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

Authors:
Nicolas Chevaugeon;Koen Hillewaert;Xavier Gallez;Paul Ploumhans;Jean-François Remacle
Affiliations:
Université catholique de Louvain, Department of Civil Engineering, Place du Levant 1, 1348 Louvain-la-Neuve, Belgium;CENAERO CFD and Multiphysics Group, Bítiment Mermoz 1, Av. J. Mermoz 30, b: 6041 Gosselies, Belgium;Free Field Technologies SA, Place de l'Université, 1348 Louvain-la-Neuve, Belgium;Free Field Technologies SA, Place de l'Université, 1348 Louvain-la-Neuve, Belgium;Université 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), Univers ...
Venue:
Journal of Computational Physics
Year:
2007

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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.