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Time-domain parallel simulation of heterogeneous wave propagation on unstructured grids using explicit, non-diffusive, discontinuous Galerkin methods

Marc Bernacki 1 Stephane Lanteri 1 Serge Piperno 2
1 CAIMAN - Scientific computing, modeling and numerical analysis
CRISAM - Inria Sophia Antipolis - Méditerranée , ENPC - École des Ponts ParisTech, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : A general Discontinuous Calerkin framework is introduced for symmetric systems of conservations laws. It is applied to the three-dimensional electromagnetic wave propagation in heterogeneous media, and to the propagation of aeroacoustic perturbations of either uniform or nonuniform, steady solutions of the three-dimensional Euler equations. In all these linear contexts, the time evolution of some quadratic wave energy is given in a balance equation, with a volumic source term for aeroacoustics in a nonuniform flow. An explicit leap-frog time scheme along with centered numerical fluxes are used in the proposed Discontinuous Galerkin Time Domain (DGTD) method, in order to achieve a discrete equivalent of the balance equation for the wave energy. The scheme introduced is genuinely nondissipative. Numerical first-order boundary conditions are developed to bound the domain and stability is proved on arbitrary unstructured meshes and discontinuous finite elements, under some CFL-like stability condition on the time step. Numerical results obtained with a parallel implementation of the method based on mesh partitioning and message passing are presented to show the potential of the method.
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Submitted on : Monday, July 11, 2011 - 10:05:54 AM
Last modification on : Thursday, February 3, 2022 - 11:15:46 AM

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Marc Bernacki, Stephane Lanteri, Serge Piperno. Time-domain parallel simulation of heterogeneous wave propagation on unstructured grids using explicit, non-diffusive, discontinuous Galerkin methods. Journal of Computational Acoustics, World Scientific Publishing, 2006, 14 (1), pp.57-82. ⟨10.1142/S0218396X06002937⟩. ⟨hal-00607725⟩

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