Journal of Computational Acoustics, fc IMACS A DISSIPATION-FREE TIME-DOMAIN DISCONTINUOUS GALERKIN METHOD APPLIED TO THREE-DIMENSIONAL LINEARIZED EULER EQUATIONS

Received (to be inserted Revised by Publisher) 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 so-lution. In the general context of a non-uniform supporting ow, we prove, using the well-known symmetrization of Euler equations, that some aeroacoustic energy satises a balance equation with source term at the continuous level, and that our numerical framework satises an equivalent bal-ance equation at the discrete level and is genuinely dissipation-free. In the case of P1 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 con rm the theoretical properties of the method. They include test-cases where Kelvin-Helmholtz instabilities appear