TY - JOUR
T1 - Hexagonal Fourier-Galerkin Methods for the Two-Dimensional Homogeneous Isotropic Decaying Turbulence
AU - Li , Huiyuan
JO - Journal of Mathematical Study
VL - 1
SP - 21
EP - 46
PY - 2014
DA - 2014/03
SN - 47
DO - http://doi.org/10.4208/jms.v47n1.14.02
UR - https://global-sci.org/intro/article_detail/jms/9948.html
KW - Fourier-Galerkin methods, hexagonal lattices, homogeneous isotropic turbulence, direct numerical simulation.
AB - <p style="text-align: justify;">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 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-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.</p>