IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Hexagonal Fourier-Galerkin Spectral Methods for Two-Dimensional Homogeneous Isotropic Decaying Turbulence

  • April 15, 2013
  • 2 p.m.
  • LeConte 312

Abstract

In this paper, we propose the hexagonal Fourier-Galkerin methods for the direct numerical simulation of the decay of two-dimensional homogeneous isotropic turbulence. We first establish the lattice Fourier analysis as a mathematical foundation. Then a universal approximation scheme is devised for our hexagonal Fourier-Galkerin method and the dual hexagonal Fourier-Galkerin method for Navier-Stokes equations in the vorticity-velocity form. The implementations of the lattice and the dual hexagonal Fourier-Galkerin methods on GPU platform are discussed in detail. Numerical experiments mainly concentrate on the decaying properties and the self-similar spectra of the two-dimensional homogeneous turbulences 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-Galkerin methods are as efficient as the classic square Fourier-Galkerin method, while provide more effective statistical quantities in general.

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