Imbalance Correction Grid Refinement Method for Lattice Boltzmann Large Eddy Simulations

To evaluate the accuracy of the lattice Boltzmann method with the zonal grid refinement for high Reynolds number turbulent flows, large eddy simulation of turbulent channel flows is carried out by the D3Q27 multiple-relaxation time lattice Boltzmann method with the imbalance-correction grid refinement method. Considering the continuity of the pressure and the momentum fluxes at the finer and coarser grid interface, the equilibrium distribution function is directly exchanged whereas the non-equilibrium part is interpolated with relaxation times to impose the velocity gradient tensor continuity. The second and third order polynomial interpolations are applied to the temporally and spatially discretized values at the grid interface, respectively. To minimizing the mass and momentum imbalances generating at the grid interface, velocity and density are corrected with mathematically optimized weighting factors. For the sub grid scale model, the wall adapting local eddy viscosity model is used and the sub-grid-scale (SGS) turbulence energy is estimated by the double filtered velocity. For the validation, large eddy simulation of turbulent channel flows at the friction Reynolds number 180, 300 and 650 is conducted. It is confirmed that the imbalance correction considerably improves the mass conservation and the prediction accuracy of the turbulent statistics is substantially improved. Furthermore, since the SGS model successfully compensates the unresolved eddies even near the finer and coarser grid interface, the sum of the resolved and modelled Reynolds stresses show smooth profiles near the grid interface.