On the application of a variant CE/SE method for solving two-dimensional ideal MHD equations
On the application of a variant CE/SE method for solving two-dimensional ideal MHD equations
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DOI：
10.1016/j.apnum.2010.02.005
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发表时间：
2010-06
影响因子：
2.8
通讯作者：
Shamsul Qamar;Sidrah Mudasser
中科院分区：
文献类型：
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作者：
Shamsul Qamar;Sidrah Mudasser
本文提出了一种变时空守恒元和解元（CE/SE）方法，用于求解二维理想磁流体动力学方程。目前的方法使用规则的矩形网格单元的区域离散在两个空间维度。在该方法中，每个网格点上的一个单一的守恒单元被用来求解守恒律，无论在一，二，三个空间维。该格式只使用守恒单元计算流动变量，而流动变量的梯度由中心差分重构过程计算。虽然本格式不满足无发散条件，但有无发散清除程序的数值结果几乎相同。本手稿中包括几个二维测试用例。这些问题是那些不满足发散自由条件的数值方法的硬测试用例。因此，测试问题进一步验证了所提出的方案的性能。与中心格式的比较表明，CE/SE方法的结果具有更好的分辨率。
In this article we implement a variant space–time conservation element and solution element (CE/SE) method for the numerical solution of two-dimensional ideal magnetohydrodynamic (MHD) equations. The current method uses regular rectangular mesh elements for the domain discretization in two space dimensions. In the method, a single conservation element at each grid point is employed for solving conservation laws no matter in one, two, and three space dimensions. The present scheme uses the conservation element to calculate flow variables only, while the gradients of flow variables are calculated by a central differencing reconstruction procedure. Although the present scheme does not satisfy the divergence free condition, the numerical results obtained with and without divergence cleaning procedure are almost similar. Several two-dimensional test cases are included in this manuscript. These problems are hard test cases for those numerical methods which do not satisfy the divergence free condition. Therefore, the test problems further verify the performance of proposed scheme. A comparison with central schemes shows better resolution of the CE/SE method results.