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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.

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)
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