A Nodal Method for Phase Change Moving Boundary Problems

International Journal of Computational Fluid Dynamics

Volumn 11, Issue 3-4, 1999, Pages 211-221

  Rizwan Uddin, ^a  

^a University of Illinois at Urbana Champaign   (United States)

Author keywords

Moving boundary problem; Nodal integral approach; Stefan problem

Indexed keywords

EID: 0345979813     PISSN: 10618562     EISSN: None     Source Type: Journal    
DOI: 10.1080/10618569908940875     Document Type: Article

References (16)

1. Azmy, Y. Y. and Dorning, J. J. (1983) A Nodal Integral Approach to the Numerical Solution of Partial Differential Equations, in Advances in Reactor Computations, Volume II, pp. 893-909. American Nuclear Society, LaGrange Park, IL.
2. Furzeland, R. M. (1980) A Comparative Study of Numerical Methods for Moving Boundary Problems, J. Inst. Maths. Applics., 26, 411-429.
3. Hennart, J. P. (1986) A General Family of Nodal Schemes, SIAM J. Sci. Stat. Comp., 7(1), 264-287.
4. Michael, E. P. E., Doming, J. J., Gelbard, E. M. and Rizwan-uddin (1993) A Nodal Integral Method for the Convection-Diffusion Heat Equation, Trans. Am. Nucl. Soc., 69, 239-241.
5. Marshall, G. (1986) A Front Tracking Method for One-Dimensional Moving Boundary Problems, SIAM J. Sci. Stat. Comput., 7(1), 252-263.
6. Menning, J. and Özişik, M. N. (1985) Coupled Integral Equation Approach for Solving Melting or Solidification, Int. J. Heat Mass Transfer, 28(8), 1481-1485.
7. Ockendon, J. R. and Hodgkins, W. R. (Eds.) (1975) Moving Boundary Problems in Heat Flow and Diffusion, Clarendon Press, Oxford.
8. Özişik, N. (1993) Heat Conduction, 2nd Edition, Wiley, NY.
9. Rizwan-uddin (1997a) A Second Order Space and Time Nodal Method for the One-Dimensional Convection Diffusion Equation, Comp. and Fluids, 26(3), 233-247.
10. Rizwan-uddin (1997b) An Improved Coarse-Mesh Nodal Integral Method for Partial Differential Equations. Num. Methods for Partial Differential Equations, 13, 113-145.
11. Rizwan-uddin (1997c) "A Hybrid Nodal-Integral/Finite-Element Method for Arbitrary Geometries," Trans. American Nuclear Society, 76, 170-172.
12. Rizwan-uddin (1998) "An Approximate-Solution-Based Numerical Scheme for Stefan Problem with Time-Dependent Boundary Conditions," Numerical Heat Transfer, Part B, 33, 269-285.
13. Samarskii, A. A., Vabishchevich, P. N., Iliev, O. P. and Churbanov, A. G. (1993) Numerical Simulation of Convection/Diffusion Phase Change Problems - A Review, Int. J. Heat Mass Transfer, 36, 17, 4095-4106.
14. Wilson, G. L. and Rydin, R. A. (1988) A Comparison of Two Efficient Nonlinear Heat Conduction Methodologies Using a Two-Dimensional Time-Dependent Benchmark Problem, Nuclear Technology, 82, 94-105.
15. Wilson, G. L., Rydin, R. A. and Azmy, Y. Y. (1988) Time-Dependent Nodal Integral Method for the Investigation of Bifurcation and Nonlinear Phenomena in Fluid Flow and Natural Convection, Nucl. Sci. Eng., 100, 414-425.
16. Yao, L. S. and Prusa, J. (1989) "Melting and Freezing," Adv. in Heat Transfer, 19, 1-95.