Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 724578, 13 pages
Research Article

An Alternative Scheme to Calculate the Strain Rate Tensor for the LES Applications in the LBM

State Key Laboratory of Hydroscience and Engineering, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China

Received 7 September 2010; Revised 17 November 2010; Accepted 18 November 2010

Academic Editor: Mehrdad Massoudi

Copyright © 2010 Jun Li and Zhengwei Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Large eddy simulations (LES) based on the Smagorinsky model can be conveniently used in the lattice Boltzmann method (LBM) because the strain rate tensor, 𝑆 𝑖 𝑗 , used to determine the eddy kinematic viscosity can be calculated from the second-order moment of the nonequilibrium distribution function, and the current total nondimensional relaxation time can be determined explicitly. A new method is developed where the distribution function after the relaxation subroutine differs from that after the motion subroutine leading to a similar method to determine 𝑆 𝑖 𝑗 , but its application is inconvenient due to the implicit feature. However, the derivation also leads to an alternative explicit scheme for calculating 𝑆 𝑖 𝑗 based on physical analysis of the momentum transport process, where the stress tensor, 𝑇 𝑖 𝑗 , is calculated first, and then 𝑆 𝑖 𝑗 is determined from 𝑇 𝑖 𝑗 using the constitutive relationship for Newtonian fluid. The current total nondimensional relaxation time is also given explicitly so that this LES model can be easily used in the LBM.