2D differentially heated cavity

The simulation highlights a strongly unsteady natural convection regime, characteristic of a high Rayleigh number (Ra = 10¹⁰). After an initial conduction-dominated phase, the flow quickly becomes unsteady, with upward motion along the hot wall and downward motion along the cold wall.

The cavity core is strongly mixed. Thermal structures continuously deform, break up, and interact with each other. Thin thermal boundary layers develop along the hot and cold walls.

A clear transition toward a highly convective regime is observed. Thermal plumes become unsteady and actively contribute to mixing within the cavity.

Simulations performed for Rayleigh numbers ranging from 10³ to 10⁸ accurately reproduce the standard reference quantities of the differentially heated cavity. These results validate the model across a wide range of regimes, from conduction-dominated cases to well-established natural convection.

The table below compares Fugu predictions with the reference results of Dixit and Babu (2006) for the maximum horizontal velocity Umax and its location Y, the maximum vertical velocity Vmax and its location X, as well as the average Nusselt number Nu. The good agreement observed across all these indicators confirms the relevance of the model for this natural convection benchmark.