Perfectly matched layer boundary condition for two-dimensional Euler equations in generalized coordinate system

Abstract

In the past, perfectly matched layer (PML) equations have been constructed in Cartesian and spherical coordinates. In this article, the focus is on the development of a PML absorbing technique for treating numerical boundaries, especially those with unbounded domains, in a generalized coordinate system for a flow in an arbitrary direction. The PML equations for two-dimensional Euler equations are developed in split form through a space–time transformation involving a complex variable transformation with the application of a pseudo-mean-flow in the PML domain. A numerical solver is developed using conventional numerical schemes without employing any form of filtering or artificial dissipation to solve the governing PML equations for two-dimensional Euler equations in a generalized coordinate system. Physical domains of arbitrary shapes are considered and numerical simulations are carried out to validate and demonstrate the effectiveness of the PML as an absorbing boundary condition in generalized coordinates.