  Since its introduction 30 years ago, the lattice Boltzmann (LB) method has
achieved great success in simulating fluid flows and modeling physics in
fluids. Owing to its kinetic nature, the LB method has the capability to
incorporate the essential microscopic or mesoscopic physics, and it is
particularly successful in modeling transport phenomena involving complex
boundaries and interfacial dynamics. The LB method can be considered to be an
efficient numerical tool for fluid flow and heat transfer in porous media.
Moreover, since the LB method is inherently transient, it is especially useful
for investigating transient solid-liquid phase-change processes wherein the
interfacial behaviors are very important. In this article, a comprehensive
review of the LB methods for single-phase and solid-liquid phase-change heat
transfer in porous media at both the pore scale and representative elementary
volume (REV) scale. The review first introduces the fundamentals of the LB
method for fluid flow and heat transfer. Then the REV-scale LB method for fluid
flow and single-phase heat transfer in porous media, and the LB method for
solid-liquid phase-change heat transfer, are described. Some applications of
the LB methods for single-phase and solid-liquid phase-change heat transfer in
porous media are provided. In addition, applications of the LB method to
predict effective thermal conductivity of porous materials are also provided.
Finally, further developments of the LB method in the related areas are
discussed.

Computational Physics