Abstract
We introduce a front tracking method for the numerical solution of one-dimensional Stefan problems. It consists in the formulation of the Stefan problem as an ordinary differential initial-value problem for the moving boundary coupled with a parabolic partial differential equation for the distribution of temperatures. We present a variable time step procedure in which the initial-value problem is solved with a predictor-corrector scheme; in the corrector step the function evaluation is done, iteratively, through an implicit time discretization of the parabolic equation. Numerical results for one-dimensional, one-phase Stefan problems with straight and curved moving boundary trajectories are presented. For these cases the front tracking method presented gives greatly improved results.
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