Convection modeling in directional solidification

Mathematical and numerical models of solidification of binary and multicomponent dendritic alloys that can model the dynamics of the mushy zone as well as the all liquid region are examined. The discussion is centered around models based on finite element discretization of the governing equations that have been developed by the authors during the last fifteen years. The capabilities of existing simulation codes to model the effects of convection and the resulting macrosegregation in castings, and in particular, the development of 'freckles' in vertically solidified dendritic monocrystals are discussed. The current capabilities of the models as well as the areas in which more improvement is needed are noted. Numerical examples are presented to illustrate the different aspects of the simulations. (C) 2004 Academie des sciences. Published by Elsevier SAS. All rights reserved.