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An Efficient Parallel Implementation of the SIMPLE Algorithm Based on a Multigrid Method

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ABSTRACT

This paper deals with a parallel implementation of the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm to numerically solve the Navier–Stokes system of equations for viscous incompressible flows. A mechanism of interprocess communication using a mesh decomposition with virtual cells and an algebraic multigrid method is proposed. A method of distributed matrix storage and an algorithm for matrix-vector operations reducing the number of interprocess communications are presented. The results of a series of numerical experiments on structured and unstructured grids (including a problem of external aerodynamics) are presented. Based on the results obtained, an analysis of the influence of multigrid solver settings on the overall efficiency of the algorithm is made. It is shown that the parallel algorithm based on an algebraic multigrid technique proposed for the SIMPLE method makes it possible to efficiently calculate problems on hundreds of processors.

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Notes

  1. Our experience shows that the use of synchronous communication functions slows down the calculation by 5–10%.

  2. For instance, in calculating compressible problems it is more reasonable to use an F-cycle, because it is more robust. These default settings are used in the LOGOS software package.

  3. For instance, for a subdomain consisting of 10, 000 cells, the layer of virtual cells (the size of the boundary) constitutes ∼ 30% of the number of all cells in the subdomain of one MPI process. This is largely the reason of increasing differences between the real efficiency and the STK efficiency with decreasing size of the subdomains, since the STK calculations in virtual and non-virtual cells do not differ.

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Funding

The work was performed under a state assignment in the field of scientific activity (project nos. 5.4568.2017/6.7 and 5.1246.2017/4.6) and supported by the Council for Grants (under RF President) and State Aid of Leading Scientific Schools (grant NSh-2685.2018.5), by the Grants Council (under RF President), grant no. MD-4874.2018.9, and by RFBR (project no. 16-01-00267).

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Correspondence to A. S. Kozelkov, S. V. Lashkin, A. A. Kurkin, A. V. Kornev or A. M. Vyalykh.

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Kozelkov, A.S., Lashkin, S.V., Kurkin, A.A. et al. An Efficient Parallel Implementation of the SIMPLE Algorithm Based on a Multigrid Method. Numer. Analys. Appl. 13, 1–16 (2020). https://doi.org/10.1134/S1995423920010012

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  • DOI: https://doi.org/10.1134/S1995423920010012

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