Numerical Eulerian method for linearized gas dynamics in the high frequency regime

Youness Noumir; François Dubois; Olivier Lafitte

hal-00713031, version 1

Numerical Eulerian method for linearized gas dynamics in the high frequency regime

Youness Noumir ¹, François Dubois ^2, 3, Olivier Lafitte ¹

(2011-12-22)

Abstract: We study the propagation of an acoustic wave in amoving fluid in the high frequency regime. We calculate a high-frequency approximation of the solution of this problemusing an Eulerianmethod. The model retained is a linearized Euler system around a mean fluid flow. For any regular mean flow, we derive a conservative transport equation for the geometrical optics approximation. We introduce the stretching matrix corresponding to this system, from which we deduce the geometrical spreading, key tool for computing the geometrical optics approximation. Finally, we construct and implement a numerical scheme in the Eulerian framework for the eikonal equation. This Eulerian formulation applies also for the transport equation on the stretching matrix.

1: Laboratoire Analyse, Géométrie et Application (LAGA)
CNRS : UMR7539 – Université Paris XIII - Paris Nord – Université Paris VIII - Vincennes Saint-Denis
2: Laboratoire de Mathématiques d'Orsay (LM-Orsay)
CNRS : UMR8628 – Université Paris XI - Paris Sud
3: Conservatoire National des Arts et Métiers (CNAM Paris)
Conservatoire National des Arts et Métiers (CNAM)

hal-00713031, version 1
http://hal.archives-ouvertes.fr/hal-00713031
oai:hal.archives-ouvertes.fr:hal-00713031
From: Younes Nou <>
Submitted on: Thursday, 28 June 2012 20:36:52
Updated on: Friday, 29 June 2012 08:39:00

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