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波动方程有限差分数值模拟过程中 ,由于人为边界的引入 ,必然会导致边界反射 ,从而影响数值模拟的效果。为此人们提出了各种吸收边界条件方程 ,但是大部分吸收边界条件都很少专门考虑如何处理好模型边界角点的反射问题。本文在研究前人工作的基础上 ,提出了一种有效的处理边界角点反射的方法———插值预测波场法 ,即利用波前面的概念估算出边界角点上入射波的方向 ,再根据边界角点附近模型内部的波场值 ,利用非线性插值预测出边界角点处的波场值。数值算例表明了这种方法的有效性。
In the process of finite difference numerical simulation of wave equation, the introduction of artificial boundary will inevitably lead to boundary reflection, which will affect the numerical simulation results. For this reason, various kinds of equations for absorbing boundary conditions are proposed, but most of the absorbing boundary conditions seldom specifically consider how to deal with the reflection problem at the corners of the model boundary. Based on the research of predecessors’ work, this paper proposes an effective method to deal with the reflection of the boundary corner --- the interpolation predicted wavefield method, which uses the concept of wave front to estimate the direction of the incident wave at the boundary corner, and then Based on the wavefield values inside the model near the corner of the boundary, the wavefield values at the corner of the boundary are predicted by nonlinear interpolation. Numerical examples show the effectiveness of this method.