Finite element simulation of solid-liquid phase transitions with a free melt surface

Introduction. The Collaborative Research Centre 747 “Micro cold forming” studies aspects of the production of micro components. Motivated by the engineering application of melting the end of thin wires by laser heating in order to accumulate material for a subsequent forming process, we study the melting and solidification of material with a free capillary melt surface. The model leads to a coupled system of Stefan and Navier-Stokes equations, where the solution of the Stefan problem defines the solid subdomain Ωs(t) and the solution of Navier-Stokes with capillary boundary gives the shape of the liquid subdomain Ωl(t). An Arbitrary Lagrangian Eulerian Finite Element method is presented that is able to compute a numerical solution without spurious oscillations.