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首页> 外文期刊>Japanese journal of applied physics >Diagonally Staggered Grid for the Analysis of Elastic Wave Fields in Isotropic and Anisotropic Solids Using the Finite-Difference Time-Domain Method
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Diagonally Staggered Grid for the Analysis of Elastic Wave Fields in Isotropic and Anisotropic Solids Using the Finite-Difference Time-Domain Method

机译：有限差分时域法分析各向同性和各向异性固体中的弹性波场的对角交错网格

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摘要

In engineering fields there have recently been a number of studies that have applied the finite-difference time-domain (FDTD) numerical method to elastodynamic problems. These studies include those of ultrasonic transducers and electro-mechanical devices. In FDTD formulations, the first-order set of partial differential equations given by the constitutive equations are discretized using a leap-frog finite-difference scheme. When a high-contrast discontinuity, especially a free surface, is present, some difficulties arise due to the spatially staggered nature of the grid of the FDTD approach, with neither all the velocity variables nor all the stress variables appearing on the same grid lines. The present study considers the following modifications to the FDTD approach: a standard staggered grid for anisotropic elastic wave fields is rotated so that the diagonal directions of the standard grid lie parallel to the axes of the analysis region. This configuration, called the diagonally staggered grid (DSG), improves the accuracy of the implementation of free boundaries without requiring virtual grids in a vacuum area. The effectiveness of DSG was verified by applying this method to model problems of isotropic and anisotropic solid materials.
机译：在工程领域，最近有许多研究将有限差分时域（FDTD）数值方法应用于弹性动力学问题。这些研究包括超声换能器和机电设备的研究。在FDTD公式中，由本构方程给出的一阶偏微分方程组使用跳蛙式有限差分格式离散化。当存在高对比度的不连续性，尤其是自由表面时，由于FDTD方法的网格在空间上错开，因此会出现一些困难，所有速度变量和所有应力变量都不会出现在同一网格线上。本研究考虑对FDTD方法的以下修改：旋转各向异性弹性波场的标准交错网格，以使标准网格的对角线方向平行于分析区域的轴。这种配置称为对角交错网格（DSG），可以提高实现自由边界的准确性，而无需在真空区域中使用虚拟网格。通过将该方法应用于各向同性和各向异性固体材料的模型，验证了DSG的有效性。

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