岩土力学Issue(9)：2715-2720,6.
非均匀层状介质一维波动方程精确解的有限差分算法
A new kind of finite difference scheme for exact solutions of one-dimensional wave equation in heterogeneous layer media
摘要
Abstract
The plane-wave propagation can be generalized as a definite-solution problem of one-dimensional wave equation. In spite of the simple formality, solutions of one-dimensional wave equation in inhomogeneous media have to be solved with the aid of numerical methods. The classic three-level five-point finite difference scheme is a usual numerical method to calculate partial differential equations, which must meet the stable condition as an explicit iteration method. The stable condition is / 1a=vDt Dx≤ , where v is wave velocity, Dt is time sample interval, and Dx is space sample interval. When a=1 or Dx=vDt , the finite difference scheme is just up to the critical stable state. In such a case a space sample interval Dx just equals wave propagation distance in a time sample interval Dt , so the classic difference scheme exactly expresses plane-wave propagation theory and can be used to obtain exact solutions of one-dimensional wave equations. However, because of existence of wave impedance interfaces, the algorithm is unable to calculate wave fields in heterogeneous layer media. In order that the classic difference scheme in the critical stable state can be generalized to apply to heterogeneous layer media, an improved scheme is put forward, which can deal with impedance interfaces. Its stable condition is also given by Fourier transform analysis and the correctness is proved by some numerical model tests.关键词
一维波动方程/有限差分法/古典差分格式/层状介质/精确解Key words
one-dimensional wave equation/finite difference method/classic finite difference scheme/layer media/exact solutions分类
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范留明..非均匀层状介质一维波动方程精确解的有限差分算法[J].岩土力学,2013,(9):2715-2720,6.基金项目
陕西高校省级重点实验室重点科研计划项目(No.2010JS085)。 （No.2010JS085）
