Double multiple-relaxation-time lattice Boltzmann model for solid-liquid phase change with natural convection in porous media

In this paper, a double multiple-relaxation-time lattice Boltzmann model is developed for simulating transient solid-liquid phase change problems in porous media at the representative elementary volume scale. The model uses two different multiple-relaxation-time lattice Boltzmann equations, one for the flow field and the other for the temperature field with nonlinear latent heat source term. The model is based on the generalized non-Darcy formulation, and the solid-liquid phase change interface is traced through the liquid fraction which is determined by the enthalpy method. The model is validated by numerical simulations of conduction melting in a semi-infinite space, solidification in a semi-infinite corner, and convection melting in a square cavity filled with porous media. The numerical results demonstrate the efficiency and accuracy of the present model for simulating transient solid-liquid phase change problems in porous media.