加权吸收边界条件的优化设计

Optimization design of weighted absorption boundary condition

（大庆石油学院地球科学学院，黑龙江大庆 163318）

College of Earth Science,Daqing Petroleum Institute,Daqing 163318,China

基于声波波动方程的旁轴近似吸收边界条件可以通过提高泰勒级数展开的旁轴近似阶数获得更好的吸收效果，但这样不仅增加了差分计算的复杂性，同时还导致计算过程不稳定。针对这一问题，提出了优化加权吸收边界条件。首先从理论上讨论了优化加权吸收边界条件，提出了加权因子概念，通过调节加权因子来拓展边界反射完全吸收角度；然后利用脉冲响应和数值模拟对优化加权吸收边界条件的吸收效果进行了分析。结果表明，选择合适的加权因子可以将边界处的完全吸收角度拓宽到60°以上，反射系数误差不超过2.5%。该方法简单易行，计算量小，而吸收效果比常规旁轴近似吸收边界条件更好。

Paraxial approximation absorption boundary condition based on acoustic wave equation can obtain better absorption results by increasing paraxial approximation order of Taylor series.However,this kind of operation will increase the complexity of difference computation,and result in instability of computation process.In order to solve the problem,we proposed optimized weighted absorption boundary condition.Firstly,optimized weighted absorption boundary condition was discussed theoretically,the concept of weighted factor was proposed,and the perfect absorption angle of boundary reflection was extended by adjusting weighted factor.Then,impulse response and numerical simulation were used to analyze the absorption effect of optimized weighted absorption boundary condition.Results showed that properly selected weighted factor can extend the perfect absorption angle at boundary to more than 60°,and the error of reflection coefficient is no more than 25%.The method is easily realized with small computation amount,and its absorption effect is better than conventional paraxial approximation absorption boundary condition.