Comparisons of different implementations of turbulence modelling in lattice Boltzmann method

In this paper, we present an alternative approach for the turbulence modelling in the single-relaxation-time lattice Boltzmann method (LBM) framework by treating the turbulence term as an extra forcing term, in addition to the traditional approach of modifying the relaxation time. We compare these two different approaches and their mixture in large-eddy simulation (LES) of three-dimensional decaying isotropic homogenous turbulence using the Smagorinsky model and the mixed similarity model. When the LES was conducted using the Smagorinsky model, where the Boussinesq eddy-viscosity approximation is adopted, the results showed that these three different implementations are equivalent. However, when the mixed similarity model is adopted, which is beyond the Boussinesq eddy-viscosity approximation, our results showed that an equivalent eddy-viscosity will lead to errors, while the forcing approach is more straightforward and accurate. This provides an alternative and more general framework of simulation of turbulence with models in LBM, especially when the Boussinesq eddy-viscosity approximation is invalid.