Recirculation of Viscous Incompressible Flows in Enclosures

The unsteady Navier-Stokes equations in primitive variables that govern viscous incompressible fluid flow are numerically solved by a simple projection method which involves an operator splitting technique of three steps in the time discretization process. The numerical scheme does not involve any iteration, is independent of the spatial dimension, and its costly part relies on the solution of elliptic problems for which very efficient solvers exist regardless of the spatial discretization. The scheme is tested with the well known two-dimensional lid-driven cavity problem at moderate and high Reynolds numbers Re in the range 400 ≤ Re ≤ 15000. For moderate Reynolds numbers the results are compared, in order to validate the scheme, with previously published results supposed to be correct; for these results the time when the flow converges to the asymptotic steady state is reported. Then, going one step further: the transient stage for Re =4000 is shown at various times before the steady state is reached; flows at Re =10000 and 15000 are reported close from its departure from rest; flows for Re = 1000 and 3200 are also reported in rectangular cavities up to aspect ratio A = 3.