On solving the Galbrun equation via SEM

Propagation of acoustic disturbances in nonuniform flows is a subject of great interest in many practical problems, particularly in transport engineering with automotive exhaust systems, aeronautical turbofan engine inlet ducts, etc. In this paper, we consider the initial- and Dirichlet boundary-value problem for the generalized Galbrun equation. Precisely, we study the existence, uniqueness and stability properties of the solution for the continuous problem. Then we develop a numerical method based on the classical Newmark scheme in time and a spectral element method (SEM) in space. Several numerical tests are carried out to show the stability and convergence, especially the exponential error convergence.