A novel enthalpy formulation for multidimensional solidification and melting of a pure substance

Abstract

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 enthalpy formulation is now removed. The formulation derived provides a simple method for "local" tracking of the interface using the enthalpy variable in a novel way. During the solution of the finite-difference equations, the present formulation obviates the need for "book-keeping" of the phase-change nodes, and hence allows solution of the equations by tridiagonal matrix algorithm. It is argued that the benefits of enthalpy formulation can be extended to phase-change problems involving convection by solving the equations of motion on non-staggered grid. © 1994 Indian Academy of Sciences.