A Perfectly Matched Layer Method for the Navier-Stokes equations

Abstract

The Perfectly Matched Layer Method (PML) has found widespread application as a high-accuracy, non-reflecting boundary treatment in many wave propagation simulations. However, in the area of computational fluid dynamics, its application has been mostly limited to the linearized Euler equations. Attempts to apply PML to the nonlinear Euler equations have found a tendency for the method to go unstable. Even so, in light of the method's computational efficiency and high accuracy, finding a robust and stable implementation is highly desirable. Here, the method is extended to the Navier-Stokes equations, and is implemented with a high-order discontinuous Galerkin finite element method (DGFEM). The weaknesses and strengths of the method are investigated, and its performance is assessed when applied to complex flows; in particular, a viscous cavity flow is investigated. Stabilizing adjustments to the method are made, and future work is indicated for increased utility and flexibility of the method.