Solving the MHD equations by the space-time conservation element and solution element method
Solving the MHD equations by the space-time conservation element and solution element method
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DOI：
10.1016/j.jcp.2005.10.006
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发表时间：
2006-05
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影响因子：
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通讯作者：
Moujin Zhang;S. Yu;S. Lin;Sin-Chung Chang;I. Blankson
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文献类型：
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作者：
Moujin Zhang;S. Yu;S. Lin;Sin-Chung Chang;I. Blankson
我们应用时空守恒元和解元（CESE）方法求解理想MHD方程，特别强调满足磁场的无散度约束，即∇·B=0。在CESE方法的设置中，采用了四种方法：(i)没有任何额外处理的原始CESE方法，（ii）一个简单的校正程序，在每个时间推进步骤后更新磁场B的空间导数，使所有网格节点上的∇·B=0, （iii）使用特殊交错网格的约束传输法计算磁场B，以及（iv）在每个时间推进步骤后求解泊松求解器的投影法。为了证明这些方法的能力，计算了两个基准MHD流动：(i)旋转一维MHD激波管问题和（ii） MHD涡旋问题。结果显示不同方法之间没有差异，所有结果与先前报道的数据相比都是有利的。
We apply the space–time conservation element and solution element (CESE) method to solve the ideal MHD equations with special emphasis on satisfying the divergence free constraint of magnetic field, i.e., ∇·B=0. In the setting of the CESE method, four approaches are employed: (i) the original CESE method without any additional treatment, (ii) a simple corrector procedure to update the spatial derivatives of magnetic field B after each time marching step to enforce ∇·B=0 at all mesh nodes, (iii) a constraint-transport method by using a special staggered mesh to calculate magnetic field B, and (iv) the projection method by solving a Poisson solver after each time marching step. To demonstrate the capabilities of these methods, two benchmark MHD flows are calculated: (i) a rotated one-dimensional MHD shock tube problem and (ii) a MHD vortex problem. The results show no differences between different approaches and all results compare favorably with previously reported data.