Hexagonal Fourier-Galerkin Methods for the Two-Dimensional Homogeneous Isotropic Decaying Turbulence (Journal of Mathematical Study, 2014)
In this paper, we propose two hexagonal Fourier-Galerkin methods for thedirect numerical simulation of the two-dimensional homogeneous isotropic decayingturbulence. We first establish the lattice Fourier analysis as a mathematical foundation. Then a universal approximation scheme is devised for our hexagonal Fourier-Galerkin methods for Navier-Stokes equations. Numerical experiments mainly concentrate on the decaying properties and the self-similar spectra of the two-dimensionalhomogeneous turbulence at various initial Reynolds numbers with an initial flow fieldgoverned by a Gaussian-distributed energy spectrum. Numerical results demonstratethat both the hexagonal Fourier-Galerkin methods are as efficient as the classic squareFourier-Galerkin method, while provide more effective statistical physical quantitiesin general.