Time-parallel simulation of the decay of homogeneous turbulence using Parareal with spatial coarsening

  • Thibaut Lunet
  • Julien Bodart
  • Serge Gratton
  • Xavier Vasseur
Special Issue Parallel-in-Time Methods


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.


Direct numerical simulation Explicit time integrator High-order method in space Navier–Stokes equations Parareal Space–time parallelism 



The authors thank the two reviewers for their comments. The authors would like to acknowledge CALMIP for the dotation of computing hours on the EOS computer. This work was granted access to the HPC resources of CALMIP under allocation P1425 and P17005. Thibaut Lunet would like to thank Daniel Ruprecht, Michael Minion, Debasmita Samaddar, Jacob B. Schroder, Martin J. Gander, Robert Speck, Andreas Schmidt, Felix Kwok, Beth Wingate and Raymond J. Spiteri for the interesting discussions at the 5th Workshop on Parallel-in-time integration at the Banff International Research Station (BIRS), and the Jülich Supercomputing Center for granting a Student Travel Award for attending this conference.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Thibaut Lunet
    • 1
    • 2
  • Julien Bodart
    • 1
  • Serge Gratton
    • 3
  • Xavier Vasseur
    • 1
  1. 1.ISAE-SUPAEROToulouse Cedex 4France
  2. 2.CERFACSToulouse Cedex 1France
  3. 3.INPT-IRITUniversity of Toulouse and ENSEEIHTToulouse Cedex 7France

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