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Title: Optimal numerical parameterization of discontinuous Galerkin method applied to wave propagation problems

Abstract

This paper deals with the high-order discontinuous Galerkin (DG) method for solving wave propagation problems. First, we develop a one-dimensional DG scheme and numerically compute dissipation and dispersion errors for various polynomial orders. An optimal combination of time stepping scheme together with the high-order DG spatial scheme is presented. It is shown that using a time stepping scheme with the same formal accuracy as the DG scheme is too expensive for the range of wave numbers that is relevant for practical applications. An efficient implementation of a high-order DG method in three dimensions is presented. Using 1D convergence results, we further show how to adequately choose elementary polynomial orders in order to equi-distribute a priori the discretization error. We also show a straightforward manner to allow variable polynomial orders in a DG scheme. We finally propose some numerical examples in the field of aero-acoustics.

Authors:
 [1];  [2];  [3];  [3];  [4]
  1. Universite catholique de Louvain, Department of Civil Engineering, Place du Levant 1, 1348 Louvain-la-Neuve (Belgium). E-mail: chevaugeon@gce.ucl.ac.be
  2. CENAERO CFD and Multiphysics Group, Batiment Mermoz 1, Av. J. Mermoz 30, b: 6041 Gosselies (Belgium)
  3. Free Field Technologies SA, Place de l'Universite, 1348 Louvain-la-Neuve (Belgium)
  4. Universite catholique de Louvain, Department of Civil Engineering, Place du Levant 1, 1348 Louvain-la-Neuve (Belgium) and Center for Systems Engineering and Applied Mechanics (CESAME), Universite catholique de Louvain, 1348 Louvain-la-Neuve (Belgium). E-mail: remacle@gce.ucl.ac.be
Publication Date:
OSTI Identifier:
20991571
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 223; Journal Issue: 1; Other Information: DOI: 10.1016/j.jcp.2006.09.005; PII: S0021-9991(06)00432-3; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; ACOUSTICS; CONVERGENCE; ERRORS; ONE-DIMENSIONAL CALCULATIONS; POLYNOMIALS; WAVE PROPAGATION

Citation Formats

Chevaugeon, Nicolas, Hillewaert, Koen, Gallez, Xavier, Ploumhans, Paul, and Remacle, Jean-Francois. Optimal numerical parameterization of discontinuous Galerkin method applied to wave propagation problems. United States: N. p., 2007. Web. doi:10.1016/j.jcp.2006.09.005.
Chevaugeon, Nicolas, Hillewaert, Koen, Gallez, Xavier, Ploumhans, Paul, & Remacle, Jean-Francois. Optimal numerical parameterization of discontinuous Galerkin method applied to wave propagation problems. United States. doi:10.1016/j.jcp.2006.09.005.
Chevaugeon, Nicolas, Hillewaert, Koen, Gallez, Xavier, Ploumhans, Paul, and Remacle, Jean-Francois. Tue . "Optimal numerical parameterization of discontinuous Galerkin method applied to wave propagation problems". United States. doi:10.1016/j.jcp.2006.09.005.
@article{osti_20991571,
title = {Optimal numerical parameterization of discontinuous Galerkin method applied to wave propagation problems},
author = {Chevaugeon, Nicolas and Hillewaert, Koen and Gallez, Xavier and Ploumhans, Paul and Remacle, Jean-Francois},
abstractNote = {This paper deals with the high-order discontinuous Galerkin (DG) method for solving wave propagation problems. First, we develop a one-dimensional DG scheme and numerically compute dissipation and dispersion errors for various polynomial orders. An optimal combination of time stepping scheme together with the high-order DG spatial scheme is presented. It is shown that using a time stepping scheme with the same formal accuracy as the DG scheme is too expensive for the range of wave numbers that is relevant for practical applications. An efficient implementation of a high-order DG method in three dimensions is presented. Using 1D convergence results, we further show how to adequately choose elementary polynomial orders in order to equi-distribute a priori the discretization error. We also show a straightforward manner to allow variable polynomial orders in a DG scheme. We finally propose some numerical examples in the field of aero-acoustics.},
doi = {10.1016/j.jcp.2006.09.005},
journal = {Journal of Computational Physics},
number = 1,
volume = 223,
place = {United States},
year = {Tue Apr 10 00:00:00 EDT 2007},
month = {Tue Apr 10 00:00:00 EDT 2007}
}