A grid redistribution method for singular problems
A grid redistribution method for singular problems
复制标题
DOI：
10.1016/j.jcp.2008.11.035
复制
发表时间：
2009-04
期刊：
影响因子：
--
通讯作者：
A. Ditkowski;N. Gavish
中科院分区：
文献类型：
--
作者：
A. Ditkowski;N. Gavish
许多物理现象在局部区域产生奇异或近乎奇异的行为，例如边界层或爆炸解决方案。当解决方案接近奇点时，使用统一网格来解决此类问题在计算上变得令人望而却步。 Ren 和 Wang 开发了一种半静态自适应网格方法 [W.任X.P. Wang，多维奇异问题的迭代网格重新分配方法，J. Comput。物理。 159 (2000) 246–273]用于解决这些问题，称为迭代网格重新分配（IGR）方法。在这项研究中，我们为奇异问题的半静态自适应网格方法奠定了理论基础。基于这一理论，我们获得了本研究的关键结果——一种设计鲁棒权函数的方法，该方法确保奇异区域的网格分辨率，以及外部区域最大网格间距的控制。使用这种方法，我们引入了一种半静态自适应网格方法，它不涉及网格重新分布的迭代过程，如 IGR 方法。我们通过局部化超过九个数量级的解决方案的数值示例证明了该方法的有效性。
Many physical phenomena develop singular, or nearly singular behavior in localized regions, e.g. boundary layers or blowup solutions. Using uniform grids for such problems becomes computationally prohibitive as the solution approaches singularity. Ren and Wang developed a semi-static adaptive grid method [W. Ren, X.P. Wang, An iterative grid redistribution method for singular problems in multiple dimensions, J. Comput. Phys. 159 (2000) 246–273] for the solution of these problems, known as the iterative grid redistribution (IGR) method. In this study we develop a theoretical basis for semi-static adaptive grid method for singular problems. Based on this theory, we obtain the key result of this study – a methodology for designing robust weight functionals which ensures grid resolution in the singular region, as well as control of the maximal grid spacing in the outer region. Using this methodology, we introduce a semi-static adaptive grid method, which does not involve an iterative procedure for grid redistribution, as in the IGR method. We demonstrate the efficacy of this method with numerical examples of solutions which localize by more than nine orders of magnitude.