Large Eddy Simulation Using Lattice Boltzmann Method Based on Sigma Model

The Lattice Boltzmann Method (LBM) is a novel method for simulating convection-diffusion type of problems. It has direct advantages over other available methods. One advantage of LBM is that it can be easily parallelized and hence can be used to simulate fluid flow in multi-core computers using parallel computing. In this paper we have used the Lattice Boltzmann Method to simulate turbulent flow in a channel using the Sigma Model for Large Eddy Simulation (LES). LES is widely used in simulating turbulent flows in industries because of its less computational needs compared to Direct Numerical Simulation (DNS) where the Kolmogorov Eddies have to be resolved. Unlike the static Smagorinsky Model this model has the potential to simulate turbulent flow in complex geometries. The eddy viscosity in the sigma model becomes zero at the boundary O(y3) and thus eliminates the use of artificial damping function that is used with the static Smagorinsky model. The sigma model also ensures a positive eddy viscosity which ensures that there are no numerical instabilities. The eddy viscosity also vanishes when the flow is two dimensional or axisymmetric.