A numerical method for flow and solidification

A front tracking method is presented for simulating dendritic growth of pure substances in the presence of convection. The governing equations are discretized using conservative finite difference scheme. The liquid/solid interface is explicitly tracked and the interface boundary conditions are satisfied at all time steps. The latent heat released during solidification is calculated using the normal temperature gradient across the interface. The Navier-Stokes equations are solved using a projection method. The method is validated by a comparison with a standard Stefan problem and its convergence is tested through grid refinement. The effect of introducing uniform metal flow on the dendrite growth is simulated. The results are qualitatively in good agreement with published experimental results.