Stability analysis of penetrative convection in anisotropic porous media with variable permeability

In this paper we study the penetrative convection in an anisotropic porous medium, for fluids with quadratic density law with the anisotropic permeability and thermal diffusivity effects. Both linear instability and global non-linear energy stability analyses are tested using a three-dimensional simulation. Our results show that the linear threshold accurately predicts on the onset of instability in the basic steady state. However, the required time to arrive at the steady state increases significantly as the Rayleigh number tends to the linear threshold.