The University of Southampton
University of Southampton Institutional Repository

Discontinuous Galerkin methods with plane waves for the displacement-based acoustic equation

Discontinuous Galerkin methods with plane waves for the displacement-based acoustic equation
Discontinuous Galerkin methods with plane waves for the displacement-based acoustic equation
Several special finite element methods have been proposed to solve Helmholtz problems in the mid-frequency regime, such as the Partition of Unity Method, the Ultra Weak Variational Formulation and the Discontinuous Enrichment Method. The first main purpose of this paper is to present a discontinuous Galerkin method with plane waves (which is a variant of the Discontinuous Enrichment Method) to solve the displacement-based acoustic equation. The use of the displacement variable is often necessary in the context of fluid–structure interactions. A well-known issue with this model is the presence of spurious vortical modes when one uses standard finite elements such as Lagrange elements. This problem, also known as the locking phenomenon, is observed with several other vector based equations such as incompressible elasticity and electromagnetism. So this paper also aims at assessing if the special finite element methods suffer from the locking phenomenon in the context of the displacement acoustic equation. The discontinuous Galerkin method presented in this paper is shown to be very accurate and stable, i.e. no spurious modes are observed. The optimal choice of the various parameters are discussed with regards to numerical accuracy and conditioning. Some interesting properties of the mixed displacement–pressure formulation are also presented. Furthermore, the use of the Partition of Unity Method is also presented, but it is found that spurious vortical modes may appear with this method.
0029-5981
549-569
Gabard, G.
bfd82aee-20f2-4e2c-ad92-087dc8ff6ce7
Gabard, G.
bfd82aee-20f2-4e2c-ad92-087dc8ff6ce7

Gabard, G. (2006) Discontinuous Galerkin methods with plane waves for the displacement-based acoustic equation. International Journal for Numerical Methods in Engineering, 66, 549-569. (doi:10.1002/nme.1571).

Record type: Article

Abstract

Several special finite element methods have been proposed to solve Helmholtz problems in the mid-frequency regime, such as the Partition of Unity Method, the Ultra Weak Variational Formulation and the Discontinuous Enrichment Method. The first main purpose of this paper is to present a discontinuous Galerkin method with plane waves (which is a variant of the Discontinuous Enrichment Method) to solve the displacement-based acoustic equation. The use of the displacement variable is often necessary in the context of fluid–structure interactions. A well-known issue with this model is the presence of spurious vortical modes when one uses standard finite elements such as Lagrange elements. This problem, also known as the locking phenomenon, is observed with several other vector based equations such as incompressible elasticity and electromagnetism. So this paper also aims at assessing if the special finite element methods suffer from the locking phenomenon in the context of the displacement acoustic equation. The discontinuous Galerkin method presented in this paper is shown to be very accurate and stable, i.e. no spurious modes are observed. The optimal choice of the various parameters are discussed with regards to numerical accuracy and conditioning. Some interesting properties of the mixed displacement–pressure formulation are also presented. Furthermore, the use of the Partition of Unity Method is also presented, but it is found that spurious vortical modes may appear with this method.

Text
gabard06b.pdf - Version of Record
Restricted to Repository staff only
Request a copy

More information

Published date: 2006
Organisations: Acoustics Group

Identifiers

Local EPrints ID: 28388
URI: https://eprints.soton.ac.uk/id/eprint/28388
ISSN: 0029-5981
PURE UUID: a35df2ac-48cc-4d5c-b9c5-3d7bdf3f96fa

Catalogue record

Date deposited: 02 May 2006
Last modified: 07 Oct 2019 17:50

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of https://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×