Numerical solution of vector stefan problems with cross-diffusion

ECCOMAS 2004 - European Congress on Computational Methods in Applied Sciences and Engineering

Volumn , Issue , 2004, Pages

  Vermolen, F J ^a   Vuik, C ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Cross diffusion; Numerical methods; Vector valued stefan problem

Indexed keywords

CROSS-DIFFUSION; DIFFUSION EQUATIONS; DIFFUSION MATRICES; EXISTENCE OF SOLUTIONS; MULTI-COMPONENT ALLOY; NUMERICAL SOLUTION; SELF-SIMILAR SOLUTION; VECTOR-VALUED STEFAN PROBLEM;

COMPUTATIONAL METHODS; EQUATIONS OF MOTION; NUMERICAL METHODS; VECTORS;

DIFFUSION;

EID: 84893436613     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (17)

1. F.J. Vermolen, C. Vuik and S. van der Zwaag. Particle dissolution and cross-diffusion in multi-component alloys. Materials Science and Engineering, A347, 265-279, 2003.
2. F.J. Vermolen, C. Vuik and S. van der Zwaag. Diffusion controlled particle dissolution and cross-diffusion in metallic alloys. Computation and Visualization in Science, accepted, 2003.
3. F.J. Vermolen and C. Vuik. Solution of vector-Stefan problems with cross-diffusion. Report at the Delft University of Technology, section Applied Mathematical Analysis, TWA-03-14, http://ta.twi.tudelft.nl.
4. M.H. Protter and H.F. Weinberger. Maximum principles in differential equations. Prentice-Hall. Englewood Cliffs, 1967.
5. G. Birkhoff and S. MacLane. A survey of modern algebra. Macmillan, New York, 1953.
6. G.H. Golub and C.F. van Loan. Matrix computations. Third Edition. The Johns Hopkins University Press. Baltimore, 1996.
7. M.E. Glicksman. Diffusion in solids. John Wiley and Sons, New York, 2000.
8. J. Crank. Free and Moving boundary problems. Clarendon Press, Oxford, 1984.
9. J. Chadam and H. Rasmussen. Tree boundary problems involving solids. Longman, Scientific and technical Harlow, f 993.
10. A. Visintin. Models of phase transitions. Progress in nonlinear differential equations and their application: 38 Birkhauscr, Boston 1996.
11. F.J. Vermolen and C. Vuik. A mathematical model for the dissolution of particles in multi-component alloys. Journal of computational and applied mathematics, 126, 233-254, 2001.
12. E. Kreyzig. Introductory functional analysis with applications. Wiley, New York, 1989.
13. W.D. Murray and F. Landis. Numerical and machine solutions of transient heat conduction problems involving freezing and melting. Transactions ASME (C), Journal of heat transfer. 245, 106-112, 1959.
14. R., Kobayashi. Modeling and numerical simulations of dendritic crystal growth. Physics D. 63, 410-423, 1993.
15. S. Osher and J.A. Sethian. Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-, Jacobi formulations. Journal of Computational physics. 79. 12-49, 1988.
16. S. Chen and B. Merriman and S. Osher and P. Smereka. A simple level-set method for solving Stefan problems. Journal of Computational Physics. 135. 8-29, 1997.
17. U. Grafe and B. Bottger and J. Tiaden and S.G. Fries. Coupling of multicomponent thermodynamics to a phase field model: application to solidification and solid-state transformations of superalloys. Script a Materialia. 42. 1179-1186, 2000.