A Performance Study of High-order Finite Elements and Wave-based Discontinuous Galerkin Methods for a Convected Helmholtz Problem

The finite element method (FEM) remains one of the most established computational method used in industry to predict acoustic wave propagation. However, the use of standard FEM is in practice limited to low frequencies because it suffers from large dispersion errors when solving short wave problems (also called pollution effect). Various methods have been developed to circumvent this issue and we compare two numerical methods for convected Helmholtz problems. The methods chosen for this study are the polynomial high-order FEM and the wave-based Discontinuous Galerkin Method (DGM). The polynomial method takes advantage of the superior approximation properties of the Lobatto shape functions compared to the conventional Lagrange basis. The wave-based DGM is part of the physics-based methods which include a priori knowledge about the local behaviour of the solution into the numerical model. Previous studies have shown that both methods can control of the pollution effect. Common belief is that compared to polynomial methods, physics-based methods can provide a significant improvement in performance, at the expense of a deterioration of the conditioning. However, the results presented in this paper indicate that the differences in accuracy, efficiency and conditioning between the two approaches are more nuanced than generally assumed.