The long-time behaviour of the thermoconvective flow in a porous medium
- Efendiev, Messoud A.
- Fuhrmann, Jürgen
- Zelik, Sergei V.
2010 Mathematics Subject Classification
- 37L25 37L30 35B40 35B45 65M99
- equations of coupled heat and fluid flow in a porous medium, Boussinessq approximation, global attractor, upper and lower bounds, Rayleigh number, Hausdorff and fractal dimension, finite volumes, numerical solution
For the Boussinesq approximation of the equations of coupled heat and fluid flow in a porous medium we show that the corresponding system of partial differential equations posesses a global attractor. We give lower and upper bounds of the Hausdorff dimension of the attractor depending on a physical parameter of the system, namely the Rayleigh number of the flow. Numerical experiments confirm the theoretical findings and raise new questions on the structure of the solutions of the system.
- Mathematical Methods in the Applied Sciences, 27(4), pp. 907-930, 2004