Parallel-in-Space-and-Time Simulation of the Three-Dimensional, Unsteady Navier-Stokes Equations for Incompressible Flow
In this paper we combine the Parareal parallel-in-time method together with spatial parallelization and investigate this space-time parallel scheme by means of solving the three-dimensional incompressible Navier-Stokes equations. Parallelization of time stepping provides a new direction of parallelization and allows to employ additional cores to further speed up simulations after spatial parallelization has saturated. We report on numerical experiments performed on a Cray XE6, simulating a driven cavity flow with and without obstacles. Distributed memory parallelization is used in both space and time, featuring up to 2,048 cores in total. It is confirmed that the space-time-parallel method can provide speedup beyond the saturation of the spatial parallelization.
KeywordsDomain Decomposition Spatial Parallelization Total Speedup Drive Cavity Flow Distribute Memory Parallelization
This research is funded by the Swiss “High Performance and High Productivity Computing” initiative HP2C. Computational resources were provided by the Swiss National Supercomputing Centre CSCS.
- 2.Croce, R., Engel, M., Griebel, M., Klitz, M.: NaSt3DGP – a Parallel 3D Flow Solver. http://wissrech.ins.uni-bonn.de/research/projects/NaSt3DGP/index.htm
- 10.Lions, J.L., Maday, Y., Turinici, G.: A “parareal” in time discretization of PDE’s. C. R. Acad. Sci. – Ser. I – Math. 332, 661–668 (2001)Google Scholar
- 15.Trindade, J.M.F., Pereira, J.C.F.: Parallel-in-time simulation of two-dimensional, unsteady, incompressible laminar flows. Numer. Heat Trans., Part B 50, 25–40 (2006)Google Scholar