An efficient discontinuous Galerkin method for aeroacoustic propagation

Abstract

SUMMARY An efficient discontinuous Galerkin formulation is applied to the solution of the linearized Euler equations and the acoustic perturbation equations for the simulation of aeroacoustic propagation in two‐dimensional and axisymmetric problems, with triangular and quadrilateral elements. To improve computational efficiency, a new strategy of variable interpolation order is proposed in addition to a quadrature‐free approach and parallel implementation. Moreover, an accurate wall boundary condition is formulated on the basis of the solution of the Riemann problem for a reflective wall. Time discretization is based on a low dissipation formulation of a fourth‐order, low storage Runge–Kutta scheme. Along the far‐field boundaries a perfectly matched layer boundary condition is used. For the far‐field computations, the integral formulation of Ffowcs Williams and Hawkings is coupled with the near‐field solver. The efficiency and accuracy of the proposed variable order formulation is assessed for realistic geometries, namely sound propagation around a high‐lift airfoil and the Munt problem. Copyright © 2011 John Wiley & Sons, Ltd.

Validation of a Discontinuous Galerkin Implementation of the Time-Domain Linearized Navier–Stokes Equations for Aeroacoustics

“…These errors are assumed to be small for low mean vorticity levels. There are several formulations for the APE; in Section 4, some results are obtained with the APE-4 formulation [12,17].…”

Hybrid Discontinuous Galerkin and Finite Volume Method for Launch Environment Acoustics Prediction

“…Many of these approaches are so-called acoustic analogies, and among others, these include the original analogy of Lighthill [2,3], Kirchhoff's method [4][5][6], the Ffowcs-Williams-Hawkings (FWH) method [7], boundary element methods (BEMs), † † linearized Euler equations (LEEs) [8][9][10], acoustic perturbation equations (APEs) [10,11], etc. Kirchhoff and FWH formulations have often been favored for many freejet noise predictions, which are characterized by acoustic propagations through an unobstructed field.…”

“…The development and maturation of the DG method for hyperbolic conservation laws was pioneered by Cockburn and Shu [13], Atkins and Shu [14], and Toulopoulos and Ekaterinaris [15] in a series of papers, which ushered in tremendous progress in the development of the method for aerospace applications, as summarized in the review paper by Mavriplis et al [16] and the references therein. The DG solver used for this work is developed in the same massively parallel production framework (Loci) [17] as the CFD solver and solves the nonlinear Euler equations for improved fidelity in modeling inherently nonlinear launch-induced acoustic physics that are lost in techniques that make use of linearized equations sets such as LEEs [8][9][10] and APEs [10,11]. This methodology permits acoustic predictions in the presence of obstructions in both the CFD and CAA domains and thus offers improved acoustics modeling near complex geometry, where attenuation, reflection, and diffraction are important.…”

Performance of the DGM for the Linearized Euler Equations With Non-Uniform Mean-Flow

“…8,9 However, for aeroacoustics applications, problems are often governed by the linearized Euler equations (LEE). 10,11,12,13,14,15,16 Therefore, while dispersion analyses gave estimates of the performance of the DGM for model problems, considering the full form of the linearized Euler Equations may provide additional insight into the performance of the scheme, specifically for aeroacoustics problems. These problems typically involve highly non-uniform mean flows and the e↵ects of this on the stability and accuracy of the scheme have not yet been fully realized.…”