Phase-field method for computationally efficient modeling of solidification with arbitrary interface kinetics

We present mathematical results which dramatically enhance the computational efficiency of the phase-field method for modeling the solidification of a pure material. These results make it possible to resolve a smaller capillary length to interface thickness ratio and thus render smaller undercooling and three-dimensional computations accessible. Furthermore, they allow one to choose computational parameters to produce a Gibbs-Thomson condition with an arbitrary kinetic coefficient. The method is tested for dendritic growth in two dimensions with zero kinetic coefficient. Simulations yield dendrites with tip velocities and tip shapes which agree within a few percent with numerical Green's function solutions of the steady-state growth problem.