Sound Wave Propagation in Non-Uniform Flow Using an Eulerian-Lagrangian Description

摘要

The aim of this paper is to present a non-standard equation for studying the acoustic propagation in multidirectional non-uniform mean flows. This equation is obtained using a mixed Eulerian-Lagrangian description. Some elementary concepts are recalled, as well as their physical significance and the specificity of the Eulerian-Lagrangian description is outlined. Then, equation that governs sound propagation is derived from Euler equations. When the associate variational formulation is directly used, solutions are corrupted by spurious rotational modes. In this paper, a mixed variational formulation is proposed to avoid this problem. Finally, results obtained by finite element discretization are compared with semi-analytical solutions obtained from the Pridmore-Brown equation. The ability of the method to take into account convection and refraction phenomena is shown. Furthermore, wave propagation in a complex geometry is investigated.