Modeling dendritic growth of a binary alloy

A two-dimensional model for simulation of the directional solidification of dendritic alloys is presented. It solves the transient energy and solute conservation equations using finite element discretizations. The energy equation is solved in a fixed mesh of bilinear elements in which the interface is tracked; the solute conservation equation is solved in an independent, variable mesh of quadratic triangular elements in the liquid phase only. The triangular mesh is regenerated at each time step to accommodate the changes in the interface position using a Delaunay triangulation. The model is tested in a variety of situations of differing degrees of difficulty, including the directional solidification of Pb–Sb alloys.