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Discontinuous Galerkin methods with plane waves for time-harmonic problems

Discontinuous Galerkin methods with plane waves for time-harmonic problems
Discontinuous Galerkin methods with plane waves for time-harmonic problems
A general framework for discontinuous Galerkin methods in the frequency domain with numerical flux is presented. The main feature of the method is the use of plane waves instead of polynomials to approximate the solution in each element. The method is formulated for a general system of linear hyperbolic equations and is applied to problems of aeroacoustic propagation by solving the two-dimensional linearized Euler equations. It is found that the method requires only a small number of elements per wavelength to obtain accurate solutions and that it is more efficient than high-order DRP schemes. In addition, the conditioning of the method is found to be high but not critical in practice. It is shown that the Ultra-Weak Variational Formulation is in fact a subset of the present discontinuous Galerkin method. A special extension of the method is devised in order to deal with singular solutions generated by point sources like monopoles or dipoles. Aeroacoustic problems with non-uniform flows are also considered and results are presented for the sound radiated from a two-dimensional jet.
discontinuous galerkin methods, plane wave, aeroacoustics
0021-9991
1961-1984
Gabard, G.
bfd82aee-20f2-4e2c-ad92-087dc8ff6ce7
Gabard, G.
bfd82aee-20f2-4e2c-ad92-087dc8ff6ce7

Gabard, G. (2007) Discontinuous Galerkin methods with plane waves for time-harmonic problems. Journal of Computational Physics, 225 (2), 1961-1984. (doi:10.1016/j.jcp.2007.02.030).

Record type: Article

Abstract

A general framework for discontinuous Galerkin methods in the frequency domain with numerical flux is presented. The main feature of the method is the use of plane waves instead of polynomials to approximate the solution in each element. The method is formulated for a general system of linear hyperbolic equations and is applied to problems of aeroacoustic propagation by solving the two-dimensional linearized Euler equations. It is found that the method requires only a small number of elements per wavelength to obtain accurate solutions and that it is more efficient than high-order DRP schemes. In addition, the conditioning of the method is found to be high but not critical in practice. It is shown that the Ultra-Weak Variational Formulation is in fact a subset of the present discontinuous Galerkin method. A special extension of the method is devised in order to deal with singular solutions generated by point sources like monopoles or dipoles. Aeroacoustic problems with non-uniform flows are also considered and results are presented for the sound radiated from a two-dimensional jet.

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Published date: 10 August 2007
Keywords: discontinuous galerkin methods, plane wave, aeroacoustics
Organisations: Acoustics Group

Identifiers

Local EPrints ID: 48141
URI: https://eprints.soton.ac.uk/id/eprint/48141
ISSN: 0021-9991
PURE UUID: aacb2763-ee18-41e5-bf05-3828a6981833

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Date deposited: 30 Aug 2007
Last modified: 13 Mar 2019 20:57

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