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EDP Sciences, ESAIM: Proceedings, (29), p. 89-107

DOI: 10.1051/proc/2009057

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Wavelet Regularization of a Fourier-Galerkin Method for Solving the 2d Incompressible Euler Equations

Journal article published in 2009 by Romain Nguyen van yen, Nguyen R. Yen, Romain Nguyen van Yen, Marie Farge ORCID, Kai Schneider,
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

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 L 2 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 L 2 convergence to the reference solution without any regularization, in contrast to what is obtained for the 1D Burgers equation.