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) |
