Implicit Finite—difference Solutions of the Enthalpy Formulation of Stefan Problems

Abstract

When related to a phase-change problem, an implicit finite-difference discretization of the enthalpy formulation results in a system of non-linear equations at each time step. In this paper, various numerical enthalpy methods based on such discretizations are outlined and examined. An alternative discretization for an enthalpy formulation is developed on separating the sensible and latent heat terms. This approach also results in a non-linear system of equations but with the non-linearity isolated as a source term of nodal latent heat. This offers an advantage over the previous techniques in that only one variable (i.e. temperature) is solved for in the resulting iterative scheme. Comparison with simple one- and two-dimensional test problems indicate that the computing requirements, with the alternative discretization, are reduced by between 20 and 50%.