Modelling the Navier-Stokes-Darcy-Boussinesq system

To investigate convection in coupled fluid-porous media systems, we analyze the Navier-Stokes-Darcy Heat model with numerical simulations conducted via a finite element method. To help validate numerical results, we compare our simulations against stability thresholds for the system.

Additionally, we investigate various parameter regimes of the system and present a notable case with altering the depth ratio of the two regions. In these superposed fluid-porous media systems, the ratio of the fluid height to the porous medium height exerts a significant influence on the behavior of the coupled system with its impact on resulting convection cells. Altering the depth ratio slightly can trigger a transition from  deep convection where convection cells encapsulate the entire domain to shallow convection where cells occupy only the fluid region. With current interest surrounding superposed fluid-porous medium systems in numerous projects of industrial, environmental, and geophysical importance (oil recovery, carbon dioxide sequestration, contamination in sub-soil reservoirs, etc.), being able to predict the critical depth ratio where this convection shift occurs is particularly timely.