SUMMARYBenchmark problems are solved with the steady incompressible Navier-Stokes equations discretized with a finite volume method in general curvilinear co-ordinates on a staggered grid. The problems solved are skewed driven cavity problems, recently proposed as non-orthogonal grid benchmark problems. The system of discretized equations is solved efficiently with a non-linear multigrid algorithm, in which a robust line smoother is implemented. Furthermore, another benchmark problem is introduced and solved in which a 90" change in grid line direction occurs.

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For the solution of practical ow problems in arbitrarily shaped domains, simple Schwarz domain decomposition methods with minimal overlap are quite e cient, provided Krylov subspace methods, such as the GMRES method, are used to accelerate convergence. With accurate subdomain solution, the amount of time spent in solving these problems may be quite large. To reduce computing time, inaccurate solution of subdomain problems is considered, which requires a di erent, GCR based, acceleration technique. Much emphasis is put on the multiplicative domain decomposition algorithm since we also want an algorithm which is fast on a single processor. Nevertheless, the prospects for parallel implementation are also investigated.

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