Abstract
SUMMARY An improved projection scheme is proposed and applied to pseudospectral collocation-Chebyshev approximation for the incompressible Navier‐Stokes equations. It consists of introducing a correct predictor for the pressure, one which is consistent with a divergence-free velocity field at each time step. The main objective is to allow a time variation of the pressure gradient at boundaries. From different test problems, it is shown that this method, associated with a multistep second-order time scheme, provides a time accuracy of the same order as the temporal scheme used for the pressure, and also improves the prediction of the velocity slip. Moreover, it does not exhibit any numerical boundary layer mentioned as a drawback of fractional steps algorithm, and does not require the use of staggered grids for the velocity and the pressure. Its effectiveness is validated by comparison with a previous time-splitting algorithm proposed by Goda (K. Goda, J. Comput. Phys., 30, 76‐95 (1979)) and implemented by Gresho (P. Gresho, Int. j. numer. methods fluids, 11, 587‐620 (1990)) to finite element approximations. Steady and unsteady solutions for the regularized driven cavity and the rotating cavity submitted to throughflow are also used to assess the efficiency of this algorithm. © 1998 John Wiley & Sons, Ltd.
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