A computationally efficient solution technique for moving-boundary problems in finite media

A new technique is developed for plane or spherical moving-boundaryproblems, such as occur in freezing or melting problems. A coordinatetransformation for immobilization of the moving boundary isused. The technique involves the use of a semidiscrete Petrov—Galerkinmethod with the piecewise-exponential test functions and thepiecewise-linear trial functions to approximate the timedependentgoverning equation and the use of a predictor-corrector methodto integrate the boundary motion equation. Computed resultsfor the plane or spherical moving boundary are numerically evaluatedfor comparison with results of previous authors. This methodis simple and there is no limit on the range of the parameters.We argue that the method is well-suited to a variety of movingboundaryproblems.