Numerical methods for improved efficiency in macrosegregation modeling

New algorithms developed for the simulation of macrosegregation in directionally solidified alloys are presented. The work has been motivated by the inefficiency of models that have been used in the past. Three different developments are reported, the use of a fractional step projection finite element method to solve the momentum equations, the use of mesh-less element free Galerkin formulations, and the combination of the Galerkin finite element method with adaptive mesh refinement. The formulation of the different algorithms is given and a two-dimensional example of application in which the efficiency of the methods is compared is presented. The results of a three-dimensional calculation using the Galerkin finite element method show that very significant gains are effected when compared with previously published simulations. Copyright (C) 2010 John Wiley & Sons, Ltd.