Direct Numerical Simulations of turbulent flow in a driven cavity

Direct numerical simulations (DNS) of 2 and 3D turbulent flows in a lid-driven cavity have been performed. DNS are numerical solutions of the unsteady (here: incompressible) Navier-Stokes equations that compute the evolution of all dynamically significant scales of motion. In view of the large computing resources needed for DNS cost-effective and accurate numerical methods are to be selected. Here, various-order accurate spatial discretization methods for DNS have been evaluated by applying them to the 2D driven cavity at Re = 22,000. To analyze the results of the DNS of the 2D flow in a driven cavity at Re = 22,000 the proper orthogonal decomposition (POD) technique has been applied. POD is an unbiased method to determine coherent structures. The Galerkin projection of the Navier-Stokes equations on the space spanned by the POD-basis-functions yields a relatively low-dimensional set of ordinary differential equations that mimics the dynamics of the Navier-Stokes equations. 3D DNS with no-slip conditions at all walls of the cavity have been performed at both Re = 3,200 and Re = 10,000. The results reproduce the experimentally observed Taylor-Görtler-like vortices