A two-relaxation-time lattice Boltzmann model for simulating incompressible thermal flows in porous media

Abstract

In this work, a two-relaxation-time (TRT) lattice Boltzmann (LB) model for simulating incompressible thermal flows in porous media at the representative elementary volume (REV) scale is developed. In the REV-scale TRT-LB model, the framework of the TRT-LB equations with forcing and source terms is described clearly as simply as possible. Specifically, the forcing (or source) term is divided into two parts: the symmetric part and the anti-symmetric part, which is consistent with the philosophy of the TRT model. Through the Chapman-Enskog expansion procedure, the macroscopic governing equations can be derived from the present model. Numerical simulations of several benchmark problems are carried out to validate the present model, and the present results match well with the analytical solutions and/or those numerical results in the literature.