Fast and accurate adaptive finite difference method for dendritic growth

We propose a fast and accurate adaptive numerical method for solving a phase-field model for dendritic growth. The phase-field model for dendritic growth consists of two equations. One is for capturing the interface between solid and melt. The other is for the temperature distribution. For the phase-field equation, we apply a hybrid explicit method on a time-dependent narrow-band domain, which is defined using the phase-field function. For the temperature equation, we apply the explicit Euler method on the whole computational domain. The novelties of the proposed numerical algorithm are that it is very simple and that it does not require the conventional complex adaptive data structures. Our numerical simulation results are consistent with previous results. Furthermore, the computational time required (CPU time) is shorter.