Phase-field lattice kinetic scheme for the numerical simulation of dendritic growth

A phase-field lattice kinetic model is presented for the numerical simulation of the dendritic growth of a pure crystal in the presence of thermal transport. A finite-difference scheme for the phase field is combined with an explicit lattice kinetic scheme for the temperature field. The resulting scheme is advanced in time with an adaptive time-marching procedure which permits us to achieve long simulation times with larger time steps than explicit finite-difference and previous kinetic methods. The method is demonstrated for the case of dendritic growth of a single crystal over a wide range of Stefan and capillarity numbers.