  Convection heat transfer in porous media is a universal phenomenon in nature,
and it is also frequently encountered in scientific and engineering fields. An
in-depth understanding of the fundamental mechanism of convection heat transfer
in porous media requires efficient and powerful numerical tools. In this paper,
a cascaded lattice Boltzmann (CLB) method for convection heat transfer in
porous media at the representative elementary volume (REV) scale is presented.
In the CLB method, the flow field is solved by an isothermal CLB model with the
D2Q9 lattice based on the generalized non-Darcy model, while the temperature
field is solved by a temperature-based CLB model with the D2Q5 lattice. The key
point is to incorporate the influence of the porous media into the CLB method
by introducing the porosity and heat capacity ratio into the shift matrices.
The effectiveness and practicability of the present method are validated by
numerical simulations of several heat transfer problems in porous media at the
REV scale. It is shown that the present method for convection heat transfer in
porous media is second-order accurate in space. Moreover, in comparison with
the Bhatnagar-Gross-Krook lattice Boltzmann method, the present method has
sufficient tunable parameters and possesses better numerical stability.
