Proposed a novel LB model for the solid–liquid phase change with the convection in the porous media at the REV scale.

An effective total enthalpy energy conservation equation is derived.

An LB evolution equation without a phase change source term and a newly modified equilibrium distribution function are constructed.

Temperature and heat flux continuity conditions at the interface are inherently satisfied.

Numerical diffusion across the phase interface can be reduced by the MRT scheme.