ON DISCRETE PROJECTION METHODS FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS - AN ALGORITHMICAL APPROACH

We derive a general class of iteration schemes for the incompressible Navier-Stokes equations which contains fully coupled solution techniqu es as well as operator splitting/projection methods. We combine the ad vantages of both, namely accuracy/stability and efficiency, and obtain a special form of discrete projection schemes. In combination with a nonlinear iteration of quasi-Newton type one may use these schemes ana logously to the well known pure projection schemes, e.g. of Chorin and Van Kan, or apply them as preconditioners in a defect correction appr oach to obtain the fully coupled Galerkin solution. The corresponding complexity analysis shows that in combination with certain nonconformi ng finite element discretizations a huge gain in efficiency may be obt ained, particularly in the highly nonstationary case. Our theoretical results are confirmed by comparative numerical tests for both types of schemes. It turns out that the appropriate time steps for the pure pr ojection approach are only moderately smaller than those for the fully implicitly coupled schemes, but that the work to obtain comparative r esults with the discrete projection methods as solvers is much lower. An interesting observation is that in the case of higher Reynolds numb ers no significant pressure boundary layers occur, even for the pure p rojection schemes. These considerations and first numerical tests in 3 D give hope to obtain a powerful CFD-tool.