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Parallel-in-Space-and-Time Simulation of the Three-Dimensional, Unsteady Navier-Stokes Equations for Incompressible Flow

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Modeling, Simulation and Optimization of Complex Processes - HPSC 2012

Abstract

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.

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Acknowledgements

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.

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Authors and Affiliations

  1. Institute of Computational Science, Via Giuseppe Buffi 13, CH-6906, Lugano, Switzerland

    Roberto Croce, Daniel Ruprecht & Rolf Krause

Authors
  1. Roberto Croce
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  2. Daniel Ruprecht
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  3. Rolf Krause
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Corresponding author

Correspondence to Roberto Croce .

Editor information

Editors and Affiliations

  1. Interdisciplinary Center for Scientific Computing (IWR), University of Heidelberg, Heidelberg, Germany

    Hans Georg Bock

  2. Vietnam Academy of Science and Technology(VAST), Hanoi, Vietnam

    Xuan Phu Hoang

  3. Interdisciplinary Center for Scientific Computing (IWR), University of Heidelberg, Heidelberg, Germany

    Rolf Rannacher

  4. Interdisciplinary Center for Scientific Computing (IWR), University of Heidelberg, Heidelberg, Germany

    Johannes P. Schlöder

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© 2014 Springer International Publishing Switzerland

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Croce, R., Ruprecht, D., Krause, R. (2014). Parallel-in-Space-and-Time Simulation of the Three-Dimensional, Unsteady Navier-Stokes Equations for Incompressible Flow. In: Bock, H., Hoang, X., Rannacher, R., Schlöder, J. (eds) Modeling, Simulation and Optimization of Complex Processes - HPSC 2012. Springer, Cham. https://doi.org/10.1007/978-3-319-09063-4_2

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