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Godunov Method for Stefan Problems with Enthalpy Formulations

Published online by Cambridge University Press:  28 May 2015

D. Tarwidi  and
S.R. Pudjaprasetya
D. Tarwidi*
Affiliation:
Department of Computational Science, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha 10, Bandung 40132, Indonesia
S.R. Pudjaprasetya*
Affiliation:
Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha 10, Bandung 40132, Indonesia
*
Corresponding author. Email: dede.tarwidi@yahoo.com
Corresponding author. Email: sr_pudjap@math.itb.ac.id
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Abstract

A Stefan problem is a free boundary problem where a phase boundary moves as a function of time. In this article, we consider one-dimensional and two-dimensional enthalpy-formulated Stefan problems. The enthalpy formulation has the advantage that the governing equations stay the same, regardless of the material state (liquid or solid). Numerical solutions are obtained by implementing the Godunov method. Our simulation of the temperature distribution and interface position for the one-dimensional Stefan problem is validated against the exact solution, and the method is then applied to the two-dimensional Stefan problem with reference to cryosurgery, where extremely cold temperatures are applied to destroy cancer cells. The temperature distribution and interface position obtained provide important information to control the cryosurgery procedure.

Keywords

65M1078A48Stefan problemsGodunov methodsolidificationenthalpycryosurgery
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 3 , Issue 2 , May 2013 , pp. 107 - 119
Copyright
Copyright © Global-Science Press 2013

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