An immersed boundary-thermal lattice Boltzmann method for solid–liquid phase change

In this work, an immersed boundary-thermal lattice Boltzmann method (IB-TLBM) is proposed to simulate solid–liquid phase change problems. To treat the velocity and temperature boundary conditions on the solid–liquid interface, immersed boundary method (IBM) is adopted, in which the solid–liquid interface is represented as a sharp interface rather than a diffusive interface and is tracked explicitly by Lagrangian grid. The surface forces along the immersed boundary, including the “momentum force” for velocity boundary condition and the “energy force” for temperature boundary condition, are calculated by the direct-forcing scheme. The moving velocity of solid–liquid interface induced by phase change is calculated by the amount of latent heat absorbed or released in a time step directly, with no need to compute temperature gradients in solid and liquid phases separately. The temperature on the solid–liquid interface is specified as the melting temperature, which means phase change happens at a constant temperature. As the solid–liquid interface evolves with time, the identification of phase of Eulerian points and the rearrangement of Lagrangian points are also considered. With regard to the velocity and temperature fields, passive scalar thermal lattice Boltzmann method (TLBM) with multiple-relaxation-time (MRT) collision schemes is adopted. Numerical examples, including conduction-induced melting in a semi-infinite space and melting in a square cavity, are carried out to verify the present method and good results are obtained. As a further application, melting in a circular cylinder with considering the motion of solid phase is simulated successfully by the present method; numerical results show that the motion of solid phase accelerates the melting process obviously.