Parallel multilevel algorithms for solving the incompressible Navier-Stokes equations

This paper presents results of a numerical study for unsteady three—dimensional, incompressible flow. A finite element multigrid method is used in combination with an operator splitting technique and upwind discretization for the convective term. A nonconforming element pair, living on hexahedrons, which is of order O(h2/h) for velocity and pressure, is used for the spatial discretization. The second order fractional—step—θ—scheme is employed for the time discretization.For this approach we present the parallel implementation of a multigrid code for MIMD computers with message passing and distributed memory. Multiplicative multigrid methods as stand alone iterations are considered. We present a very efficient implementation of Gauß-Seidel resp. SOR smoothers, which have the same amount of communication as a Jacobi smoother.As well we present measured MFLOP for Blas 1 and Lin routines (as SAXPY) for different vector length. The measured performance are between 20 MFLOP for large vectorlength and 450 MFLOP for short vectorlength.