Diagonally Staggered Grid for Elastodynamic Analysis Using the Finite-Difference Time-Domain Method
Diagonally Staggered Grid for Elastodynamic Analysis Using the Finite-Difference Time-Domain Method
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使用时域有限差分法进行弹性动力学分析的对角交错网格
DOI：
10.1143/jjap.46.4514
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发表时间：
2007
影响因子：
1.5
通讯作者：
Masahiro Sato
中科院分区：
文献类型：
--
作者：
Masahiro Sato
本文提出了一种新的对角交错网格结构，用于弹性波时域有限差分分析。网格的结构与标准交错网格相同，但标准网格的对角线平行于这种新配置中分析场的坐标轴。采用这种网格配置允许反对称应力边界条件的自然实现，例如实现自由边界时所需的。在实现这些边界条件，没有虚拟网格周围的分析区域是必需的，所以自由表面的复杂边界形状很容易处理。到目前为止，自由边界通常被处理使用零应力公式（CANF），真空公式（VCF）等CANF是相对精确的，但需要在真空区域创建虚拟网格。另一方面，VCF不需要使用虚拟网格，但精度和稳定性相对于CNOF有所降低。另外，自由边界实现的其他方法也有一些缺点。通过对一个模型试验问题的计算结果与现有有限差分方法的计算结果进行比较，证实了对角交错网格的有效性。
A new diagonally staggered grid configuration is proposed for the finite-difference time-domain analysis of elastic wave fields. The structure of the grid is the same as a standard staggered grid, but the diagonals of the standard grid lie parallel to the coordinate axes of the field of analysis in this new configuration. Adopting this grid configuration allows a natural implementation of antisymmetric stress boundary conditions, as is required when implementing free boundaries for example. In implementing these boundary conditions no virtual lattice around the analysis region is required, and so free surfaces with complex boundary shapes are easily treated. To date, free boundaries have usually been treated using the zero-stress formulation (ZSF), the vacuum formulation (VCF), etc. The ZSF is relatively precise, but requires the creation of virtual grids in the vacuum region. On the other hand, the VCF does not require the use of virtual grids, but accuracy and stability are reduced relative to the ZSF. Also, other methods of free boundary implementation have some demerits. The validity of the diagonally staggered grid is confirmed by comparing the calculation results of the present scheme with those derived by existing finite-difference methods for a model test problem.