一种求解三维声腔声压分布问题的无网格法  

A MESHLESS METHOD FOR SOLVING THE 3D SOUND PRESSURE DISTRIBUTION PROBLEM

作　　者：李亚立[1] 李鹏[2] 郭铃红 赵高煜[3] 

机构地区：[1]中国空空导弹研究院,洛阳471009 [2]中国舰船研究设计中心,武汉430064 [3]华中科技大学土木工程与力学学院,武汉430074

出　　处：《固体力学学报》2015年第6期530-536,共7页Chinese Journal of Solid Mechanics

基　　金：西北工业大学基础研究基金项目(JC20110219)资助

摘　　要：利用传统有限元法求解声压分布问题常常受到污染误差和色散误差的困扰.加权最小二乘无网格法(MWLS)是一种基于移动最小二乘(MLS)近似的无网格方法,求解声腔声压分布问题具有低色散、高精度的特点.然而传统的MLS近似有时容易产生病态矩阵,利用加权正交基函数构建改进的移动最小二乘(IMLS)近似,得到的系统方程为非病态的.论文基于改进的加权最小二乘无网格法(IMWLS)求解三维声腔内部声压分布.计算得到的声压分布和声压频响曲线都与参考值十分吻合,峰值误差和污染误差都比FEM的小,计算成本相比无单元伽辽金法显著降低.计算结果表明IMWLS相比传统的FEM,能在更高的频段内达到高精度,并且相比EFGM能大幅提高计算效率.The traditional FEM suffers from pollution and dispersion problems when it is used to com- pute sound pressure distribution. The meshless weighted least-square （MWLS） method based on the mov- ing least-square （MLS） approximation is characterized with low dispersion and high precision in solving sound pressure distribution problems. However, the MLS approximation may lead to ill-conditioned sys- tem of equations, an accurate solution of which is difficult to obtain. In this study, an improved moving least-square （IMLS） approximation was constructed by using the weighted orthogonal basis function. For- mulas were derived for an improved meshless weighted least-square （IMWLS） method with dispersion a- nalysis in solving three-dimensional （3D） sound pressure distribution problems. The results showed that the calculated sound pressure distribution and the sound pressure frequency response curve agreed very well with the reference values. The errors of peak and pollution of the proposed method were smaller than those of the FEM. The computational cost was significantly reduced compared with the element free Galer- kin method. The results also demonstrated that the proposed method could easily reach higher frequency without losing accuracy.

关 键 词：最小二乘近似 赫尔姆霍兹方程 无网格法 

分 类 号：O241.82[理学—计算数学]