Direct Simulation of Unsteady Flow in a Three-Dimensional Lid-Driven Cavity

This paper deals with the direct simulation of the three-dimensional unsteady laminar flow of an incompressible viscous fluid in a lid-driven cavity at a Reynolds number equal to 3200. The dimensionless Navier-Stokes equations, using a velocity-pressure formulation, are written in conservative form. The discretization is based on a semi-implicit finite difference method with non-staggered variable arrangement. Central difference schemes are used for temporal and spatial discretization and are both second-order accurate. Pressure is obtained by solving a Poisson-like equation with a discrete divergence velocity minimization algorithm. Unsteady numerical results related to velocity, vorticity and pressure fields are given for three characteristic times after the upper surface of the cavity is impulsively started from rest.