Numerical Simulation of Dendritic Solidification

It is well known that the dendritic microstructure of alloys is a consequence of morphological instability of the solidification process, which is a result of the coupling of heat and mass transfer with the composition-dependent phase equilibrium condition mediated by the surface energy. There have been many numerical simulations of dendritic solidification. However, many successful simulations of dendritic growth have used non-discrete front tracking method such as artificial source method or phase field method, with demonstrably first order accuracy. Many also found it necessary to continuously inject random noise during simulation. The continuous injection of random noise raises the suspicion that the numerical schemes used may be overly dissipative. The noise is apparently capable of creating nonuniform solidification, but not sufficient to ensure growth with a clear dendritic pattern. In the present study, to rule out the numerical diffusivity as a cause of the damping of dendritic perturbations, artificial perturbations are either not used, or injected only as initial conditions. Under the unstable solidification mode, the initial perturbation triggers the onset of interface instability. Computations were performed for both sub-cooled pure material as well as directional solidification of alloys. The successful simulation of dendritic solidification without the intentional injection of random noise provided evidence that the present method has less numerical diffusion than many existing front tracking methods.