Modeling and Finite Element Formulation for Acoustic Problems Including Rotating Domains

Abstract

A finite element formulation for the efficient numerical simulation of sound in computational domains, including rotating regions, is presented. The mathematical description is based on an arbitrary Lagrangian–Eulerian framework and results in a convective wave equation for the scalar acoustic potential. Numerically, the capability of nonconforming grids is explored by applying a Nitsche-type mortaring between stationary and rotating regions. The formulation can be applied to classical acoustics (stagnant fluid) as well as moving fluids in the case of aeroacoustics. The validation with the analytical solution of a rotating point source in three dimensions demonstrates the accuracy and robustness of the developed numerical scheme. Additionally, the convergence study shows that the intersection mesh operations needed in the nonconforming setting do not deteriorate the accuracy of the numerical solution.