Perfectly Matched Layers (PMLs) appear as a popular alternative to non-reflecting boundary conditions for wave-type problems. The core idea is to extend the computational domain by a fictitious layer with specific absorption properties such that the wave amplitude decays significantly and does not produce back reflections. In the context of convected acoustics, it is well-known that PMLs are exposed to stability issues in the frequency and time domain. It is caused by a mismatch between the phase velocity on which the PML acts, and the group velocity which carries the energy of the wave. The objective of this study is to take advantage of the Lorentz transformation in order to design stable perfectly matched layers for generally shaped convex domains in a uniform mean flow of arbitrary orientation. We aim at presenting a pedagogical approach to tackle the stability issue. The robustness of the approach is also demonstrated through several two-dimensional high-order finite element simulations of increasing complexity.

完全匹配层（PML）似乎是波动类型问题的非反射边界条件的流行替代方法。核心思想是通过具有特定吸收特性的虚拟层来扩展计算域，以使波幅显着衰减并且不会产生背反射。在对流声学的背景下，众所周知，PML在频域和时域面临稳定性问题。它是由PML所作用的相速度与承载波能量的群速度之间的不匹配引起的。这项研究的目的是利用Lorentz变换来设计稳定的，完美匹配的层，以均匀取向的任意方向的均值流为大体形状的凸域。我们旨在提出一种解决稳定性问题的教学方法。该方法的鲁棒性还通过增加复杂性的几个二维高阶有限元模拟得到了证明。