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A parallel time-dependent incompressible flow solver and a parallel multigrid elliptic kernel are described. The flow solver is based on a second-order projection method applied to a staggered finite-difference grid. The multigrid algorithms implemented in the elliptic kernel, which is needed by the flow solver, are V-cycle and full V-cycle schemes. A grid-partition strategy is used in the parallel implementations of both the flow solver and the multigrid elliptic kernel on all fine and coarsedoi:10.1006/jcph.1996.0090 fatcat:wugxjvupcngwbkdokhnnx2rd7y