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

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.& COPY; 2023 Elsevier B.V. All rights reserved.

Automated summary

This paper presents a numerical method to solve the propagation of sound waves in a two-dimensional domain with rotating obstacles without flow. The method utilizes domain decomposition and the Arbitrary Lagrangian Eulerian framework to incorporate the rotating components within a circular domain. The transmission conditions at the interface between the domains are achieved via the Frequency Scattering Boundary Conditions, which, after discretization with the Finite Element Method (FEM), result in a series of coupled problems associated with discrete frequencies. The method's performance is demonstrated through various increasingly complex test cases.