The aero-acoustic Galbrun equation in the time domain with perfectly matched layer boundary conditions

This paper presents a solution for aero-acoustic problems using the Galbrun equation in the time domain with a non-uniform steady mean flow in a two-dimensional coordinate system and the perfectly matched layer technique as the boundary conditions corresponding to an unbounded domain. This approach is based on an Eulerian-Lagrangian description corresponding to a wave equation written only in terms of the Lagrangian perturbation of the displacement. It is an alternative to the Linearized Euler Equations for solving aero-acoustic problems. The Galbrun equation is solved using a mixed pressure-displacement Finite Element Method. A complex Laplace transform scheme is used to study the time dependent variables. Several numerical examples are presented to validate and illustrate the efficiency of the proposed approach. (C) 2016 Acoustical Society of America.