Volume 47, Issue 1
Hexagonal Fourier-Galerkin Methods for the Two-Dimensional Homogeneous Isotropic Decaying Turbulence

Huiyuan Li

10.4208/jms.v47n1.14.02

J. Math. Study, 47 (2014), pp. 21-46.

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  • Abstract

In this paper, we propose two hexagonal Fourier-Galerkin methods for the direct numerical simulation of the two-dimensional homogeneous isotropic decaying turbulence. We first establish the lattice Fourier analysis as a mathematical founda- tion. Then a universal approximation scheme is devised for our hexagonal Fourier- Galerkin methods for Navier-Stokes equations. Numerical experiments mainly con- centrate on the decaying properties and the self-similar spectra of the two-dimensional homogeneous turbulence at various initial Reynolds numbers with an initial flow field governed by a Gaussian-distributed energy spectrum. Numerical results demonstrate that both the hexagonal Fourier-Galerkin methods are as efficient as the classic square Fourier-Galerkin method, while provide more effective statistical physical quantities in general.

  • History

Published online: 2014-03

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