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A differential constraint approach to obtain global stability for radiation‐induced double‐diffusive convection in a porous medium
Author(s) -
Hill Antony A.
Publication year - 2008
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1073
Subject(s) - porous medium , constraint (computer aided design) , stability (learning theory) , nonlinear system , convection , coupling (piping) , mathematics , partial differential equation , darcy's law , mass transfer , differential equation , mechanics , mathematical analysis , porosity , physics , chemistry , materials science , computer science , geometry , quantum mechanics , organic chemistry , machine learning , metallurgy
The stability of double‐diffusive porous convection with a concentration‐based internal heat source is studied. Owing to the significant sensitivity of standard energy method, a highly desirable reduction in the number of required coupling parameters is achieved through the novel energy method of van Duijn et al. ( Environmental Mechanics: Water, Mass and Energy Transfer in the Biosphere. American Geophysical Union: Washington, DC, 2002; 155–169). This approach incorporates the Darcy equation as a differential constraint, and has been shown by van Duijn et al. to generally yield sharper nonlinear results. Owing to the widespread use of coupling parameters in analysing porous media stability, this result strongly advocates the differential constraint approach for obtaining optimal nonlinear stability thresholds. Copyright © 2008 John Wiley & Sons, Ltd.