基于精确几何-边界元法的二维声场问题分析

2D Acoustic Analysis Based on Exact Geometric Boundary Element Method

基于精确几何的思想,建立考虑边界几何形状,减小单元划分过程中产生几何误差的边界积分方程.积分过程中,积分项的奇异性问题通过采用Cauchy主值积分和Hadamard有限部分积分的方法来进行克服.同时,在边界元法求解声场问题过程中,出现的由非真实频率而引起的结果偏差可以通过Burton-Miller方法来解决.数值算例表明,考虑真实边界的精确几何-边界元方法具有较好的精确度.

Based on the theory of exact geometric analysis,the real geometric boundaries are considered,the error created by meshing is decreased,and a new boundary integral equation is introduced.The method of Cauchy principle value integrals and Hadamard finite-part integral are used to solve the problem of singular term integrals.Besides,non-unique solution caused by fictitious frequency is circumvented through the Burton-Miller method.Numerical examples show that the method considering the exact geometric boundary has a good accuracy.