Lunet, Thibaut, Bodart, Julien, Gratton, Serge and Vasseur, Xavier (2018) Time-parallel simulation of the decay of homogeneous turbulence using Parareal with spatial coarsening. Computing and Visualization in Science. pp. 1-14.

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Abstract

Direct Numerical Simulation of turbulent flows is a computationally demanding problem that requires efficient parallel algorithms. We investigate the applicability of the time-parallel Parareal algorithm to an instructional case study related to the simulation of the decay of homogeneous isotropic turbulence in three dimensions. We combine a Parareal variant based on explicit time integrators and spatial coarsening with the space-parallel Hybrid Navier-Stokes solver. We analyse the performance of this space-time parallel solver with respect to speedup and quality of the solution. The results are compared with reference data obtained with a classical explicit integration, using an error analysis which relies on the energetic content of the solution. We show that a single Parareal iteration is able to reproduce with high fidelity the main statistical quantities characterizing the turbulent flow field.