THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

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Zhao-Chun Wu

,

Jianping Luo

,

Jingmei Feng

A NOVEL ALGORITHM FOR SOLVING THE CLASSICAL STEFAN PROBLEM

ABSTRACT
A novel algorithm for solving the classic Stefan problem is proposed in the paper. Instead of front tracking, we preset the moving interface locations and use these location coordinates as the grid points to find out the arrival time of moving interface respectively. Through this approach, the difficulty in mesh generation can be avoided completely. The simulation shows the numerical result is well coincident with the exact solution, implying the new approach performs well in solving this problem.
KEYWORDS
Stefan problem, moving interface, finite difference method, numerical simulation
PAPER SUBMITTED: 2010-05-10
PAPER REVISED: 2010-08-14
PAPER ACCEPTED: 2010-11-11
DOI REFERENCE: https://doi.org/10.2298/TSCI11S1039W
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2011, VOLUME 15, ISSUE Supplement 1, PAGES [S39 - S44]
REFERENCES
  1. Crank, J., Free and Moving Boundary Problems, Clarendon Press, Oxford, UK, 1984, pp. 140-141
  2. Gupta, S. C., Laitinen, E., Valtteri, T., Moving Grid Scheme for Multiple Moving Boundaries, Computer Methods in Applied Mechanics and Engineering, 167 (1998), 3-4, pp. 345-353
  3. Mackenzie, J. A., Robertson, M. L., The Numerical Solution of One-Dimensional Phase Change Problems Using an Adaptive Moving Mesh Method, Journal of Computational Physics, 161 (2000), 2, pp. 537-557
  4. Jeong, J. H., Yang, D. Y., Application of an Adaptive Grid Refinement Technique to Three-Dimensional Finite Element Analysis of the Filling Stage in the Die-Casting Process, Journal of Materials Processing Technology, 111 (2001), 1-3, pp. 59-63
  5. Beckett, G., Mackenzie, J. A., Robertson, M. L., A Moving Mesh Finite Element Method for the Solution of Two-Dimensional Stefan Problems, Journal of Computational Physics, 168 (2001), 2, pp. 500-518
  6. Wu, Z. C., Finite Difference Approach to Single-Phase Stefan Problems by Using Fixed-Time Step and Variable Space Interval Method, Chinese Journal of Computational Physics, 20 (2003), 6, pp. 521-524
  7. Verma, K., Chandra, S., Dhindaw, B. K., An Alternative Fixed Grid Method for Solution of the Classical One-Phase Stefan Problem, Applied Mathematics and Computation, 158 (2004), 2, pp. 573-584
  8. Kutluay, S., Esen, A., An Isotherm Migration Formulation for One-Phase Stefan Problem with a Time Dependent Neumann Condition, Applied Mathematics and Computation, 150 (2004), 1, pp. 59-67
  9. Tan, L. J., Zabaras, N., Modeling the Growth and Interaction of Multiple Dendrites in Solidification Using a Level Set Method, Journal of Computational Physics, 226 (2007), 1, pp. 131-155
  10. Chen, H., Min, C., Gibou, F., A Numerical Scheme for the Stefan Problem on Adaptive Cartesian Grids with Supralinear Convergence Rate, Journal of Computational Physics, 228 (2009), 16, pp. 5803-5818
  11. Wu, K. T., et al., Moving Boundary Problem Arising in Explosion and Impact: An Algorithm for Youngs' Interface Reconstruction, Int. J. Nonlin. Sci. Num., 10 (2009), 8, pp. 1051-1057
  12. Liu, S. H., et al., Vorticity Analysis of a Cavitating Two-Phase Flow in Rotating，Int. J. Nonlin. Sci. Num., 10 (2009), 5, pp. 601-616
  13. Geng, X. M., Aluminum Alloy Gravity Die Casting, Defence Industry Press, Beijing, China, 1976
  14. Ozisik, M. N., Heat Conduction, A Wiley-Interscience Publication, John Wiley & Sons, New York, USA, 1980
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A novel algorithm for solving the classical Stefan problem

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence