The Alternating Phase Truncation Method for Numerical Solution of a Stefan Problem

A numerical scheme for solving heat conduction problems involving a change of phase is presented. The numerical solution is obtained for heat flow in a two phase medium by using a method which treats each phase alternately, The resulting scheme avoids geometrical front tracking, and requires only simple algebraic operations. A maximum principle for the method and results of numerical experiments are given. An analytical version of the algorithm for a one dimensional one phase Stefan problem is shown to have an O(Δ t · ln 1/Δ t)^1/2 rate of convergence. Numerical experiments indicate that this estimate is sharp.