用切比雪夫谱元方法求解均匀流场中的声传播问题  

Chebychev Spectral Elements Method for Acoustic Propagation Problem in a Uniform Mean Flow

作　　者：张荣欣[1] 秦国良[1] 

机构地区：[1]西安交通大学流体机械研究所,西安710049

出　　处：《西安交通大学学报》2009年第7期120-124,共5页Journal of Xi'an Jiaotong University

摘　　要：利用谱元方法中的无穷光滑插值函数的高阶精度特点,结合隐式时间推进算法的稳定性,推导并实现了低马赫数均匀流场中声波动方程的切比雪夫谱元解法,进而得到了流场影响下的声传播问题的数值解.该解法对均匀流场中的声传播问题在空间上进行谱元离散,在边界上引入Clay-ton-Engquist-Majda吸收边界条件,在时间上利用隐式Newmark积分方法推进求解.算例与解析解的对比验证表明:该解法在空间上可以实现高阶精度,在时间上达到2阶精度;使用的隐式New-mark时间积分方法稳定性好,计算工作量相对较小;当数值解达到稳态传播时和解析解吻合得非常好.随着计算条件的飞速发展,加密网格并采用更高阶的切比雪夫谱逼近可以进一步提高精度,以适应计算气动声学的精度要求,另外可尝试采用更高精度的吸收边界条件以改善边界反射对计算声场的干扰.High order accuracy is of great significance for computational aero-acoustics （CAA）. On the basis of the high order accuracy of the infinite smooth interpolation function adopted in the spectral elements method, a Chebychev spectral elements approximation for the acoustic propagation problem in the subsonic uniform mean flow is applied in this study. In this approach, the discretization is based on spectral elements in space with first-order Clayton-Engquist-Majda absorbing boundary conditions and the implicit Newmark method in time marching. The numerical results with sixth-order spectral accuracy in space and up to second-order in time agree well with the analytical solutions. The Newmark method in time with less computing resource consumption also has the advantages of stability. The higher order spectral approximation can be employed to further enhance the accuracy and higher order absorbing boundary conditions might be applied to improve the spectral element approach.

关 键 词：计算气动声学 谱元方法 吸收边界条件 高精度 

分 类 号：O42[理学—声学]