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

• Published in: Computing and visualization in science Vol. 19; no. 1-2; pp. 31 - 44
• Main Authors: Lunet, Thibaut, Bodart, Julien, Gratton, Serge, Vasseur, Xavier
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2018; Springer Nature B.V; Springer Verlag
• Series: Special Issue Parallel-in-Time Methods
• Subjects: Algorithms; Calculus of Variations and Optimal Control; Optimization; Coarsening; Computational fluid dynamics; Computational Mathematics and Numerical Analysis; Computer Applications in Chemistry; Computer simulation; Decay; Direct numerical simulation; Engineering Sciences; Error analysis; Homogeneous turbulence; Integrators; Isotropic turbulence; Iterative methods; Mathematics; Mathematics and Statistics; Navier-Stokes equations; Numerical Analysis; Other; Simulation; Special Issue Parallel-in-Time Methods; Turbulent flow; Visualization; Space–time parallelism; Navier–Stokes equations; Direct numerical simulation; High-order method in space; Explicit time integrator; Direct Numerical Simulation
• ISSN: 1432-9360; 1433-0369
• DOI: 10.1007/s00791-018-0295-0

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.