Solving the stefan problem with the radial basis function collocation mehod

Numerical Heat Transfer, Part B: Fundamentals

Volumn 44, Issue 6, 2003, Pages 575-599

  Kovacevic I ^a   Poredos A ^a   Sarler, B ^b  

^a UNIVERSITY OF LJUBLJANA   (Slovenia)

^b University of Nova Gorica   (El Salvador)

Author keywords

[No Author keywords available]

Indexed keywords

ENTHALPY; FINITE ELEMENT METHOD; FINITE VOLUME METHOD; INTERPOLATION; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; RADIAL BASIS FUNCTION NETWORKS; THERMAL EFFECTS;

RADIAL BASIS FUNCTION COLLOCATION METHOD; THERMAL STORAGE;

PHASE TRANSITIONS;

EID: 18344415726     PISSN: 10407790     EISSN: 15210626     Source Type: Journal    
DOI: 10.1080/716100496     Document Type: Article

References (25)

1. B. Sarler and G. Kuhn, Dual Reciprocity Boundary Element Method for Convective-Diffusive Solid-Liquid Phase Change Problems, Part I. Formulation Examples, Eng. Anal. Bound. Elem., vol. 21, pp. 53-63, 1998.
2. J. Franke, Scattered Data Interpolation: Tests of Some Methods, Math. Comput, vol. 48, pp. 181-200, 1982.
3. E. J. Kansa, Multiquadrics-A Scattered Data Approximation Scheme with Application to Computation Fluid Dynamics-I, Comput. Math. Appl., vol. 19, pp. 127-145, 1990.
4. E. J. Kansa, Multiquadrics-A Scattered Data Approximation Scheme with Application to Computation Fluid Dynamics-II, Comput. Math. Appl., vol. 19, pp. 147-161, 1990.
5. W. Chen and M. Tanaka, New Insights into Boundary-Only and Domain-Type RBF Methods, J. Nonlinear Sci. Numer. Simul., vol. 1, pp. 145-151, 2000.
6. W. Chen and M. Tanaka, A Meshless, Exponential Convergence, Integration-Free, and Boundary-Only RBF Technique, Comput. Math. Appl., vol. 43, pp. 379-391, 2002.
7. M. Zerroukat, H. Power, and C. S. Chen, A Numerical Method for Heat Transfer Pro-bems Using Collocation and Radial Basis Functions, Int. J. Numer. Meth. Eng., vol. 42, pp. 1263-1278, 1998.
8. M. Zerroukat, K. Djidjeli, and A. Charafi, Explicit and Implicit Meshless Methods for Linear Advection-Diffusion-Type Partial Differential Equations, Int. J. Numer. Meth. Eng., vol. 48, pp. 19-35, 2000.
9. N. Mai-Duy and T. Tran-Cong, Numerical Solution of Navier-Stokes Equations Using Radial Basis Function Networks, Int. J. Numer. Meth. Fluids, vol. 37, pp. 65-86, 2001.
10. B. Sarler, J. Perko, C. S. Chen, and G. Kuhn, A Meshless Approach to Natural Convection, in S. N. Atluri (ed.), Int. Conf. On Computer Engineering and Sciences-2001, CD-ROM Proc., pp. 3-9, 2001.
11. J. Perko, C. S. Chen, and B. Sarler, A Polygon-Free Numerical Solution of Steady Natural Convection in Solid-Liquid Systems, in B. Sarler and C. A. Brebbia (eds.), Computational Modelling of Moving and Free Boundary Problems, pp. 111-122, WIT Press, Southampton, UK, 2001.
12. B. Sarler, J. Perko, and C. S. Chen, Natural Convection in Porous Media-Radial Basis Function Collocation Method Solution of the Darcy Model, in H. A. Mang, F. G. Rammerstorfer, and J. Eberhardsteiner (eds.), Proc. Fifth World Congress on Computational Mechanics (WCCM V), Vienna, Austria, 2002.
13. B. Sarler, Stefan’s Work on Solid-Liquid Phase Changes, Eng. Anal. Bound. Elem., vol. 16, pp. 83-92, 1995.
14. W. D. Bennon and F. P. Incropera, A Contimuum Model for Momentum, Heat and Species Transport in Binary Solid-Liquid Phase Change Systems-I. Model Formulation, Int. J. Heat Mass Transfer, vol. 30, pp. 2161-2170, 1987.
15. V. R. Voller and C. R. Swaminathan, General Source-Based Method for Solidification Phase Change, Numer. Heat Transfer B, vol. 19, pp. 175-189, 1991.
16. V. R. Voller, A Numerical Scheme for Solidification of an Alloy, Can. Metall. Quart., vol. 37, pp. 169-177, 1998.
17. H. Power and V. Barraco, A Comparison Analysis between Unsymmetric and Symmetric Radial Basis Function Collocation Methods for the Numerical Solution of Partial Differential Equations, Comput. Math. Appl., vol. 43, pp. 551-583, 2002.
18. K. A. Rathjen and L. M. Jiji, Heat Conduction with Melting or Freezing in a Corner, J. Heat Transfer, vol. 18, pp. 101-109, 1971.
19. B. Sarler and G. Kuhn, Dual Reciprocity Boundary Element Method for Convective-Diffusive Solid-Liquid Phase Change Problems, Part 2. Numerical Examples, Eng. Anal. Bound. Elem., vol. 21, pp. 65-79, 1998.
20. A. J. Dalhuijsen and A. Segal, Comparison of Finite Element Techniques for Solidification Problems, Int. J. Numer. Meth. Eng., vol. 23, pp. 1807-1829, 1986.
21. N. Mai-Duy and T. Tran-Cong, Numerical Solution of Differential Equations Using Multiquadric Radial Basis Function Networks, Neural Networks, vol. 14, pp. 185-199, 2001.
22. X. Zhang, K. Z. Song, M. W. Lu, and X. Liu, Meshless Methods Based on Collocation with Radial Basis Functions, Comput. Mech., vol. 26, pp. 333-343, 2000.
23. J. G. Wang and G. R. Liu, On the Optimal Shape Parameters of Radial Basis Functions Used for 2-D Meshless Methods, Comput. Meth. Appl. Mech. Eng., vol. 191, pp. 2611-2630, 2002.
24. C. E. Dorgan and J. S. Elleson, Design Guide for Cool Thermal Storage, American Society of Heating, Refrigeration and Air-Conditioning Engineers, Atlanta, GA, 1993.
25. J. Crank, Free and Moving Boundary Problems, Oxford Science Publications, Oxford, UK, 1984.