管道声传播问题的一种高精度数值模拟

High-accuracy numerical simulation of acoustic propagation problem in pipe

采用高精度的切比雪夫谱元法对管道声学模型的声场进行数值模拟。该解法对基于线性化欧拉方程的声场传播控制方程在空间上进行谱元离散,并推导了隐式时间积分的公式。通过Gaussian扰动波问题进行了算法测试,然后对带有管壁反射边界和进出口吸收边界的管道声学模型进行数值模拟,并给出具体算例进行求解分析,其结果符合线性声学理论,表明谱元方法对求解和分析计算气动声学问题具有良好的适应性和有效性。

A Chebychev spectral elements approximate solution of the acoustic propagation problem in subsonic pipe was introduced.The discretization was carried out based on spectral elements in space with sound-hard boundary on the rigid wall and sound-soft boundary at the inlet and outlet of the pipe.An implicit Newmark method was used for time marching.Gaussian perturbation as a test measure was calculated with good results obtained and the boundary reflections were analyzed as well.The absorbing boundary condition is suitable in static medium while losing some accuracy in subsonic flow.The numerical simulation of acoustic propagation with sixth order accuracy was implemented,and its results coincide well with those according to the linear acoustic theory,illustrating the high performance of spectral elements method in solving CAA problems.