A comparative study of some time { stepping

We present a numerical comparison of some time{stepping schemes for the discretization and solution of the nonstationary incompressible Navier{Stokes equations. The spatial discretization is by nonconforming quadrilateral nite elements which satisfy the LBB{condition. The major focus is on the diierences in accuracy and eeciency between the Backward Euler-, Crank{Nicolson-or Fractional{step{{scheme, used in discretizing the momentum equations. Further, the diierences between fully coupled solvers and operator splitting techniques (projection methods) and the innuence of the treatment of the nonlinear advection term are considered. The combination of both discrete projection schemes and nonconforming nite elements allows the comparison of schemes which are representative for many methods used in practice. On cartesian grids, this approach encompasses some well-known staggered grid nite diierence discretizations, too. The results which are obtained for several typical ow problems are thought to be representative, and should be helpful for a fair rating of solution schemes, particularly in long time simulations.