二阶微小项声波动方程的同伦分析近似解

The approximation of second-order miniterm approximation acoustic wave equation via homotopy analysis method

由于声波在大气中的传播复杂性,数值模拟方法被广泛采用,但其不能给出解析解的表达式,且其精度有限.文章利用同伦分析方法求解二阶微小项声波动方程的近似解,该方程可以描述声波在大气中传播时的衰减和非线性效应.首先,引入包含衰减项的初始近似解,利用同伦分析方法迭代公式求得一次、二次近似解以及三阶近似解;之后利用Monin-Obukhov相似理论得到的多云、有风的夜晚天气条件下的声速剖面、风速剖面、温度剖面,并对近似解进行了空间数值模拟.结果表明,由于非线性和衰减效应,近似解波形发生了畸变,且声压随着传播距离的增加而减小,因此对研究大气中的声波传播特性具有重要意义.

Due to the complexity of sound waves in the atmosphere, the numerical simulation method is widely applied, but the expressions of the analytical solution are not given, and its precision is limited. In this paper, the second-order miniterm approximation acoustic wave equation containing the attenua- tion and nonlinear effects is solved using the homotopy analysis method （HAM）. Firstly, initial approx- imate solution with attenuation term is introduced, the first, the second approximation and the 3rd-order approximation solutions are obtained by iterative formula of HAM; and then sound speed profile, wind speed profile, temperature profile of a cloudy windy night are obtained using the Monin-Obukhov simi- larity theory , and numerical simulation of the approximate solutions is made. Results show that the waveform of the approximate solutions have distortion and the sound pressure decreases with the in- crease of propagation distance, so it is of great significance to research the sound wave propagation in the atmosphere.