转子问题、严格爆炸问题以及云-激波相互作用问题。
This paper presents an adaptive moving mesh algorithm for two-dimensional (2D) ideal magnetohydrodynamics (MHD) that utilizes a staggered constrained transport technique to keep the magnetic field divergence-free. The algorithm consists of two independent parts: MHD evolution and mesh-redistribution. The first part is a high-resolution, divergence-free, shock-capturing scheme on a fixed quadrangular mesh, while the second part is an iterative procedure. In each iteration, mesh points are first redistributed, and then a conservative-interpolation formula is used to calculate the remapped cell-averages of the mass, momentum, and total energy on the resulting new mesh; the magnetic potential is remapped to the new mesh in a non-conservative way and is reconstructed to give a divergence-free magnetic field on the new mesh. Several numerical examples are given to demonstrate that the proposed method can achieve high numerical accuracy, track and resolve strong shock waves in ideal MHD problems, and preserve divergence-free property of the magnetic field. Numerical examples include the smooth Alfvén wave problem, 2D and 2.5D shock tube problems, two rotor problems, the stringent blast problem, and the cloud–shock interaction problem.