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

• Main Authors: Caldwell James, Kwan Yuen-Yick
• Format: Article
• Language: English
• Published: VINCA Institute of Nuclear Sciences 2009-01-01
• Series: Thermal Science
• Subjects: moving boundary problem; Stefan problem
• Online Access: http://www.doiserbia.nb.rs/img/doi/0354-9836/2009/0354-98360902061C.pdf

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.