A 2D frequency domain finite element formulation for solving the wave equation in the presence of rotating obstacles

Abstract

A numerical method is presented to solve the propagation of sound waves in a two-dimensional domain in the presence of rotating obstacles without flow. It relies on a domain decomposition whereby rotating components are all embedded in a circular domain and the Arbitrary Lagrangian Eulerian framework which consists in writing the wave equation in the rotating reference frame. The transmission conditions at the interface between both domains is accomplished via the Frequency Scattering Boundary Conditions which, after classical discretization with the Finite Element Method (FEM), give rise to a series of coupled problems associated with a discrete set of frequencies. The performances of the method are demonstrated through several test cases of increasing complexity.