Cerfacs Enter the world of high performance ...

Nowadays, the problem size required to simulate physical phenomena may  be extremely large in order to correctly predict increasingly complex physical behaviours. This is especially true for the numerical simulations of turbulent flows, whose size has recently reached more than 10^11 degrees of freedom (Lee & Moser, 2013). In order to further develop computing capabilities, new supercomputers will appear in the coming decades, being able to compute up to 10^15 FLOPS. However, classical parallel algorithms (usually based on domain partitioning in space) become less and less efficient when used in such a massively parallel context. For the past ten years, the HPC community has been studying the possibility to exploit time decomposition as a new degree of parallelism.

This thesis aims at presenting the current state of the art for time-parallel methods, in order to identify space-time parallelism strategies that can be applied to an explicit CFD code in a massively parallel context. After a first analysis, the Parareal algorithm with spatial coarsening is selected. First, this time parallel algorithm is then studied on a simplified model of the Navier-Stokes equations (advection equation) by means of a Fourier analysis and multiple numerical experiments. This allows us to identify the important parameters influencing the accuracy and the convergence of the algorithm.
Then, secondly, a specific attention is devoted to the definition of two three-dimensional canonical turbulent problems that can serve as relevant test cases for time-parallel algorithms: the decay of isotropic homogeneous turbulence and the turbulent channel flow. Detailed studies are being conducted on both problems to determine the performance brought by Parareal with space coarsening as part of a combined space-time parallelization, as well as its ability to correctly represent the physical properties of the turbulent flows. Finally, this thesis describes the gains that can bring time parallelism for CFD, as well as its perspectives on tomorrow’s high performance computing architectures.

 

Jury :

Martin Gander              (Université de Genève)                               Rapporteur
Rolland Masson            (Université de Nice)                                    Rapporteur
Marc Massot                 (École polytechnique)                                 Rapporteur
Qiqi Wang                     (Massachussets Institute of Technology)   Jury
Daniel Ruprecht            (University of Leeds)                                  Jury
Serge Gratton                (Toulouse-INP-IRIT)                                   Directeur
Julien Bodart                 (ISAE-Supaero, DAEP)                              Encadrant
Xavier Vasseur              (ISAE-Supaero, DISC)                               Encadrant