TY - JOUR
TI - A brief review of several numerical methods for one-dimensional Stefan problems
AU - Caldwell James
AU - Kwan Yuen-Yick
JN - Thermal Science
PY - 2009
VL - 13
IS - 2
SP - 61
EP - 72
PT - Article
AB - 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.