Two very accurate and efficient methods for computing eigenvalues and eigenfunctions in porous convection problems

Journal of Computational Physics

Volumn 127, Issue 1, 1996, Pages 128-141

  Straughan, B ^a,b   Walker, D W ^a,c  

^a OAK RIDGE NATIONAL LABORATORY   (United States)

^b UNIVERSITY OF GLASGOW   (United Kingdom)

^c CARDIFF UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

POROUS MATERIALS;

CHEBYSHEV TAU METHODS; COMPOUND MATRICES; CONVECTION IN POROUS MEDIAS; CONVECTION PROBLEM; EIGENVALUE AND EIGENFUNCTIONS; HIGHLY ACCURATE; LINEAR STABILITY; MATRIX METHODS; NON-LINEAR STABILITIES; STABILITY PROBLEM;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 0030210322     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1996.0163     Document Type: Article

References (26)

1. 1. E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, and D. Sorensen, LAPACK Users' Guide, 2nd ed. (SIAM, Philadelphia, 1995).
2. 2. J. J. Dongarra, B. Straughan, and D. W. Walker, to appear.
3. 3. J. J. Dongarra and D. W. Walker, SIAM Rev. 37, 151 (1995).
4. 4. P. G. Drazin and W. H. Reid, Hydrodynamic Stability (Cambridge Univ. Press, Cambridge, 1981).
5. 5. L. Fox, Computer J. 4, 318 (1962).
6. 6. D. R. Gardner, S. A. Trogdon, and R. W. Douglas, J. Comput. Phys. 80, 137 (1989).
7. 7. D. B. Haidvogel and T. Zang, J. Comput. Phys. 30, 167 (1979).
8. 8. I. Kim and A. J. Pearlstein, J. Fluid Mech. 211, 73 (1990).
9. 9. K. A. Lindsay and R. R. Ogden, Int. J. Numer. Methods Fluids 15, 1277 (1992).
10. 10. C. B. Moler and G. W. Stewart, SIAM. J. Numer. Anal. 10, 241 (1973).
11. 11. B. S. Ng and W. H. Reid, J. Comput. Phys. 30, 125 (1979).
12. 12. B. S. Ng and W. H. Reid, J. Comput. Phys. 33, 70 (1979).
13. 13. B. S. Ng and W. H. Reid, J. Comput. Phys. 58, 209 (1985).
14. 14. D. A. Nield, Int. J. Heat Mass Transf. 37, 3021 (1994).
15. 15. D. A. Nield and A. Bejan, Convection in Porous Media (Springer-Verlag, Berlin/Heidelberg/New York, 1992).
16. 16. D. A. Nield, D. M. Manole, and J. L. Lage, J. Fluid Mech. 257, 559 (1993).
17. 17. S. A. Orszag, J. Fluid Mech. 50, 689 (1971).
18. 18. A. J. Pearlstein, R. M. Harris, and G. Terrones, J. Fluid Mech. 202, 443 (1989).
19. 19. D. Powers, K. O'Neill, and S. C. Colbeck, J. Geophys. Res. (D) 90, 10641 (1985).
20. 20. B. Straughan, The Energy Method, Stability, and Nonlinear Convection (Springer-Verlag, Berlin/Heidelberg/New York, 1992).
21. 21. B. Straughan, Mathematical Aspects of Penetrative Convection (Longman, Harlow, 1993).
22. 22. B. Straughan and D. W. Walker, Proc. R. Soc. London A 452, 97 (1996).
23. 23. B. Straughan and D. W. Walker, to appear.
24. 24. A. Zebib, J. Comput. Phys. 53, 443 (1984).
25. 25. A. Zebib, J. Comput. Phys. 70, 521 (1987).
26. 26. A. Zebib, J. Eng. Math. 21, 155 (1987).