Yang Jie, Zhang Xinyu, Liu G R, Mao Zirui, Zhang Wenping
College of Power and Energy Engineering, Harbin Engineering University, 150001, People's Republic of China.
Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati, Cincinnati, Ohio 45221-0070, USA.
J Acoust Soc Am. 2020 Feb;147(2):1311. doi: 10.1121/10.0000648.
Absorbing boundary conditions (ABCs) play a critical role in the simulation of sound or wave propagation problems. This paper proposes a technique of space-time transformed perfectly matched layer (PML) boundary condition implemented in a widely used mesh-free method called smoothed particle hydrodynamic (SPH) method, to absorb the outgoing sound waves with oblique shear mean flow. Special consideration is given to the particle features of the SPH, and the PMLs are formulated to correct the truncation error of SPH and absorb the outgoing wave at the same time, aiming to reduce the storage and computational cost in the infinite computational domain. Because the group velocity and phase velocity of the outgoing sound waves in the PMLs may be in different directions, exponentially growing pseudo reflections can result. The authors thus employ space-time transformation to eliminate the reflections effectively in PML boundaries for stable solutions. Moreover, a uniform framework of PML absorbing boundary conditions for Euler equations in the cases of arbitrary oblique mean flow and static media is derived. Finally, the present PML-SPH method with this stable absorbing boundary is applied to simulate sound waves propagating with mean flow. The obtained numerical results agree very well with the reference results.
吸收边界条件（ABCs）在声音或波传播问题的模拟中起着关键作用。本文提出了一种时空变换完全匹配层（PML）边界条件技术，该技术应用于一种广泛使用的无网格方法——光滑粒子流体动力学（SPH）方法中，以吸收具有斜切变平均流的出射声波。文中特别考虑了SPH的粒子特性，通过制定PMLs来校正SPH的截断误差并同时吸收出射波，旨在降低无限计算域中的存储和计算成本。由于PMLs中出射声波的群速度和相速度可能方向不同，可能会产生指数增长的伪反射。因此，作者采用时空变换来有效消除PML边界中的反射以获得稳定解。此外，还推导了任意斜切变平均流和静态介质情况下欧拉方程的PML吸收边界条件的统一框架。最后，将具有这种稳定吸收边界的PML-SPH方法应用于模拟有平均流时的声波传播。获得的数值结果与参考结果非常吻合。
