A Parallel Multigrid Algorithm for Solving the Navier-Stokes Equations

We consider the numerical solution of the stationary incompressible Navier-Stokes equations for a wide range of Reynolds numbers by a nonconforming finite element discretization of upwind type in primitive variables. For solving the discrete systems of equations within an outer nonlinear iteration, we propose an efficient and robust multigrid algorithm which admits a slightly modified parallel version with nearly the same good properties. The multigrid method is based on a blockwise Gauss-Seidel smoother where each block is determined by the unknowns of a finite element. For the parallelization, we decompose our domain into macroelements which are the finite elements of the coarsest grid level. These macroelements are assigned to different processors, each of which is responsible for all operations with data belonging to the corresponding macroelement. We study the parallel efficiency for an implementation on a transputer system when changing the number of employed processors and the number of used grid levels.