A Two-Scale Method for the Computation of Solid–Liquid Phase Transitions with Dendritic Microstructure

A two-scale model for liquid–solid phase transitions with equiaxed dendritic microstructure in binary material in the case of slow solute diffusion is presented. The model consists of a macroscopic energy transport equation and, for each point of the macroscopic domain, a local cell problem describing the evolution of the microstructure and the microsegregation. It is derived by formal homogenization of a sharp interface model, including the Gibbs–Thomson law and kinetic undercooling. Based on the two-scale model, a numerical two-scale method for the simulation of phase transitions with dendritic microstructure is developed, and numerical examples are presented.