“…Methods based on the Lattice Boltzmann equations (LBE) have recently evolved as an approach to direct solutions of the macroscopic equations in porous media [15][16][17][18], nanofluid [19], phase change [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35], shock tube problem [36], droplet formation [37,38], turbulent natural convection [39] and so on [40][41][42]. Due to its particulate nature, the LBM has some benefits over the conventional Computational fluid dynamics (CFD) techniques such as handling complex boundaries and physical phenomena, the straightforward implementation on parallel machines, the incorporation of microscopic interactions and high speed of solving.…”