IJPAM: Volume 58, No. 4 (2010)
BINARY SOLIDIFICATION -- THE CLASSICAL
TWO-PHASE STEFAN PROBLEM
Department of Mathematics
Taichung, 40704, TAIWAN, R.O.C.
Department of Mathematical Physics
Ural State University
51, Lenin Ave., Ekaterinburg, 620083, RUSSIAN FEDERATION
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