Computation of dendritic microstructures using a level set method

The authors demonstrate that the level set method can be used to solve the free-boundary problem for solidification to calculate quantitatively accurate solutions for dendritic growth. They present results from simulations in two dimensions and show that the solutions converge to the steady-state predicted by the microscopic solvability theory. Time-dependent results are also compared with calculations using a phase-field model and good agreement is found for all times. Furthermore, the authors perform simulations with unequal diffusivities (a case which is not yet possible with phase-field models) and find that the prediction of A. Barbieri and J.S. Langer (1989) provides a fair quantitative fit to their results.