A brief review of several numerical methods for one-dimensional Stefan problems

Abstract

This paper describes and compares several effective methods for the numerical solution of one-dimensional Stefan problems. The intention is not to make an exhaustive review and so we restrict our attention to a range of problems and geometries which include melting in the halfplane, outward cylindrical solidification and outward spherical solidification. Effectively, a range of methods is introduced for the solution of Stefan problems, including (1) enthalpy method, (2) boundary immobilization method, (3) perturbation method, (4) nodal integral method, and (5) heat-balance integral method. The above methods are then applied to a selection of test problems. As a result of this comparison some helpful comments can be made and conclusions drawn which may prove valuable in the future use of these methods

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