Unconditional nonlinear stability for convection in a porous medium with vertical throughflow

Acta Mechanica

Volumn 193, Issue 3-4, 2007, Pages 197-206

  Hill, A A ^a,b  

^a DURHAM UNIVERSITY   (United Kingdom)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

LINEAR STABILITY ANALYSIS; MATHEMATICAL MODELS; POROUS MATERIALS;

ENERGY ANALYSIS; LINEAR INSTABILITY; NONLINEAR STABILITY;

HEAT CONVECTION;

EID: 34748862942     PISSN: 00015970     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00707-007-0473-5     Document Type: Article

References (22)

1. Zhao C., Hobbs B. E. and Muhlhaus A. B. (1999). Theoretical and numerical analyses of convective instability on porous media with upward throughflow. Int. J. Numer. Anal. Meth. Geomech. 23: 629-646
2. Krishnamurti R. (1975). On cellular cloud patterns. Part 1: Mathematical model. J. Atmos. Sci. 32: 1351-1363
3. Somerville R. C. J. and Gal-Chen T. (1979). Numerical simulation of convection with mean vertical motion. J. Atmos. Sci. 36: 805-815
4. Nield D. A. (1998). Convection in a porous medium with an inclined temperature gradient and vertical throughflow. Int. J. Heat Mass Transf. 41: 241-243
5. Nield D. A. and Bejan A. (1999). Convection in porous media. Springer, New York
6. Hill, A. A., Rionero, S., Straughan, B.: Global stability for penetrative convection with throughflow in a porous material (in preparation).
7. Giorgi T. (1997). Derivation of the Forchheimer law via matched asymptotic expansions. Trans. Porous Media 29: 191-206
8. Whitaker S. (1996). The Forchheimer equation: a theoretical development. Transp. Porous Media 25: 27-62
9. Gilver R. C. and Altobelli S. A. (1994). A determination of effective viscosity for the Brinkman-Forchheimer flow model. J. Fluid. Mech. 258: 355-370
10. Néel M. C. (1998). Convection forcée en milieu poreux: écarts à la loi de Darcy C. R. Acad. Sci. Paris, série IIb 326: 615-620
11. Flavin J. N. and Rionero S. (2002). Note on a versatile Liapunov functional: applicability to an elliptic equation. Math. Meth. Appl. Sci. 25: 1299-1305
12. Flavin J. N. and Rionero S. (2003). Stability properties for the nonlinear diffusion in porous media and other media. J. Math. Anal. Appl. 28: 221-232
13. Lombardo S., Mulone G. and Rionero S. (2001). Global nonlinear exponential stability of the conduction-diffusion solution for Schmidt numbers greater than Prandtl numbers. J. Math. Anal. Appl. 262: 191-207
14. Payne L. E. and Straughan B. (2000). Unconditional nonlinear stability in temperature-dependent viscosity flow in a porous medium. Stud. Appl. Math. 105: 59-81
15. Carr M. (2003). Unconditional nonlinear stability for temperature dependent density flow in a porous medium. Math. Models Meth. App. Sci. 13: 207-220
16. Straughan B. and Walker D. W. (1996). Two very accurate and efficient methods for computing eigenvalues and eigenfunctions in porous convection problems. J. Comput. Phys. 127: 128-141
17. Dongarra J. J., Straughan B. and Walker D. W. (1996). Chebyshev tau-QZ algorithm methods for calculating spectra of hydrodynamic stability problems. Appl. Numer. Math. 22: 399-434
18. Christopherson D. G. (1940). Note on the vibration of membranes. Quart. J. Math. 11: 63-65
19. Molar C. B. and Stewart G. W. (1973). An algorithm for generalized matrix eigenproblems. SIAM J. Numer. Anal. 10: 241-256
20. Straughan B. (2004). The energy method, stability and nonlinear convection. Springer, New York
21. Qiao Z. and Kaloni P. (1998). Nonlinear convection in a porous medium with inclined temperature gradient and vertical throughflow. Int. J. Heat Mass Transf. 41: 2549-2552
22. Rionero S. and Galdi G. (1985). Weighted energy methods in fluid dynamics and elasticity. Springer, Berlin