https://hal-mines-paristech.archives-ouvertes.fr/hal-01858317Piperno, SergeSergePipernoCERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École des Ponts ParisTechBernacki, MarcMarcBernackiCEMEF - Centre de Mise en Forme des Matériaux - MINES ParisTech - École nationale supérieure des mines de Paris - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche ScientifiqueStabilization of Kelvin-Helmholtz instabilities in 3D linearized Euler equations using a non-dissipative discontinuous Galerkin methodHAL CCSD2006aeroacousticsacoustic energylinearized Euler equationsnon-uniform steady-state flowDiscontinuous Galerkin methodtime domainenergy-conservation[SPI.MECA.MEFL] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph][SPI.MAT] Engineering Sciences [physics]/MaterialsBernacki, Marc2018-09-11 10:00:482022-01-12 09:08:022018-09-13 14:25:11enConference papersapplication/pdf1We 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 non-uniform 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. Moreover, there exists a correction term in aeroacoustic variables such that the aeroacoustic energy is exactly preserved, and therefore the stability of the scheme can be proved. This leads to a new filtering of Kelvin-Helmholtz instabilities. 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 and can be eliminated by addition of the source term.