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A dissipation-free time domain Discontinuous Galerkin method applied to three dimensional linearized Euler equations around a steady-state non uniform inviscid flow

Marc Bernacki 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 : We present in this paper a time-domain discontinuous Galerkin dissipation-free method for the transient solution of the three-dimensional linearized Euler equations around a steady-state solution. In the general context of a nonuniform supporting flow, we prove, using the well-known symmetrization of Euler equations, that some aeroacoustic energy satisfies a balance equation with source term at the continuous level, and that our numerical framework satisfies an equivalent balance equation at the discrete level and is genuinely dissipation-free. In the case of P-1 Lagrange basis functions and tetrahedral unstructured meshes, a parallel implementation of the method has been developed, based on message passing and mesh partitioning. Three-dimensional numerical results confirm the theoretical properties of the method. They include test-cases where Kelvin-Helmholtz instabilities appear.
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https://hal-enpc.archives-ouvertes.fr/hal-00607713
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Soumis le : lundi 11 juillet 2011 - 09:33:41
Dernière modification le : jeudi 9 janvier 2020 - 01:23:17

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Marc Bernacki, Serge Piperno. A dissipation-free time domain Discontinuous Galerkin method applied to three dimensional linearized Euler equations around a steady-state non uniform inviscid flow. Journal of Computational Acoustics, World Scientific Publishing, 2006, 14 (4), pp.445-467. ⟨10.1142/S0218396X0600313X⟩. ⟨hal-00607713⟩

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