Applications of the discontinuous Galerkin method to propagating acoustic wave problems

Jan Nytra,Miroslav Jícha,Libor Čermák

doi:10.1177/1687814017703631

Jan Nytra, Miroslav Jícha + Show 1 more

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https://doi.org/10.1177/1687814017703631

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Abstract

The purpose of this article is to demonstrate that the discontinuous Galerkin method is efficient and suitable to solve linearized Euler equations, modelling sound propagation phenomena. Several benchmark problems were chosen for this purpose. We studied the effect of the underlying computational mesh on the convergence rate and showed the importance of high-quality meshes in order to achieve the theoretical convergence rates. Various acoustic boundary conditions were examined. Perfectly matched layer was used as a non-reflecting boundary condition.

Highlights

The linearized Euler equations (LEE) are often used as the mathematical model to simulate acoustic propagation
The first successful application of the discontinuous Galerkin method (DGM) was presented in Reed and Hill[3] to solve the neutron transport equation
We presented the nodal DGM as a suitable method for acoustic simulations

Summary

Introduction

The linearized Euler equations (LEE) are often used as the mathematical model to simulate acoustic propagation. An alternative to the LEE is the acoustic perturbation equation (APE).[1] High-order methods are necessary to achieve the desirable accuracy of acoustic simulations. It allows one to reach high-order accuracy while maintaining the ability to deal with complex geometries. This is achieved by combining features of the finite element method (high-order solution) and finite volume method (local element-based solution). Examples of the successful application of DGM to acoustic problems are Reymen et al.[4] or Bauer et al.[5] In Reymen et al.,[4] the DGM was applied to three-dimensional (3D) acoustic pulse propagation problem to analyse the convergence rate of the method. Different meshing algorithms were tested to analyse the effect of the computational mesh on the convergence rate of the method

Objectives

Conclusion