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

Large eddy simulations LES based on the Smagorinsky model can be conveniently used in the lattice Boltzmann method LBM because the strain rate tensor, Sij , 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 Sij , but its application is inconvenient due to the implicit feature. However, the derivation also leads to an alternative explicit scheme for calculating Sij based on physical analysis of the momentum transport process, where the stress tensor, Tij , is calculated first, and then Sij is determined from Tij 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.