Numerical simulation of dendritic solidification with convection

A front tracking method is presented for simulations of dendritic solidification of pure substances in the presence of flow. The liquid-solid interface is explicitly tracked and the latent heat released during solidification is calculated using the normal temperature gradient near the interface. A projection method is used to solve the Navier-Stokes equations. The no-slip condition on the interface is enforced by setting the velocities in the solid phase to zero and this method is validated by comparing the numerical results to analytical solutions of Stokes flow over periodic arrays of cylinders and spheres in two and three dimensions, respectively. Two strategies are used to accelerate the method and allow for larger domains: a multigrid method and parallelization of the codes. The method is validated through a comparison with exact solutions for two- and three-dimensional Stefan problems, grid refinement test, and a comparison with a solution obtained by a boundary integral method.; The presented two-dimensional simulations include: a comparison with the simulations of Beckermann et al.; a study of the effect of different flow velocities; a study of the effect of the Prandtl number on the growth of a group of dendrites growing together; and a simulation of dendritic growth with natural convection. Three-dimensional simulations are compared to two-dimensional simulations. The results from the two- and the three-dimensional simulations are both in good agreement with the trends observed in published experimental results. In particular, the simulations are able to predict the correct trend of the effect of the flow on the upstream tip radius that is not correctly predicted by other published methods.; The three and two-dimensional simulations show that on the upstream side of the dendrite the tip velocity and the tip Peclet number increase and the tip radius decreases as the flow velocity increases. The flow also promotes the formation of the side branches on the upstream side. The flow has the opposite effect on the downstream side. The effect of the flow on the upstream and the perpendicular tips is stronger in two dimensions while its effect on the formation of side branches is stronger in three dimensions.