Large Eddy Simulations using Lattice Boltzmann algorithms. Final report

Abstract

This report contains the results of a study performed to implement eddy-viscosity models for Large-Eddy-Simulations (LES) into Lattice Boltzmann (LB) algorithms for simulating fluid flows. This implementation requires modification of the LB method of simulating the incompressible Navier-Stokes equations to allow simulation of the filtered Navier-Stokes equations with some subgrid model for the Reynolds stress term. We demonstrate that the LB method can indeed be used for LES by simply locally adjusting the value of the BGK relaxation time to obtain the desired eddy-viscosity. Thus, many forms of eddy-viscosity models including the standard Smagorinsky model or the Dynamic model may be implemented using LB algorithms. Since underresolved LB simulations often lead to instability, the LES model actually serves to stabilize the method. An alternative method of ensuring stability is presented which requires that entropy increase during the collision step of the LB method. Thus, an alternative collision operator is locally applied if the entropy becomes too low. This stable LB method then acts as an LES scheme that effectively introduces its own eddy viscosity to damp short wavelength oscillations.