A DIRECT SPECTRAL SOLVER OF THE 2D/3D UNSTEADY STOKES PROBLEM - APPLICATION TO THE 2D SQUARE DRIVEN CAVITY

This paper presents, firstly, an original direct solver (named ''projection-diffusion'') of the 2D/3D unsteady Stokes problem, in which, in contrast to the fractional step (or time splitting) methods, the uncoupling of the velocity and pressure fields is not based on an annex time scheme. This method has been applied (with a Chebyshev collocation space discretization) to determine the threshold Re(c) of transition to unsteadiness of the flows in four square driven cavities, each provided with a (polynomial) regularization stiffer than the previous one. Preliminary comparative results are given on the threshold values and on these transitional flows.