An improved Chebyshev collocation algorithm for direct simulation of 2D turbulent convection in differentially heated cavities

We present a modified Chebyshev collocation algorithm for direct numerical simulations of 2D turbulent convection in differentially heated cavities. The numerical algorithm integrates the Navier-Stokes equations in velocity-pressure formulation with a Chebyshev spatial approximation and a second order finite difference time-stepping scheme. A coordinate stretching is introduced which allows one to redistribute the collocation points where needed in order to resolve more economically the small scales that appear at cavity mid-height. This algorithm is used to perform simulations in a square differentially heated cavity with adiabatic top and bottom walls filled with a fluid of Prandtl number equal to 0.71 for Rayleigh number values up to 10¹⁰ which is almost two orders of magnitude higher than the onset of unsteadiness. The time-dependent dynamics of the solutions are investigated and the time-averaged flow structures are displayed. The influence of unsteadiness on the local and global heat transfer coefficients is examined.