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Performance of the DGM for the linearized Euler equations with non-uniform mean-flow

Performance of the DGM for the linearized Euler equations with non-uniform mean-flow
Performance of the DGM for the linearized Euler equations with non-uniform mean-flow
A dispersion analysis of the fully-discrete, nodal discontinuous Galerkin method (DGM) for the solution of the time-domain linearized Euler equations (LEE) is performed. Two dispersion analysis methods are developed, considering both uniform and non-uniform mean-flow effects. Convergence studies are performed for the dispersion, dissipation, and nodal solution errors of the acoustic, entropy, and vorticity modes. The accuracy and stability of the DGM are analyzed in the context of aeroacoustic applications, and guidelines are proposed for the choice of optimal discretizations. Computational costs are estimated for a model problem and related to the choice of the element size, polynomial order, and time step. Results indicate that temporal error can become a dominant source of error for high accuracy requirements and long distance wave propagation. The stability of the scheme is analyzed for a shear layer mean flow profile. Aliasing-type errors are found to contribute to the formation of numerical instabilities which are further strengthened by increases in the polynomial order.
Williamschen, Michael
021ce84d-c07d-4a48-9d8e-5cc38d6ccc23
Gabard, Gwenael
bfd82aee-20f2-4e2c-ad92-087dc8ff6ce7
Beriot, Hadrien
af5a12ac-8347-48b9-9e15-9319a59163a9
Williamschen, Michael
021ce84d-c07d-4a48-9d8e-5cc38d6ccc23
Gabard, Gwenael
bfd82aee-20f2-4e2c-ad92-087dc8ff6ce7
Beriot, Hadrien
af5a12ac-8347-48b9-9e15-9319a59163a9

Williamschen, Michael, Gabard, Gwenael and Beriot, Hadrien (2015) Performance of the DGM for the linearized Euler equations with non-uniform mean-flow. 21st AIAA/CEAS Aeroacoustics Conference, United States. 22 - 25 Jun 2015. 18 pp . (doi:10.2514/6.2015-3277).

Record type: Conference or Workshop Item (Paper)

Abstract

A dispersion analysis of the fully-discrete, nodal discontinuous Galerkin method (DGM) for the solution of the time-domain linearized Euler equations (LEE) is performed. Two dispersion analysis methods are developed, considering both uniform and non-uniform mean-flow effects. Convergence studies are performed for the dispersion, dissipation, and nodal solution errors of the acoustic, entropy, and vorticity modes. The accuracy and stability of the DGM are analyzed in the context of aeroacoustic applications, and guidelines are proposed for the choice of optimal discretizations. Computational costs are estimated for a model problem and related to the choice of the element size, polynomial order, and time step. Results indicate that temporal error can become a dominant source of error for high accuracy requirements and long distance wave propagation. The stability of the scheme is analyzed for a shear layer mean flow profile. Aliasing-type errors are found to contribute to the formation of numerical instabilities which are further strengthened by increases in the polynomial order.

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e-pub ahead of print date: 18 June 2015
Published date: 18 June 2015
Venue - Dates: 21st AIAA/CEAS Aeroacoustics Conference, United States, 2015-06-22 - 2015-06-25
Organisations: Acoustics Group

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Local EPrints ID: 381471
URI: https://eprints.soton.ac.uk/id/eprint/381471
PURE UUID: 2c3c67e5-49ee-4b30-b7bc-12be2efa6ffc

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Date deposited: 29 Sep 2015 10:48
Last modified: 19 Jul 2019 20:33

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