The Numerical Solution of One-Dimensional Phase Change Problems Using an Adaptive Moving Mesh Method

Journal of Computational Physics

Volumn 161, Issue 2, 2000, Pages 537-557

  Mackenzie, J A ^a   Robertson, M L ^a  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ENTHALPY; HEAT CONDUCTION; MESH GENERATION; NUMERICAL METHODS; SPOT WELDING;

ADAPTIVE MOVING MESH METHOD; ENTHALPY FORMULATIONS; HEAT CONDUCTION PROBLEMS; MESH MODIFICATION; NUMERICAL SOLUTION; ONE-DIMENSIONAL; PHASE CHANGE; PHASE CHANGE PROBLEM; SIMPLE MESHES; SMOOTH EVOLUTIONS;

NONLINEAR EQUATIONS;

EID: 0001617135     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2000.6511     Document Type: Article

References (24)

1. S. Adjerid and J. E. Flaherty, A moving finite element method with error estimation and refinement for one-dimensional partial differential equations, SIAM J. Numer. Anal. 23, 778 (1986).
2. D. R. Atthey, A finite difference scheme for melting problems, J. Inst. Math. Appl. 13, 353 (1974).
3. J. G. Blom, J. M. Sanz-Serna, and J. G. Verwer, On simple moving grid methods for one-dimensional evolutionary partial differential equations, J. Comput. Phys. 74, 191 (1988).
4. C. Bonacina, G. Comini, A. Fasano, and M. Primicerio, Numerical solution of phase-change problems, Int. J. Heat Mass Transfer 16, 1825 (1973).
5. W. Cao, W. Huang, and R. D. Russell, An r-adaptive finite element method based upon moving mesh PDEs, J. Comput. Phys. 149, 221 (1999).
6. G. F . Carey and H. T. Dinh, Grading functions and mesh redistribution, SIAM J. Numer. Anal. 22, 1028 (1985).
7. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids (Oxford Univ. Press, London, 1959).
8. J. Crank, Free and Moving Boundary Value Problems (Oxford Science Publications, 1984).
9. C. de Boor, Good approximation by splines with variables knots. II. in Lecture Notes in Mathematics (Springer-Verlag, New York/Berlin, 1974), Vol. 363, p. 12.
10. E. A. Dorfi and L. O'c. Drury, Simple adaptive grids for 1-D initial value problems, J. Comput. Phys. 69, 175 (1987).
11. D. B. Duncan, A simple and effective self-adaptive moving mesh for enthalpy formulations of phase change problems, IMA J. Numer. Anal. 11, 55 (1991).
12. P. W. Egolf and H. Manz, Theory and modeling of phase change materials with and without mushy regions, Int. J. Heat Mass Transfer 37, 2917 (1994).
13. C. M. Elliott, On the finite element approximation of an elliptic variational inequality arising from an implicit time discretisation of the Stefan problem, IMA J. Numer. Anal. 1, 115 (1981).
14. K. Farrell and L. Drury, An explicit, adaptive grid algorithm for one-dimensional initial value problems, Appl. Numer. Math. 26, 3 (1997).
15. R. M. Furzeland, A comparitive study of numerical methods for moving boundary value problems, J. Inst. Math. Appl. 26, 411 (1980).
16. W. Huang, Y. Ren, and R. D. Russell, Moving mesh PDEs based on the equidistribution principle, SIAM J. Numer. Anal. 31, 709 (1994).
17. A. A. Lacey and A. B. Taylor, A mushy region in a Stefan problem, IMA J. Appl. Math. 30, 303 (1983).
18. C. H. Li, A finite-element front-tracking enthalpy method for Stefan problems, IMA J. Numer. Anal. 3, 87 (1983).
19. G. H. Meyer, Multidimensional Stefan problems, SIAM J. Numer. Anal. 10, 522 (1973).
20. R. H. Nochetto, M. Paolini, and C. Verdi, An adaptive finite element method for two-phase Stefan problems in two space dimensions. Part II. Implementation and numerical experiments, SIAM J. Sci. Comput. 12(5), 1207 (1991).
21. R. H. Nochetto, A. Schmidt, and C. Verdi, Error control for phase change problems, in IVTAM Symposium on Variations of Domain and Free Boundary Problems, Paris (Kluwer Academic, Dordrecht, 1997).
22. J. R. Ockendon and W. R. Hodgkins, Moving Boundary Problems in Heat Flow and Diffusion (Oxford Univ. Press, London, 1975).
23. N. Shamsunder, in Moving Boundary Problems, edited by D. G. Wilson and P. T. Boggs (Academic Press, San Diego, 1978), p. 165.
24. V. Voller and M. Cross, Accurate solutions of moving boundary problems using the enthalpy method, Int. J. Heat Mass Transfer 24, 545 (1981).