Stable Perfectly Matched Layers with Lorentz transformation for the convected Helmholtz equation

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