  Through an integrated macroscale/mesoscale computational model, we
investigate the developing shape and grain morphology during the melting and
solidification of a weld. In addition to macroscale surface tension driven
fluid flow and heat transfer, we predict the solidification progression using a
mesoscale model accounting for realistic solidification kinetics, rather than
quasi-equilibrium thermodynamics. The tight coupling between the macroscale and
the mesoscale distinguishes our results from previously published studies. The
inclusion of Marangoni driven fluid flow and heat transfer, both during heating
and cooling, was found to be crucial for accurately predicting both weld pool
shape and grain morphology. However, if only the shape of the weld pool is of
interest, a thermodynamic quasi-equilibrium solidification model, neglecting
solidification kinetics, was found to suffice when including fluid flow and
heat transfer. We demonstrate that the addition of a sufficient concentration
of approximately 1 $\mu$m diameter TiN grain refining particles effectively
triggers a favorable transition from columnar dendritic to equiaxed grains, as
it allows for the latter to heterogeneously nucleate in the undercooled melt
ahead of the columnar dendritic front. This transition from columnar to
equiaxed growth is achievable for widely differing weld conditions, and its
precise nature is relatively insensitive to the concentration of particles and
to inaccurately known model parameters.
