Commun. Comput. Phys., 9 (2011), pp. 1152-1164.


A Memory-Saving Algorithm for Spectral Method of Three-Dimensional Homogeneous Isotropic Turbulence

Qing-Dong Cai 1, Shiyi Chen 2*

1 LTCS and CAPT, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China.
2 LTCS and CAPT, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China; and Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, Maryland 21218, USA.

Received 19 December 2009; Accepted (in revised version) 11 November 2010
Available online 14 January 2011
doi:10.4208/cicp.191209.111110s

Abstract

Homogeneous isotropic turbulence has been playing a key role in the research of turbulence theory. And the pseudo-spectral method is the most popular numerical method to simulate this type of flow fields in a periodic box, where fast Fourier transform (FFT) is mostly effective. However, the bottle-neck in this method is the memory of computer, which motivates us to construct a memory-saving algorithm for spectral method in present paper. Inevitably, more times of FFT are needed as compensation. In the most memory-saving situation, only 6 three-dimension arrays are employed in the code. The cost of computation is increased by a factor of 4, and that 38 FFTs are needed per time step instead of the previous 9 FFTs. A simulation of isotropic turbulence on $2048^3$ grid can be implemented on a 256G distributed memory clusters through this method.

AMS subject classifications: 80M22, 76F05, 76F65, 65T50

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Key words: Spectral method, homogeneous isotropic turbulence, DNS, FFT.

*Corresponding author.
Email: caiqd@pku.edu.cn (Q.-D. Cai), syc@coe.pku.edu.cn (S. Chen)
 

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