An algebraic subgrid scale finite element method for the convected Helmholtz equation in two dimensions with applications in aeroacoustics

Abstract

An algebraic subgrid scale finite element method formally equivalent to the Galerkin Least-Squares method is presented to improve the accuracy of the Galerkin finite element solution to the two-dimensional convected Helmholtz equation. A stabilizing term has been added to the discrete weak formulation containing a stabilization parameter whose value turns to be the key for the good performance of the method. An appropriate value for this parameter has been obtained by means of a dispersion analysis. As an application, we have considered the case of aerodynamic sound radiated by incompressible flow past a two-dimensional cylinder. Following Lighthill’s acoustic analogy, we have used the time Fourier transform of the double divergence of the Reynolds stress tensor as a source term for the Helmholtz and convected Helmholtz equations and showed the benefits of using the subgrid scale stabilization.