Analysis and computation of adaptive moving grids by deformation
Analysis and computation of adaptive moving grids by deformation
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DOI：
10.1002/(sici)1098-2426(199607)12:4
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发表时间：
1996-07
影响因子：
3.9
通讯作者：
P. Bochev;G. Liao;G. D. L. Pena
中科院分区：
文献类型：
--
作者：
P. Bochev;G. Liao;G. D. L. Pena
我们开发并分析了一种数值方法，用于在一维、二维和三维区域中创建自适应移动网格。该方法根据给定的空间和时间变量的解析或离散权函数来分配网格节点，反映了解的精细结构。权函数定义了一个向量场，用来构造计算域到物理域的转换。我们证明了生成的网格具有规定的单元大小，并且没有“网格缠结”发生。该方法的数值实现采用高效鲁棒的最小二乘求解器计算矢量场，采用四阶龙格-库塔格式确定变换。并给出了一些一维和二维数值实验的结果。这些结果表明，除其他外，该方法准确地重新分配节点并且不会纠缠网格。©1996 John Wiley & Sons, Inc
We develop and analyze a numerical method for creating an adaptive moving grid in one-, two-, and three-dimensional regions. The method distributes grid nodes according to a given analytic or discrete weight function of the spatial and time variables, which reflects the fine structure of the solution. The weight function defines a vector field, which is used to construct a transformation of the computational domain into the physical domain. We prove that the resulting grid has the prescribed cell sizes and that no “mesh tangling” occurs. Numerical implementation of the method utilizes an efficient and robust least-squares solver to compute the vector field and a fourth-order Runge-Kutta scheme to determine the transformation. Results of several numerical experiments in one- and two-dimensions are also presented. These results indicate, among other things, that the method accurately redistributes the nodes and does not tangle the mesh. © 1996 John Wiley & Sons, Inc.