We develop a stable finite difference method for the elastic wave equations in bounded media, where the material properties can be discontinuous at curved interfaces. The governing equations are discretized in second order form by a fourth or sixth order accurate summation-by-parts operator. The mesh size is determined by the velocity structure of the material, resulting in nonconforming grid interfaces with hanging nodes. We use order-preserving interpolation and the ghost point technique to couple adjacent mesh blocks in an energy-conserving manner, which is supported by a fully discrete stability analysis. In numerical experiments, we demonstrate that the convergence rate is optimal, and is the same as when a globally uniform mesh is used in a single domain. In addition, with a predictor-corrector time integration method, we obtain time stepping stability with stepsize almost the same as given by the usual Courant Friedrichs Lewy condition.
翻译:我们为封闭介质中的弹性波方程开发了一种稳定的有限差异法,在这个方法中,物质特性在曲线式界面中可以不连续。调节方程式由第四或第六顺序准确的逐个总和操作员以第二顺序形式分解。网状大小由材料的速度结构决定,导致与挂结节点的网格接口不兼容。我们使用秩序保护插图和鬼点技术,以节能的方式将相邻网状区块对齐,并辅之以完全离散的稳定分析。在数字实验中,我们证明趋同率是最佳的,与在一个单一域中使用全球统一的网格一样。此外,如果采用预测或校正时间集成法,我们用几乎与通常的Colant Friedrichs Lewy条件相同的步骤来获得时间步态稳定。