  We present a first implementation of the Dendritic Needle Network (DNN) model
for dendritic crystal growth in three dimensions including convective transport
in the melt. The numerical solving of the Navier-Stokes equations is performed
with finite differences and is validated by comparison with a classical
benchmark in fluid mechanics for unsteady flow. We compute the growth behavior
of a single equiaxed crystal under a forced convective flow. As expected, the
resulting dendrite morphology differs strongly from the case of the purely
diffusive regime and from similar two-dimensional simulations. The resulting
computationally efficient simulations open the way to studying mechanisms of
microstructure selection in presence of fluid flow, using realistic alloys and
process parameters.
