Direct Numerical Simulation in a Lid-Driven Cubical Cavity at High Reynolds Number by a Chebyshev Spectral Method

Direct numerical simulation of the flow in a lid-driven cubical cavity has been carried out at high Reynolds numbers (based on the maximum velocity on the lid), between 1.2 104 and 2.2 104. An efficient Chebyshev spectral method has been implemented for the solution of the incompressible Navier–Stokes equations in a cubical domain. The Projection-Diffusion method [Leriche and Labrosse (2000, SIAM J. Sci. Comput. 22(4), 1386–1410), Leriche et al. (2005, J. Sci. Comput., in press)] allows to decouple the velocity and pressure computation in very efficient way and the simple geometry allows to use the fast diagonalisation method for inverting the elliptic operators at a low computational cost. The resolution used up to 5.0 million Chebyshev collocation nodes, which enable the detailed representation of all dynamically significant scales of motion. The mean and root-mean-square velocity statistics are briefly presented