Bernacki, Marc (2005) Dicontinuous Galerking methods for the aeroacoustic waves propagation. PhD thesis, ENPC.
Full text available as:
|
|
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.
| Item Type: | PhD Thesis (PhD) |
|---|---|
| Thesis Supervisor: | Piperno, S |
| Date: | September 2005 |
| Board of examiners: | Bailly, C and Ehrenstein, U and Ern, A and Pironneau, S and Terrasse, I and Piperno, S |
| Collection (Fonds): | ENPC |
| Institution: | ENPC |
| Subjects: | 1. Mathematics and Applications |
| Uncontrolled Keywords: | Aeroacoustics, linearized Euler equations, Steady-state non-uniform or uniform flow, Unstructured meshes, non-dissipative time-domain discontinous Galerkin method, Energy balance equation, Kelvin-Helmholtz instabilities, Parallel implementation., Aéroacoustique, équations d'Euler linéarisées, écoulement stationnaire uniforme ou non, Maillages non structurés, méthode de type Galerkin discontinu en domaine temporel, Méthode non-dissipative, équation d'équilibre énergétique, instabilités de Kelvin- Helmholtz, Implémentation paralléle. |
| ID Code: | 1518 |
| Deposited By: | Christiane Baudry |
| Deposited On: | 22 December 2005 |
Repository Staff Only: edit this item