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

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