THERMAL SCIENCE

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James Caldwell

,

Yuen-Yick Kwan

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.
KEYWORDS
moving boundary problem, Stefan problems
PAPER SUBMITTED: 2008-10-27
PAPER REVISED: 2009-01-20
PAPER ACCEPTED: 2009-01-20
DOI REFERENCE: https://doi.org/10.2298/TSCI0902061C
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2009, VOLUME 13, ISSUE Issue 2, PAGES [61 - 72]
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A brief review of several numerical methods for one-dimensional Stefan problems

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