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

Journal Article · Tue Apr 10 04:00:00 EDT 2007 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2006.09.005· OSTI ID:20991571

Chevaugeon, Nicolas ^[1]; Hillewaert, Koen ^[2]; Gallez, Xavier ^[3]; Ploumhans, Paul ^[3]; Remacle, Jean-Francois ^[4]

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1. Universite catholique de Louvain, Department of Civil Engineering, Place du Levant 1, 1348 Louvain-la-Neuve (Belgium)
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)

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.

• OSTI ID: 20991571
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 1 Vol. 223; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ACCURACY
ACOUSTICS
CONVERGENCE
ERRORS
ONE-DIMENSIONAL CALCULATIONS
POLYNOMIALS
WAVE PROPAGATION