A multiple-relaxation-time lattice Boltzmann model for simulating   incompressible axisymmetric thermal flows in porous media
  In this paper, a multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is developed for simulating incompressible axisymmetric thermal flows in porous media at the representative elementary volume (REV) scale. In the model, a D2Q9 MRT-LB equation is proposed to solve the flow field in addition to the D2Q5 LB equation for the temperature field. The source terms of the model are simple and contain no velocity and temperature gradient terms. The generalized axisymmetric Navier-Stokes equations for axisymmetric flows in porous media are correctly recovered from the MRT-LB model through the Chapman-Enskog analysis in the moment space. The present model is validated by numerical simulations of several typical axisymmetric thermal problems in porous media. The numerical results agree well with the data reported in the literature, demonstrating the effectiveness and accuracy of the present MRT-LB model for simulating axisymmetric thermal flows in porous media. 
Qing Liu, Ya-Ling He, Qing Li
physics.comp-ph physics.flu-dyn