  We study the effect of fluid flow on three-dimensional (3D) dendrite growth
using a phase-field model on an adaptive finite element grid. In order to
simulate 3D fluid flow, we use an averaging method for the flow problem coupled
to the phase-field method and the Semi-Implicit Approximated Projection Method
(SIAPM). We describe a parallel implementation for the algorithm, using Charm++
FEM framework, and demonstrate its efficiency. We introduce an improved method
for extracting dendrite tip position and tip radius, facilitating accurate
comparison to theory. We benchmark our results for two-dimensional (2D)
dendrite growth with solvability theory and previous results, finding them to
be in good agreement. The physics of dendritic growth with fluid flow in three
dimensions is very different from that in two dimensions, and we discuss the
origin of this behavior.
