广义坐标下的波动方程

• 作 者: J.M.Careionc 三石
• 出 处: 石油物探译丛
• 发表日期: 1995年04期
• 关键词: 波动方程 广义坐标 边界条件 数值解 变换矩阵 空间转换 切比雪夫 面波 场变量 兰姆

本文介绍了将粘弹性波动方程由直角坐标变换到广义坐标的空间转换方法。应用切比雪夫法计算了场变量的空间导数及变换矩阵。在该方法中,边界条件需要做特殊处理,它是以垂直于边界的一维特征为基础的。兰姆问题的数值解要求对每一直角坐标方向做两次一维拉伸变换。结果表明,弹性数值解与解析解极为吻合。由此可以说明不同算子及边界处理产生

In this paper, a method of spatial transformation of the viscoelastic wave equation from rectangular coordinates to generalized coordinates is introduced. The spatial derivatives and transformation matrices of field variables are calculated by Chebyshev method. In this method, the boundary conditions require special treatment, which is based on a one-dimensional feature perpendicular to the boundary. The numerical solution to the Lamb problem requires one-dimensional stretching transformations for each Cartesian coordinate. The results show that the elastic numerical solution is in good agreement with the analytical solution. This shows that different operators and boundary processing