Geodesic
Effective implementation of the parallel SIMPLE algorithm based on multigrid method
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 23 (2020) no. 1, pp. 1-22

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This paper deals with the investigation of parallel SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm for the numerical solution of the Navier–Stokes system of equations for viscous incompressible flows. The interprocessor exchange mechanism with mesh decomposition with virtual cells and algebraic multigrid method is presented. The method of distributed matrix storage and the algorithm for matrix-vector operations reducing the number of interprocessor exchanges are presented. The results of a series of the numerical experiments on structured and unstructured grids (including the external aerodynamics problem) are presented. Based on the results obtained, the analysis of the influence of multigrid solver settings on the total algorithm efficiency was made. It was shown that the parallel algorithm for the SIMPLE method based on the algebraic multigrid technique proposed makes possible to efficiently calculate problems on hundreds of processors. 
@article{SJVM_2020_23_1_a0,
     author = {A. S. Kozelkov and S. V. Lashkin and A. A. Kurkin and A. V. Kornev and A. M. Vyalykh},
     title = {Effective implementation of the parallel {SIMPLE} algorithm based on multigrid method},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {1--22},
     publisher = {mathdoc},
     volume = {23},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2020_23_1_a0/}
}
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A. S. Kozelkov; S. V. Lashkin; A. A. Kurkin; A. V. Kornev; A. M. Vyalykh. Effective implementation of the parallel SIMPLE algorithm based on multigrid method. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 23 (2020) no. 1, pp. 1-22. http://geodesic.mathdoc.fr/item/SJVM_2020_23_1_a0/