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A Parallel Domain Decomposition Method for 3D Unsteady Incompressible Flows at High Reynolds Number

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Abstract

Numerical simulation of three-dimensional incompressible flows at high Reynolds number using the unsteady Navier–Stokes equations is challenging. In order to obtain accurate simulations, very fine meshes are necessary, and such simulations are increasingly important for modern engineering practices, such as understanding the flow behavior around high speed trains, which is the target application of this research. To avoid the time step size constraint imposed by the CFL number and the fine spacial mesh size, we investigate some fully implicit methods, and focus on how to solve the large nonlinear system of equations at each time step on large scale parallel computers. In most of the existing implicit Navier–Stokes solvers, segregated velocity and pressure treatment is employed. In this paper, we focus on the Newton–Krylov–Schwarz method for solving the monolithic nonlinear system arising from the fully coupled finite element discretization of the Navier–Stokes equations on unstructured meshes. In the subdomain, LU or point-block ILU is used as the local solver. We test the algorithm for some three-dimensional complex unsteady flows, including flows passing a high speed train, on a supercomputer with thousands of processors. Numerical experiments show that the algorithm has superlinear scalability with over three thousand processors for problems with tens of millions of unknowns.

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Authors and Affiliations

  1. Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055, Guangdong, China

    Rongliang Chen, Zhengzheng Yan & Yubo Zhao

  2. Department of Applied Mathematics, University of Washington, Seattle, WA, 98195, USA

    Yuqi Wu

  3. Department of Computer Science, University of Colorado Boulder, Boulder, CO, 80309, USA

    Xiao-Chuan Cai

Authors
  1. Rongliang Chen
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  2. Yuqi Wu
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  3. Zhengzheng Yan
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  4. Yubo Zhao
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  5. Xiao-Chuan Cai
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Corresponding author

Correspondence to Xiao-Chuan Cai.

Additional information

The research was supported in part by NSF of USA under grants DMS-0913089 and CCF-1216314, the Knowledge Innovation Program of the Chinese Academy of Sciences (China) under KJCX2-EW-L01, and the international cooperation project of Guangdong provience (China) under 2011B050400037.

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Chen, R., Wu, Y., Yan, Z. et al. A Parallel Domain Decomposition Method for 3D Unsteady Incompressible Flows at High Reynolds Number. J Sci Comput 58, 275–289 (2014). https://doi.org/10.1007/s10915-013-9732-x

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  • DOI: https://doi.org/10.1007/s10915-013-9732-x

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