IJPAM: Volume 58, No. 4 (2010)

NUMERICAL MODELING OF ONE-DIMENSIONAL
BINARY SOLIDIFICATION -- THE CLASSICAL
TWO-PHASE STEFAN PROBLEM

Daniel Lee$^1$, D.V. Alexandrov$^2$
$^1$Department of Mathematics
Tunghai University
Taichung, 40704, TAIWAN, R.O.C.
e-mail: [email protected]
$^2$Department of Mathematical Physics
Ural State University
51, Lenin Ave., Ekaterinburg, 620083, RUSSIAN FEDERATION
e-mail: [email protected]


Abstract.We consider in this work the heat diffusion of one-dimensional spatial variable in the semi-infinite interval. Both fixed and moving coordinates will be considered. We investigate for each model the numerical methods and discuss the issues in software design and the trade-offs between accuracy and efficiency, based on the analytic solution. In particular, we propose a threshold strategy in fixed coordinate static grid approach and show it performs very well in many tests. The observations can be helpful in practical applications of mushy layer models, for which no explicit solution is expected.

Received: November 18, 2009

AMS Subject Classification: 65-05, 65M06

Key Words and Phrases: heat transfer, solidification, Stefan problem

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 58
Issue: 4