Multiple-relaxation-time lattice Boltzmann model for simulating axisymmetric thermal flows in porous media

In this paper, a multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is developed for simulating axisymmetric thermal flows in porous media at the representative elementary volume scale. In the present model, the flow field is solved by a D2Q9 MRT-LB equation based on the generalized non-Darcy model, while the temperature field is solved by a thermal MRT-LB equation using a non-orthogonal transformation matrix with the D2Q5 lattice. The present model has the following features. First, the forcing and source terms are simple and contain no velocity or temperature gradient terms. Second, the thermal MRT-LB equation is within the framework of the standard LB method and is consistent with the philosophy of the LB method. Owing to these features, the present model retains the inherent advantages of the standard LB method and is easy to implement. The present model is tested by simulating several typical axisymmetric thermal problems in porous media, and the numerical results indicate that the present model can serve as an accurate and efficient numerical tool for studying axisymmetric thermal flows in porous media. (C) 2019 Elsevier Ltd. All rights reserved.