Real coordinate stretching perfectly matched layer for anisotropic advection-diffusion equation

Abstract

We propose a real coordinate transformation for truncating an unbounded domain to numerically solve the anisotropic advection-diffusion equation. By replacing the complex stretching with a real variant, our method eliminates auxiliary variables and maintains well-posedness. Key advantages include: (1) analytical solutions via Laplace-Fourier transforms, (2) exact handling of anisotropy through diffusion tensor diagonalization, and (3) reduced computational cost in higher dimensions. The approach is validated for 2D anisotropic problems with cross-derivatives, offering a better alternative to frequency-dependent domain truncation techniques.