LAUSR

Abstract Numerical simulations are used to probe Rayleigh–Darcy convection in fluid-saturated porous media towards the ultimate regime. The present three-dimensional dataset, up to Rayleigh–Darcy number $\textit {Ra}=8\times 10^4$, suggests that the appropriate scaling of the Nusselt number is $\textit {Nu}=0.0081\textit {Ra}+0.067\textit {Ra}^{0.61}$, fitting the computed data for $\textit {Ra}\gtrsim 10^3$. Extrapolation of current predictions to the ultimate linear regime yields the asymptotic law $\textit {Nu}=0.0081 \textit {Ra}$, about $16\,\%$ less than indicated in previous studies. Upon examination of the flow structures near the boundaries, we confirm previous indications of small flow cells hierarchically nesting into supercells, and we show evidence that the supercells at the boundary are the footprints of the megaplumes that dominate the interior part of the flow. The present findings pave the way for more accurate modelling of geophysical systems, with special reference to geological $\textrm {CO}_2$ sequestration.