High-Order Discontinuous-Galerkin Discretizations for Computational Aeroacoustics in Complex Domains

Abstract

Discontinuous Galerkin discretization is applied for the numerical solution of the linearized Euler equations governing propagation of small-amplitude acoustic disturbances. Second-, fourth-, and sixth-order-accurate numerical solutions are obtained for domain discretizations with triangular elements. In addition, discretizations with quadrilateral unstructured meshes are obtained with second- and fourth-order accuracy. Detailed comparisons with exact solutions and accuracy tests are carried out with results obtained for a pressure pulse propagation and reflection from a solid surface. It is demonstrated that for triangular meshes the numerical solutions show grid convergence according to the order of accuracy used for the discretization. The versatility of the method to obtain accurate predictions in complex geometries is demonstrated with the results obtained for sound scattering from a single cylinder and two cylinders. HE discontinuous Galerkin (DG) method is applied for the numerical solution of the linearized Euler equations that describe sound propagation in computational aeroacoustics (CAA). The main advantage of using the linearized Euler equations in practical calculations of sound propagation is computational efficiency. The intensity of sound sources, such as vortex noise, broadband turbulence noise, and impulsive noise, can be captured only with the numerical solution of the computationally intensive, nonlinear, viscous, compressible flow equations. However, propagation of the generated acoustic waves away from sources and other important effects, such as scattering from solid surfaces, can be accurately obtained from the linearized Euler equations. The linearized Euler equations, from a numerical point of view, encompass many essential features of the inviscid and viscous flow governing equations. Therefore, it is desirable to obtain predictions of sound generation and propagation with the same numerical method in different domains, for example, noise source capturing with direct numerical simulation or large-eddy simulation (LES), and for propagation away from the sources using the linearized Euler equations. Compared to computational fluid dynamics, higher-order accuracy both in space and time is required for CAA in order to minimize dissipation and dispersion errors. In the last few years,