  We present a novel hybrid computational method to simulate accurately
dendritic solidification in the low undercooling limit where the dendrite tip
radius is one or more orders of magnitude smaller than the characteristic
spatial scale of variation of the surrounding thermal or solutal diffusion
field. The first key feature of this method is an efficient multiscale
diffusion Monte-Carlo (DMC) algorithm which allows off-lattice random walkers
to take longer and concomitantly rarer steps with increasing distance away from
the solid-liquid interface. As a result, the computational cost of evolving the
large scale diffusion field becomes insignificant when compared to that 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 is solved
using a standard finite-difference algorithm that is interfaced with the DMC
algorithm using the local conservation law for the diffusing quantity. Here we
combine this algorithm with a previously developed phase-field formulation of
the interface dynamics and demonstrate that it can accurately simulate
three-dimensional dendritic growth in a previously unreachable range of low
undercoolings that is of direct experimental relevance.
