Multiscale finite-difference-diffusion Monte-Carlo method for simulating dendritic solidification

We present a novel hybrid computational method to simulate accurately dendr itic solidification in the low undercooling limit where the dendrite tip ra dius is one or more orders of magnitude smaller than the characteristic spa tial scale of variation of the surrounding thermal or solutal diffusion fie ld. The first key feature of this method is an efficient multiscale diffusi on Monte Carlo (DMC) algorithm which allows off-lattice random walkers to t ake longer and concomitantly rarer steps with increasing distance away from the solid-liquid interface. As a result, the computational cost of evolvin g the large-scale diffusion field becomes insignificant when compared to th at of calculating the interface evolution. The: second key feature is that random walks are only permitted outside of a thin liquid layer surrounding the interface. Inside this layer and in the solid, the diffusion equation i s solved using a standard finite difference algorithm that is interfaced wi th the DMC algorithm using the local conservation law for the diffusing qua ntity. Here we combine this algorithm with a previously developed phase-fie ld formulation of the interface dynamics and demonstrate that it can accura tely simulate three-dimensional dendritic growth in a previously unreachabl e range of low undercoolings that is of direct experimental relevance. (C) 2000 Academic Press.