Single Relaxation Time and Multiple Revised Matrix Lattice Boltzmann Simulations of Forced Isotropic Turbulence

Abstract The single relaxation time (SRT) and the revised matrix (RM) lattice Boltzmann models are investigated for simulations of three dimensional forced isotropic turbulence with resolutions of 1283, 2563, and 5123, respectively. It is found that the density ρ is almost unity at all lattice timesteps for the MRT case, while disturbance about unity is observed for the SRT case. Also, thinner vortex structures are observed for the MRT results in comparison with the SRT cases specially for higher resolutions. The velocity distributions for the MRT results are found similar to the results of the Navier-Stoks standard solutions. One of the disadvantages of the MRT case is the simulation time which is found more than twice the SRT simulation time, where about 24 seconds are needed for each lattice timestep in the 2563 case in comparison to 12:6 seconds for the SRT model using the same hardware resources. In the case of 5123 grid points about 648 seconds are consumed for one lattice timestep which is found as more than three times the SRT case which needs 198 seconds. The initial velocity field is chosen as u(x; 0) = 0 and the force is injected at low wave-numbers with a fixed forcing amplitude of 10 -4 for all cases. The single relaxation time is set to τ = 0.503 in all SRT simulations. Results show that the obtained turbulent velocity fields yield universal characteristics as found in previous Navier-Stoks numerical studies of the same problem.