THREE-DIMENSIONAL SOLIDIFICATION, A NUMERICAL APPROACH

Abstract

The problem of three-dimensional solidification occurs in many practical applications. A numerical grid generation approach is taken to study solidification of three-dimensional objects with arbitrary temperature distributions over one of the bounding surfaces. The formulation of the problem is based on the conduction model, and the interface is characterized by the Stefan condition. Elliptic-type grid generation expressions are used to construct a three-dimensional mesh over the solution domain, which is continuously updated to account for the moving interface. Several examples are presented to demonstrate the applicability of the technique to such moving-boundary problems.