Direct numerical simulation of the turbulent flow inside a differentially heated cavity

The turbulent flow inside a differentially heated cavity at a Rayleigh number of approximately 10 ⁹ has been studied through a fully resolved Direct Numerical Simulation using the high-order Spectral Element Method code Nek5000. The case chosen for the present paper includes two physical phenomena: the natural recirculation itself, and the flow inside a curved channel that has been added to bottom right corner of the cavity. Solutions are presented as reference for the validation of models when the two physical phenomena are superposed. Simulations have been carried out either using the Boussinesq approximation or a low-Mach compressible formulation. Significant discrepancies between the two methods inform of the extreme necessary caution to consider when using the Boussinesq approximation in the limits of its applicability. Proper resolution of the DNS has been analyzed by considering the polynomial order convergence of the solution and the computation of the Reynolds stresses budgets.