A parallel multigrid algorithm for solving the Navier-Stokes equations. (English) Zbl 0789.76065

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.


76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
65Y05 Parallel numerical computation
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
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