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 (ISPH) method to simulate melting of solids and the ensuing fluid-solid interaction. We present validations for the heat transfer across the 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. (C) 2018 Elsevier Ltd. All rights reserved.