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Dicontinuous Galerking methods for the aeroacoustic waves propagation

Marc Bernacki 
Abstract : This work is devoted to the numerical solution of three-dimensional linearized Euler equations around steady-state, smooth, subsonic flows. In order to get symmetric matrices for these equations and, in fine, an energy balance equation, we consider the linearization of symmetrized Euler equations. We propose a non-dissipative Discontinuous Galerkin Time-Domain (DGTD) method which relies on an element-centered formulation with centered numerical fluxes and an explicit leap-frog time scheme, leading to a dissipation-free approximation and allowing an accurate estimation of the aeroacoustic energy variation. Indeed, in the general case of the linearization around a non-uniform flow, a balance equation with source term for the aeroacoustic energy is also verified at the discrete level. We show that there exists a discrete source term such that the energy is exactly conserved and the stability of the scheme can be proved. Therefore the non-dissipative DGTD method provides an accurate tool for controlling phenomena like Kelvin-Helmholtz instabilities. We illustrate the efficiency of our method on many academic test cases as well as on various complex configurations thanks to a parallel implementation.
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Submitted on : Thursday, December 22, 2005 - 8:00:00 AM
Last modification on : Wednesday, January 12, 2022 - 9:08:01 AM
Long-term archiving on: : Thursday, September 30, 2010 - 7:12:18 PM


  • HAL Id : pastel-00001518, version 1



Marc Bernacki. Dicontinuous Galerking methods for the aeroacoustic waves propagation. Mathematics [math]. Ecole des Ponts ParisTech, 2005. English. ⟨pastel-00001518⟩



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