Numerical solution of phase-change problems

A three-time level implicit scheme, which is unconditionally stable and convergent, is employed for the numerical solution of phase-change problems, on the basis of an analytical approach consisting in the approximation of the latent heat effect by a large heat capacity over a small temperature range. Since the temperature dependent coefficients in the resulting parabolic equations are evaluated at the intermediate time level, the complication of solving a set of nonlinear algebraic equations at each time step is avoided. The numerical results thus obtained are satisfactorily compared with the available analytical solutions.