Parallel-in-Time Simulation of Two-Dimensional, Unsteady, Incompressible Laminar Flows

The present work reports an application of a parallel-in-time algorithm to the solution of the unsteady incompressible Navier-Stokes equations. The parallel-in-time algorithm allows one to decompose the time domain of the problem into several subdomains. The solution is based on the iterative use of a coarse- and a finer-time-grid calculation. Calculation starts with a sequential solution along the time domain on the coarse time grid, and this is followed by the iterative procedure. The temporal evolution on the finer time grid is calculated in parallel. This iterative procedure provides successive corrections for the problem solution. When solving the parabolic-elliptic Navier-Stokes and continuity equations, some problems may emerge from the use of two temporal grids in this predictor-corrector fashion. Among them, we have analyzed the influence of the number of processors, or time subdomains, and the number of iterations required for convergence. In addition, an extension of the algorithm to parallelize simultaneously the space and time domains is presented. Although the proposed methodologies are designed for a massive number of processors, significant computer time saving, compared with a single-processor calculation, could be achieved with a very small number of processors.

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