A novel lattice Boltzmann model for the solid–liquid phase change with the convection heat transfer in the porous media

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A novel lattice Boltzmann (LB) model with double distribution functions is proposed to simulate the solid–liquid phase change problems with the convection heat transfer in the porous media at the representative elementary volume scale. A generalized LB model is adopted to simulate the velocity field of the liquid region in the presence of the porous media. Based on the framework of a LB model for nonlinear convection–diffusion equation, an LB evolution equation without a phase change source term, as well as a newly modified equilibrium distribution function including the effective total enthalpy and thermal capacity ratio, are constructed to solve the effective total enthalpy energy conservation equation for the porous media. The macroscopic effective total enthalpy energy conservation equation can be exactly recovered from the present LB model by the Chapman–Enskog procedure. As compared with the most previous models, the present model can provide a higher computational efficiency, because the iterative step or linear equations solving procedure for the latent heat source term can be avoided. Furthermore, the temperature and heat flux continuity conditions at the interface between phases of different thermophysical properties are inherently satisfied for the present model. In such a case, the differences in both thermal conductivity and specific heat between phases, as well as the variation of porosity can be tackled by independently adjusting the relaxation time and the thermal capacity ratio included in the equilibrium distribution function, respectively. Additionally, the numerical diffusion across the phase interface for temperature, induced by solid–liquid phase change, can be dramatically reduced in the present model through the MRT collision scheme with a special configuration for the relaxation matrix. Numerical tests for several benchmark problems are carried out to validate the wide practicability and the accuracy of the present model. Very good agreements with analytical solutions or previous experimental and numerical results can be achieved, demonstrating the present model can be served as a promising numerical technique for simulating the transient solid–liquid phase change problems in the porous media.