Novel Strongly Implicit Enthalpy Formulation for Multidimensional Stefan Problems

This paper presents a new finite-difference formulation of the multidimensional phase-change problems involving unique phase-change temperature. The solutions obtained with this formulation show that the problem of “waviness” of the temperature histories encountered with the conventional formulations is now removed. The formulation derived provides a simple method for tracking the interface. During the solution of the finite-difference equations, the present formulation obviates the need for “bookkeeping” of the phase-change nodes, and hence allows solution of the equations by the tridiagonal matrix algorithm. This paper also provides explanations of the experiences with the conventional formulations.