A Multi-Relaxation-Time Lattice Boltzmann Method on Non- Uniform Grids for Large Eddy Simulation of Rayleigh-Bénard Convection Using Two Sub-Grid Scale Models

In the present work, for the first time, the application of a Multi-Relaxation-Time Lattice Boltzmann (MRT-LB) model for large-eddy simulation (LES) of turbulent thermally driven flows on non-uniform grids is considered. A Taylor series expansion and Least square based Lattice Boltzamnn method (TLLBM) has been implemented in order to use a nonuniform mesh. It permits to reduce the required mesh size and consequently the computational cost to simulate the turbulent buoyant flow fields. The implementation is discussed in the context of a MRT-LB model in conjunction with both Smagorinsky and mixed scale viscosity sub-grid models. At first, to validate the code, a multi-relaxation–time lattice Boltmann method on non-uniform grid is utilized to simulate a lid-driven cavity flow .Then large eddy simulation of this model is applied to simulate a turbulent Rayleigh-Bénard convection at different Rayleigh numbers in ranging 104 to 1015 for Prantdl number of 0.71. The simulation results show that lattice Boltzmann method is capable to simulate turbulent convection flow problems at high Rayleigh numbers.