A finite-volume sharp interface scheme for dendritic growth simulations: Comparison with microscopic solvability theory

We present and validate a numerical technique for computing dendritic growth of crystals from pure melts. The solidification process is computed in the diffusion-driven limit. The governing equations are solved on a fixed Cartesian mesh and a mixed Euterian-Lagrangian framework is used to treat the immersed phase boundary as a sharp solid-fluid interface. A conservative finite-volume discretization is employed which allows the boundary conditions to be applied exactly at the moving surface. The results from our calculations are compared with two-dimensional microscopic solvability theory. It is shown that the method predicts dendrite tip characteristics in good agreement with the theory. The sharp interface treatment allows discontinuous material property variation at the solid-liquid interface. Calculations with such discontinuities are also shown to produce results in agreement with solvability and with other sharp interface simulations.