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. ? 2010 Academic Publications.
Relation:
International Journal of Pure and Applied Mathematics 58 (4) , pp. 381-416
