A mesoscopic method based on the lattice Boltzmann method for thermal–solutal incompressible non-Newtonian power-law fluids through porous media is introduced. The macroscopic equations of different representative element volume (REV) models of porous media are presented, and the equations of power-law fluids through porous media for various REV models reported. The general mesoscopic model for two- and three-dimensional cases are presented, and their derivations shown. To demonstrate the ability of the proposed method, natural convection and double-diffusive natural convection of Newtonian and power-law fluids in porous cavities are studied, and the results are validated against previous findings. Finally, double-diffusive natural convection in a porous cubic cavity filled with a non-Newtonian power-law fluid is simulated by the proposed method.
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