SOLVING THE STEFAN PROBLEM WITH THE RADIAL BASIS FUNCTION COLLOCATION MEHOD

References

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