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

Huiyuan Li

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

Published online: 2014-03

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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.

  • Keywords

Fourier-Galerkin methods hexagonal lattices homogeneous isotropic turbulence direct numerical simulation.

  • AMS Subject Headings

65M70, 65T50, 76F05, 76F65, 76M22

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

huiyuan@iscas.ac.cn (Huiyuan Li)

  • BibTex
  • RIS
  • TXT
@Article{JMS-47-21, author = {Li , Huiyuan}, title = {Hexagonal Fourier-Galerkin Methods for the Two-Dimensional Homogeneous Isotropic Decaying Turbulence}, journal = {Journal of Mathematical Study}, year = {2014}, volume = {47}, number = {1}, pages = {21--46}, 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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v47n1.14.02}, url = {http://global-sci.org/intro/article_detail/jms/9948.html} }
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 KW - hexagonal lattices KW - homogeneous isotropic turbulence KW - direct numerical simulation. AB -

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.

Huiyuan Li. (2019). Hexagonal Fourier-Galerkin Methods for the Two-Dimensional Homogeneous Isotropic Decaying Turbulence. Journal of Mathematical Study. 47 (1). 21-46. doi:10.4208/jms.v47n1.14.02
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