A two-scale method for the computation of solid-liquid phase transitions with dendritic microstructure

Authors:
Christof Eck;Peter Knabner;Sergey Korotov
Affiliations:
Institute for Applied Mathematics, University of Erlangen--Nürnberg, Erlangen D-91058, Germany;Institute for Applied Mathematics, University of Erlangen--Nürnberg, Erlangen D-91058, Germany;Institute for Applied Mathematics, University of Erlangen--Nürnberg, Erlangen D-91058, Germany
Venue:
Journal of Computational Physics
Year:
2002

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Abstract

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 micro-structure 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.