×

zbMATH — the first resource for mathematics

Two very accurate and efficient methods for computing eigenvalues and eigenfunctions in porous convection problems. (English) Zbl 0858.76064
Summary: We develop the compound matrix method and the Chebyshev tau method to be applicable to linear and nonlinear stability problems for convection in porous media, in a natural way. It is shown how to obtain highly accurate answers to problems which may be stiff, and spurious eigenvalues are avoided. A detailed analysis is provided for a porous convection problem of much current interest, namely convection with a horizontally varying temperature gradient.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76E15 Absolute and convective instability and stability in hydrodynamic stability
76E30 Nonlinear effects in hydrodynamic stability
76S05 Flows in porous media; filtration; seepage
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
80A20 Heat and mass transfer, heat flow (MSC2010)
Software:
LAPACK
PDF BibTeX XML Cite
Full Text: DOI