On the solution of a generalized Stefan problem

摘要

We present a numerical treatment of a generalized two-dimensional Stefan problem which models the solidification or melting of a solid in a melt. The irregular domain is transformed into a rectangular domain by a coordinate transformation, and the resulting parabolic equations are discretized using fourth-order difference formulae. The free surface and field equations are solved using Crank–Nicolson procedures.The results are found to be in good agreement with the linear perturbation analysis of Chadam and Ortoleva (1983). Additionally, an improvement in the estimate of Baillon et al. (1984) for breakdown time in the one-dimensional problem and corroborating numerical results are presented.