Acceleration of steady-state lattice Boltzmann simulations on non-uniform mesh using local time step method

In this paper, the local time step method is applied to the lattice Boltzmann method (LBM) on non-uniform grid (generalized form of interpolation supplemented LBM: GILBM) for steady flow simulations. The local time step method is known to be an effective technique to accelerate the solution to the converged steady state on non-uniform grid. First, code validation for global time step method is performed by solving flow around a cylinder at low Reynolds numbers. Our results show good agreement with previous studies. Two-dimensional flow simulations around an airfoil were performed in order to validate the code using the local time step method and the results are compared with the global time step solutions. The pressure distribution and the aerodynamic coefficients of global and local time step results are in good agreement. They are also consistent with the previous studies. At the same time, CPU time required to obtain the steady-state solutions using the local time step are reduced by 70–80% compared with that using global time step.