波叠加法解的非唯一性问题改进及声源位置优化研究

Research on the non-uniqueness improvement of wave superposition method and location optimization of monopole sources

本文提出一种有效满足声场整体计算精度需求且能保证声场唯一解的改进方法。该方法在单极子波叠加法的基础上,以分析波数范围内重构前后体积速度相对误差为目标函数,以同形缩小系数为优化变量对声源所在曲面位置进行优化选取,再通过辐射体内部添加适量额外的单极子源可有效保证声场的唯一解。两个数值算例表明:对于脉动球源,球心处添加一个单极子源的改进波叠加法可以有效避免解的非唯一性问题,且具有非常高的计算效率及精度;对于复杂几何体,以体积速度相对误差为目标函数优化得到的单极子源位置,添加附加源后可求得声场的唯一解,且满足整体计算精度要求。

An improved wave superposition method was given by adding additional sources inside the radiator based on monopole wave superposition method to overcome the problem of non-uniqueness.And the relative error of volume velocity was considered as objective function to optimize the location of monopole sources.Two numerical examples including pulsating sphere and complex volume were given,and the numerical results demonstrate that the non-uniqueness problem can be solved by using additional sources wave superposition method.The computation is more efficient than that of the tripole wave supposition method,and the calculation accuracy is higher.The calculation accuracy for complex volume is very high by choosing the relative error of volume velocity as objective function when the monopole source’s locations are optimizing,and the non-uniqueness is also solved by adding additional monopole sources.