Lattice Boltzmann simulation for three-dimensional natural convection with solid-liquid phase change

A three-dimensional (3D) lattice Boltzmann model is proposed to solve 3D natural convection with solid-liquid phase change. The total enthalpy-based thermal lattice Boltzmann model are incorporated in the D3Q19 particle velocity model to handle the temperature field. For the velocity field, the smoothed profile method is applied to implement the no-slip boundary condition at the solid-fluid phase interface. The present method is used to simulate several 3D natural convection problems with solid-liquid phase change, including 3D simulation of melting in a cubical cavity, 3D convection melting in an enclosure with inner rectangle cylinders and solid sphere melting in an cubical enclosure. The 3D effects on the temperature field and phase interface are discussed.