The present work reports an application of a parallel-in-time algorithm to the solution of the unsteady incompressible form of the Navier-Stokes equations to calculate the vortex shedding flow past a square obstacle in a channel for laminar Reynolds numbers. The parallel in time algorithm is based on the iterative use of coarse global sequential solvers (or integrators) with fine local parallel ones, allowing the time domain decomposition and the propagation of solution jumps on the coarse time-grid. Calculation starts with a sequential solution along the time domain of the problem on a coarse time-grid and is followed by an iterative procedure using the coarse time-grid and a finer one. The temporal evolution on the finer time-grid is calculated in parallel. This iterative procedure provides successive corrections for the problem solution. Some problems may emerge from the use of two temporal grids in this predictor-corrector fashion when solving the Navier-Stokes equations. Among them we have analyzed the influence of the number of processors and the number of iterations required for convergence. Significant computer time saving was achieved when compared with the single processor computing time.

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