Time dependent simulation of the Driven Lid Cavity at High Reynolds Number

Abstract

In this work, numerical solutions of the two dimensional time dependent incompressible flow, in a driven cavity at high Reynolds number Re, are presented. At high Re, there is a controversy. Some studies predicted that the flow is steady, others found time dependent non-steady flow, either periodic or aperiodic. In this study, the driven lid cavity is successfully solved using a very fine grid mesh, for Re up to $30 000$. We discretize the Vorticity-Stream formulation of the Navier-Stokes equation with the SSPRK(5,4) scheme in a $1024\times1024$ grid. Using this very fine grid, the results obtained converge to a stationary solution. Detailed results for Re between $5 000$ and $30 000$ are presented. The driven lid cavity problem is solved with a NVIDIA GPU using the CUDA programming environment with double precision.

20 pages, 11 figures, 2 tables. We changed the algorithm, from first order to fourth order temporal accuracy as well as the stream equation, therefore the results and figures were updated and some figures are removed. We use GPU's, with double precision capabilities, to solve this problem