Utilizing a discontinuous Galerkin method for solving Galbrun’s equation in the frame of aeroacoustics

In the research field of aeroacoustics, scientists and engineers developed broad varieties of mathematical formulations to investigate numerically flow-induced noise in an early stage of product design and development. Besides the already established theories such as the linearized Euler equations (LEE), the linearized Navier-Stokes equations (LNSE) and the acoustic perturbation equations (APE) which are all written in a pure Eulerian frame, Galbrun utilized a mixed Eulerian-Lagrangian frame to reduce the number of unknowns. Despite the advantages of fewer degrees of freedom and the reduced effort to solve the system equations, using the usual finite element method suffers from instabilities called spurious modes that pollute the solution leaving useless results. In this work, the authors apply a discontinuous Galerkin method to overcome the difficulties related to spurious modes when solving Galbrun’s equation in a mixed and pure displacement based formulation. The results achieved with the novel approach are compared with results from former attempts to solve Galbrun’s equation.