Lorentz Transform and Staggered Finite Differences for Advective Acoustics

François Dubois (1) , Eric Duceau (2) , Frédéric Marechal (2, 3) , Isabelle Terrasse (2)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 European Aeronautics Defence and Space Compagny
3 ENPC - École des Ponts ParisTech

We study acoustic wave propagation in a uniform stationary flow. We develop a method founded on the Lorentz transform and a hypothesis of irrotationality of the acoustic perturbation. After a transformation of the space-time and of the unknown fields, we derive a system of partial differential equations that eliminates the external flow and deals with the classical case of non advective acoustics. A sequel of the analysis is a new set of perfectly matched layers equations in the spirit of the work of Berenger and Collino. The numerical implementation of the previous ideas is presented with the finite differences method HaWAY on cartesian staggered grids. Relevant numerical tests are proposed.

Mots clés: Perfectly matched layers; finite differences; HaWAY method

Domaines: Analyse numérique [math.NA]

François Dubois, Eric Duceau, Frédéric Marechal, Isabelle Terrasse. Lorentz Transform and Staggered Finite Differences for Advective Acoustics. 2002. ⟨hal-00591143⟩