Sharp interface Cartesian grid method III: Solidification of pure materials and binary solutions

A numerical technique is presented for computing dendritic growth of crystals from pure melts and binary solutions. The governing equations are solved on a fixed Cartesian mesh and the immersed phase boundary is treated as a sharp solid-fluid interface. The interface is tracked using a level-set field. A finite-difference scheme is presented that incorporates the immersed phase boundary with only a small change to a standard Cartesian grid Poisson solver. The scheme is simple to implement in three-dimensions. The results from our calculations show excellent agreement with two-dimensional microscopic solvability theory for pure material solidification. It is shown that the method predicts dendrite tip characteristics in excellent agreement with the theory. The sharp interface treatment allows discontinuous material property variation at the solid-liquid interface. This facilitates sharp-interface simulations of dendritic solidification of binary solutions.