Geodesic
Wavelet regularization of a Fourier-Galerkin method for solving the 2D incompressible Euler equations
R. Nguyen van yen1 ; M. Farge1 ; K. Schneider2
1 Laboratoire de Météorologie Dynamique-IPSL-CNRS, École Normale Supérieure, Paris, France; e-mail: rnguyen@lmd.ens.fr
2 Centre de Mathématiques et d'Informatique, Université d'Aix-Marseille, France
ESAIM. Proceedings, Tome 29 (2009), pp. 89-107.

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We employ a Fourier-Galerkin method to solve the 2D incompressible Euler equations, and study several ways to regularize the solution by wavelet filtering at each timestep. Real-valued orthogonal wavelets and complex-valued wavelets are considered, combined with either linear or nonlinear filtering. The results are compared with those obtained via classical viscous and hyperviscous regularization methods. Wavelet regularization using complex-valued wavelets performs as well in terms of L2 convergence rate to the reference solution. The compression rate for homogeneous 2D turbulence is around 3 for this method, suggesting that memory and CPU time could be reduced in an adaptive wavelet computation. Our results also suggest L2 convergence to the reference solution without any regularization, in contrast to what is obtained for the 1D Burgers equation.
DOI : 10.1051/proc/2009057

R. Nguyen van yen 1 ; M. Farge 1 ; K. Schneider 2

1 Laboratoire de Météorologie Dynamique-IPSL-CNRS, École Normale Supérieure, Paris, France; e-mail: rnguyen@lmd.ens.fr
2 Centre de Mathématiques et d'Informatique, Université d'Aix-Marseille, France 
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     title = {Wavelet regularization of a {Fourier-Galerkin} method for solving the {2D} incompressible {Euler} equations},
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R. Nguyen van yen; M. Farge; K. Schneider. Wavelet regularization of a Fourier-Galerkin method for solving the 2D incompressible Euler equations. ESAIM. Proceedings, Tome 29 (2009), pp. 89-107. doi : 10.1051/proc/2009057. http://geodesic.mathdoc.fr/articles/10.1051/proc/2009057/

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