A robust moving mesh finite volume method applied to 1D hyperbolic conservation laws from magnetohydrodynamics
A robust moving mesh finite volume method applied to 1D hyperbolic conservation laws from magnetohydrodynamics
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DOI：
10.1016/j.jcp.2005.12.014
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发表时间：
2006-08
期刊：
影响因子：
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通讯作者：
A. Dam;P. Zegeling
中科院分区：
文献类型：
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作者：
A. Dam;P. Zegeling
本文介绍了一种一维自适应移动网格方法及其在磁流体力学双曲型守恒律中的应用。该方法是稳健的，因为它在考虑新模型时采用了网格自适应的自动控制，而不需要手动设置参数。自适应网格是求解含时偏微分方程组(PDE)时提高精度和降低计算成本的常用工具。网格点被移到最需要它们的位置。为了获得与时间相关的自适应网格，监控功能被用来通过为每个位置分配‘权重’值来自动‘监控’域的各个部分的重要性。基于均匀分布原则，对所有网格点按其分配的权值进行分配。我们使用复杂的监控功能，在同一解决方案中跟踪小的、局部的现象以及大的冲击。将移动网格法和高分辨率有限体积法相结合，在相对不增加额外成本的情况下，大大提高了双曲偏微分方程组的精度。给出了几个数值实验的结果，包括与h-精化的比较，这些结果涵盖了许多典型的非线性磁流体动力学的有趣方面，具有比类似出版物中经常看到的更高的精度。
In this paper we describe a one-dimensional adaptive moving mesh method and its application to hyperbolic conservation laws from magnetohydrodynamics (MHD). The method is robust, because it employs automatic control of mesh adaptation when a new model is considered, without manually-set parameters. Adaptive meshes are a common tool for increasing the accuracy and reducing computational costs when solving time-dependent partial differential equations (PDEs). Mesh points are moved towards locations where they are needed the most. To obtain a time-dependent adaptive mesh, monitor functions are used to automatically ‘monitor’ the importance of the various parts of the domain, by assigning a ‘weight’-value to each location. Based on the equidistribution principle, all mesh points are distributed according to their assigned weights. We use a sophisticated monitor function that tracks both small, local phenomena as well as large shocks in the same solution. The combination of the moving mesh method and a high-resolution finite volume solver for hyperbolic PDEs yields a serious gain in accuracy at relatively no extra costs. The results of several numerical experiments including comparisons with h-refinement are presented, which cover many intriguing aspects typifying nonlinear magnetofluid dynamics, with higher accuracy than often seen in similar publications.