Penetrative convection via internal heating in anisotropic porous media

Penetrative convection in an anisotropic porous medium is simulated via internal heating. We consider both internal heat sources and sinks, where the porous medium has constant anisotropic thermal diffusivity and non-homogeneous permeability. Both linear instability and global nonlinear energy stability analyses are performed. By adopting a differential constraint approach, the nonlinear stability boundaries are shown to be sharp when compared with the linear instability thresholds. In contrast, it is shown that adopting a standard energy analysis does not yield sharp results.