Development of Reynolds Averaged Model based on Lattice Boltzmann Equation

A Reynolds averaged model is derived from Lattice Boltzmann Equation to obtain anew Lattice Boltzmann Method to predict turbulent flows. The velocity distribution function in LBM has been taken as an ensemble average of velocity density of the ideal particles. Inthis paper, the velocity distribution function is regarded as an instantaneous value so that it is divided into ensemble-averaged value and fluctuating components. By using Chapman-Enskog procedure, a component of Reynolds stress, which has to be evaluated by other turbulent models, is introduced into the equilibrium function. The validity of the proposed model using O-equation model is also discussed by applying to a plane compound shear layer.