An object oriented implementation of a front tracking finite element method for directional solidification processes

This paper focuses on the numerical simulation of phase-change processes using a moving nite element technique. In particular, directional solidi cation and melting processes for pure materials and binary alloys are studied. The melt is modelled as a Boussinesq uid and the transient Navier{Stokes equations are solved simultaneously with the transient heat and mass transport equations as well as the Stefan condition. The various streamline-upwind=Petrov{Galerkin-based FEM simulators developed for the heat, ow and mass transport subproblems are reviewed. The use of classes, virtual functions and smart pointers to represent and link the particular simulators in order to model a phase change process is discussed. The freezing front is modelled using a spline interpolation, while the mesh motion is de ned from the freezing front motion using a trans nite mapping technique. Various two- and three-dimensional numerical tests are analysed and discussed to demonstrate the e ciency of the proposed techniques. Copyright