  The rate of melting of a solid and the rate of deformation of the resulting
melt due to capillary forces are comparable in additive manufacturing
applications. This dynamic structural change of a melting solid is extremely
challenging to study experimentally. Using meshless numerical simulations we
show the influence of the flow of the melt on the heat transfer and resulting
phase change. We introduce an accurate and robust Incompressible Smoothed
Particle Hydrodynamics method to simulate melting of solids and the ensuing
fluid-solid interaction. We present validation for the heat transfer across
free surface and the melting interface evolution, separately. We then present
two applications for this coupled multiphysics simulation method---the study of
rounding of an arbitrarily shaped particle during melting and the non-linear
structural evolution of three spheres undergoing agglomeration. In both the
studies we use realistic transport and thermal properties for the materials so
as to demonstrate readiness of the method for solving engineering problems in
additive manufacturing.
