title: The aero-acoustic Galbrun equation in the time domain with perfectly matched layer boundary conditions.
abstract: 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.
authors.affiliation: Sorbonne universités, Université de technologie de Compiègne, CNRS-UTC 7337 Roberval, Centre de recherche Royallieu, CS 60319, 60203 Compiègne Cedex, France.
authors.forename: Xue
authors.initials: X
authors.lastname: Feng
authors.affiliation: Sorbonne universités, Université de technologie de Compiègne, CNRS-UTC 7337 Roberval, Centre de recherche Royallieu, CS 60319, 60203 Compiègne Cedex, France.
authors.forename: Mabrouk
authors.initials: M
authors.lastname: Ben Tahar
authors.affiliation: Sorbonne universités, Université de technologie de Compiègne, CNRS-UTC 7337 Roberval, Centre de recherche Royallieu, CS 60319, 60203 Compiègne Cedex, France.
authors.forename: Ryan
authors.initials: R
authors.lastname: Baccouche