[Approximations rigoureuses stables par différences finies pour l'aéroacoustique numérique]
Des schémas d'approximation par différences finies d'ordre élevé ont été développés pour l'aéroacoustique numérique dans le but d'accroître la précision et la stabilité. L'une de nos méthodes correspond au schéma de Tam et Webb, à l'intérieur du domaine, avec une modification aux limites du domaine qui permet d'obtenir une stabilité rigoureuse. Notre approche repose sur l'unification des équations non linéaires d'Euler et de leur forme linéarisée. Cette même approche pourrait être appliquée aux équations de Navier–Stokes. A titre d'exemple, la méthode est appliquée ici à des problèmes à une et deux dimensions, ainsi qu'à un problème axisymétrique. Un exemple simule l'acoustique induite par une fusée avant décollage.
High order finite difference approximations with improved accuracy and stability properties have been developed for computational aeroacoustics (CAA). One of our new difference operators corresponds to Tam and Webb's DRP scheme in the interior, but is modified near the boundaries to be strictly stable. A unified formulation of the nonlinear and linearized Euler equations is used, which can be extended to the Navier–Stokes equations. The approach has been verified for 1D, 2D and axisymmetric test problems. We have simulated the sound propagation from a rocket launch before lift-off.
Mot clés : Acoustique, Méthodes de différences finies, D'ordre élevée, Aéroacoustique
@article{CRMECA_2005__333_9_699_0,
author = {Bernhard M\"uller and Stefan Johansson},
title = {Strictly stable high order difference approximations for computational aeroacoustics},
journal = {Comptes Rendus. M\'ecanique},
pages = {699--705},
publisher = {Elsevier},
volume = {333},
number = {9},
year = {2005},
doi = {10.1016/j.crme.2005.07.009},
language = {en},
}
TY - JOUR AU - Bernhard Müller AU - Stefan Johansson TI - Strictly stable high order difference approximations for computational aeroacoustics JO - Comptes Rendus. Mécanique PY - 2005 SP - 699 EP - 705 VL - 333 IS - 9 PB - Elsevier DO - 10.1016/j.crme.2005.07.009 LA - en ID - CRMECA_2005__333_9_699_0 ER -
Bernhard Müller; Stefan Johansson. Strictly stable high order difference approximations for computational aeroacoustics. Comptes Rendus. Mécanique, Volume 333 (2005) no. 9, pp. 699-705. doi : 10.1016/j.crme.2005.07.009. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2005.07.009/
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