A dissipation-free time domain Discontinuous Galerkin method applied to three dimensional linearized Euler equations around a steady-state non uniform inviscid flow - École des Ponts ParisTech Accéder directement au contenu
Article Dans Une Revue Journal of Computational Acoustics Année : 2006

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

Résumé

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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Dates et versions

hal-00607713 , version 1 (11-07-2011)

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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, 2006, 14 (4), pp.445-467. ⟨10.1142/S0218396X0600313X⟩. ⟨hal-00607713⟩
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