• Journal of the Computational Structural Engineering Institute of Korea
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• v.26 no.1
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• pp.39-48
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• 2013

This paper develops a 2-D moving least squares(MLS) difference method for Stefan problem by extending the 1-D version of the conventional method. Unlike to 1-D interfacial modeling, the complex topology change in 2-D domain due to arbitrarily moving boundary is successfully modelled. The MLS derivative approximation that drives the kinetics of moving boundary is derived while the strong merit of MLS Difference Method that utilizes only nodal computation is effectively conserved. The governing equations are differentiated by an implicit scheme for achieving numerical stability and the moving boundary is updated by an explicit scheme for maximizing numerical efficiency. Numerical experiments prove that the MLS Difference Method shows very good accuracy and efficiency in solving complex 2-D Stefan problems.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.6
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• pp.1205-1215
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• 1992

The solidification rate is of special importance in determining the casting structures and properties. The heat transfer characteristics at the interface between the mold and the casting is one of the major factors that control the solidification rate. The thermal resistance exists due to the air-gap formation at the mold/casting interface during the freezing process. In this study two-dimensional Stefan problem with air-gap resistance in the rectangular mold is considered and the heat transfer characteristics is numerically examined by using the enthalpy method. The effects of the major parameters, such as mold geometry, thermal conductivity, heat transfer coefficient, and initial temperature of casting, on the thermal characteristics are investigated.