Comptes Rendus
no. 10
Numerical Analysis
New constructions of perfectly matched layers for the linearized Euler equations
[Nouvelles constructions de couches parfaitement adaptées pour le systéme d'Euler linéarisé]

Présenté par : Olivier Pironneau

Frédéric Nataf1
1 CMAP, École polytechnique, 91128 Palaiseau cedex, France
Comptes Rendus. Mathématique, Volume 340 (2005) no. 10, pp. 775-778.

A partir d'une couche adaptée pour l'équation des ondes advectives, nous proposons deux modèles de telles couches pour les équations d'Euler linéarisées. La construction du premier modèle peut être appliqué à d'autres systèmes d'équations aux dérivées partielles. Le second modèle a été implémenté. Des résultats numériques illustrent l'intérêt de cette construction.

Based on a PML for the advective wave equation, we propose two PML models for the linearized Euler equations. The derivation of the first model can be applied to other physical models. The second model was implemented. Numerical results are shown.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.04.013
Frédéric Nataf 1

1 CMAP, École polytechnique, 91128 Palaiseau cedex, France 
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Frédéric Nataf. New constructions of perfectly matched layers for the linearized Euler equations. Comptes Rendus. Mathématique, Volume 340 (2005) no. 10, pp. 775-778. doi : 10.1016/j.crma.2005.04.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.04.013/

[1] E. Bécache; A.-S. Bonnet-Ben Dhia; G. Legendre Perfectly matched layers for the convected Helmholtz equation, SIAM J. Numer. Anal., Volume 42 (2004) no. 1, pp. 409-433 (electronic)

[2] J.P. Berenger A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., Volume 114 (1994) no. 2

[3] J. Diaz; P. Joly Stabilized perfectly matched layer for advective acoustics, Mathematical and Numerical Aspects of Wave Propagation—WAVES 2003, Springer, Berlin, 2003, pp. 115-119

[4] Th. Hagstrom A new construction of perfectly matched layers for hyperbolic systems with applications to the linearized Euler equations, Mathematical and Numerical Aspects of Wave Propagation—WAVES 2003, Springer, 2003, pp. 125-129

[5] F. Nataf A new construction of perfectly matched layers for the linearized Euler equations http://www.cmap.polytechnique.fr/preprint/repository/566.pdf (submitted for publication)

[6] A.N. Rahmouni An algebraic method to develop well-posed PML models. Absorbing layers, perfectly matched layers, linearized Euler equations, J. Comput. Phys., Volume 197 (2004) no. 1, pp. 99-115

[7] J.T. Wloka; B. Rowley; B. Lawruk Boundary Value Problems for Elliptic Systems, Cambridge University Press, Cambridge, 1995

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