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 引用本文: 谢志南 廖振鹏. 波动方程数值模拟的一种显式方法---界面节点公式的构建[J]. 力学学报, 2011, 43(1): 154-161.
Xie Zhinan Liao Zhenpeng. An explicit method for numerical simulation of wave motion---constructing recursion formula for interface point[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(1): 154-161.
 Citation: Xie Zhinan Liao Zhenpeng. An explicit method for numerical simulation of wave motion---constructing recursion formula for interface point[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(1): 154-161.

## An explicit method for numerical simulation of wave motion---constructing recursion formula for interface point

• 摘要: 针对成层介质中标量波动的数值模拟, 基于波速有限原理和波动方程柯西问题的解, 导出了界面点在一个短时间窗内的精确解, 由此给出了具有高阶精度的界面节点显式递推公式的一种构建方法, 并以构造弹性杆界面节点的递推公式为例说明其要点. 给出了与已有内节点递推公式的精度阶匹配的二阶和四阶界面节点递推公式. 由此构成的计算格式具有异质格式''编程简便的特性, 更合理地考虑了界面影响. 最后, 通过数值试验检验这一匹配方案的精度和稳定性.

Abstract: In the paper, the analytical solution for interfacepoints in a short time window is firstly deduced by combination of thefiniteness of wave velocity and solutions of Cauchy problem of waveequation, then a method of constructing a high order explicit recursionformula for interface points is provided for numerical simulation of scalarwave motion in uniformly layered model. To illustrate the main point, anexample of constructing recursion formula for interface points presented ina piecewise elastic bar is included. Second and fourth order recursionformula for interface in time and space are provided and consistent with thecurrent stable explicit formulas for interior points. Like heterogeneousscheme, the scheme presented in this paper has the same advantage of easyprogramming. Finally, the accuracy and stability of the new scheme arevalidated through numerical tests.

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