Lattice Boltzmann Method for Thermal Fluid Dynamics in Anisotropic Porous Media

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We propose the thermal lattice Boltzmann method to calculate the Brinkman-Forchheimer momentum equation by using a free-derivative optimization method to compute a nonlinear (Forchheimer) term containing the quadratic form of the velocity for the anisotropy of permeability tensor. In the numerical simulation of natural convection, the numerical results of the LBM show good agreement with the reference solutions for the streamlines, isotherms, and the average Nusselt number depending on the Darcy number and on the Rayleigh number. We apply the higher-order accurate immersed boundary method to this thermal lattice Boltzmann method for the fluid dynamics with arbitrary geometry.