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. 
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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/

[1] L. G. Loicyanskii, Mekhanika zhidkosti i gaza, Gostekhizdat, M.–L., 1950

[2] F. Moukalled, M. Darwish, “A Unified formulation of the segregated class of algorithms for fluid flow at all speeds”, Numerical Heat Transfer, 37:1 (2000), 103–139 | DOI

[3] K. S. Shterev, S. K. Stefanov, “Pressure based finite volume method for calculation of compressible viscous gas flows”, J. Computational Physics, 229:2 (2010), 461–480 | DOI | MR | Zbl

[4] A. Katz, V. Sankaran, “High aspect ratio grid effects on the accuracy of Navier-Stokes solutions on unstructured meshes”, Computers Fluids, 65 (2012), 66–79 | DOI | MR | Zbl

[5] A. S. Kozelkov, V. V. Kurulin, E. S. Tyatyushkina, O. L. Puchkova, “Modelirovanie techenii vyazkoi neszhimaemoi zhidkosti na nestrukturirovannyh setkah metodom otsoedinennyh vihrei”, Matematicheskoe modelirovanie, 26:8 (2014), 81–96 | Zbl

[6] A. S. Kozelkov, V. V. Kurulin, “Eddy-resolving numerical scheme for simulation of turbulent incompressible flows”, USSR Comput. Math. and Math. Phys., 55:7 (2015), 1232–1241 | DOI | DOI | MR | Zbl

[7] A. S. Kozelkov, R. M. Shagaliev, V. V. Kurulin, A. V. Yalozo, S. V. Lashkin, “Investigation of supercomputer capabilities for the scalable numerical simulation of computational fluid dynamics problems in industrial applications”, USSR Comput. Math. and Math. Phys., 56:8 (2016), 1506–1516 | DOI | DOI | MR | Zbl

[8] M. Barth, M. Byckling . Ilieva, S. Saarinen, M. Schliephake, Best Practice Guide — Intel Xeon Phi v1.1, 2014 (with V. Weinberg) https://www.researchgate.net/publication/260369376

[9] E. Lindholm, J. Nickolls, S. Oberman, J. Montrym, “NVIDIA Tesla: a unified graphics and computing architecture”, IEEE MICRO, 28:2 (2008), 39–55 | DOI

[10] S. A. Isaev, P. A. Baranov, A. E. Usachov, Mnogoblochnye vychislitel'nye tekhnologii v pakete VP2/3 po aerotermodinamike, LAP LAMBERT Academic Publishing, Saarbryuken, 2013

[11] L. Y. M. Gicquel, N. Gourdain, J. F. Boussuge, H. Deniau, G. Staffelbach, P. Wolf, “High performance parallel computing of flows in complex geometries”, Comptes Rendus Mecanique, 339:2–3 (2011), 104–124 | DOI | Zbl

[12] X. Guo, B. D. Rogers, S. Lind, P. K. Stansby, “New massively parallel scheme for Incompressible Smoothed Particle Hydrodynamics (ISPH) for highly nonlinear and distorted flow”, Computer Physics Communications, 233 (2018), 16–28 | DOI | MR

[13] A. D. Chow, B. D. Rogers, S. J. Lind, P. K. Stansby, “Incompressible SPH (ISPH) with fast Poisson solver on a GPU”, Computer Physics Communications, 226 (2018), 81–103 | DOI

[14] Y. Notay, A. Napov, “A massively parallel solver for discrete Poisson-like problems”, J. Computational Physics, 281 (2015), 237–250 | DOI | MR | Zbl

[15] M. Emans, “Performance of parallel AMG-preconditioners in CFD-codes for weakly compressible flows”, Parallel Computing, 36:5–6 (2010), 326–338 | DOI | MR | Zbl

[16] A. S. Kozelkov, Yu. N. Deryugin, S. V. i dr. Lashkin, “Implementation in Logos software of a computational scheme for a viscous incompressible fluid using the multigrid method based on algorithm SIMPLE”, VANT. Ser.: Mat. Mod. Fiz., 4, 2013, 31–43

[17] A. Brandt, “Guide to multigrid development”, Multigrid Methods, Proc. Conf. Held at Koln-Porz, November 23–27, 1981, Lect. Notes in Mathematics, 960, eds. W. Hackbusch, U. Trottenberg, Springer, 1982, 220–312 | DOI | MR

[18] Y. Saad, Iterative Methods for Sparse Linear Systems, Second ed., SIAM, Minneapolis, 2003 | MR | Zbl

[19] P. Vanek, J. Mandel, M. Brezina, “Algebraic multigrid by smoothed aggregation for second and fourth order problems”, Computing, 56:3 (1996), 179–196 | DOI | MR | Zbl

[20] K. N. Volkov, Yu. N. Deryugin, V. N. Emel'yanov, A. S. Kozelkov, I. V. Teterina, “Algebraicheskii mnogosetochnyi metod v zadachah vychislitel'noi gidrodinamiki”, Vychislitel'nye metody i programmirovanie, 15 (2014), 183–200

[21] A. S. Kozelkov, V. V. Kurulin, O. L. Puchkova, S. V. Lashkin, “Modelirovanie turbulentnyh techenii s ispol'zovaniem algebraicheskoi modeli reinol'dsovyh napryazhenii s universal'nymi pristenochnymi funkciyami”, Vychislitel'naya mekhanika sploshnyh sred, 7:1 (2014), 40–51

[22] A. V. Boiko, Yu. M. Nechepurenko, R. N. Zhuchkov, A. S. Kozelkov, “Blok rascheta polozheniya laminarno-turbulentnogo perekhoda dlya paketa programm LOGOS”, Teplofizika i aeromekhanika, 21:2 (2014), 201–220

[23] A. V. Safronov, Yu. N. Deryugin, R. N. Zhuchkov i dr., “Rezul'taty validacii mnogofunkcional'nogo paketa programm LOGOS pri reshenii zadach aerogazodinamiki starta i poleta raket-nositelei”, Matematicheskoe modelirovanie, 26:9 (2014), 83–95 | Zbl

[24] A. S. Kozelkov, A. A. Kurkin, E. N. Pelinovskii, V. V. Kurulin, E. S. Tyatyushkina, “Modeling the disturbances in the lake Chebarkul caused by the fall of the meteorite in 2013”, Fluid Dynamics, 50:6 (2015), 828–840 | DOI | MR | Zbl

[25] A. S. Kozelkov, A. A. Kurkin, E. N. Pelinovskii, “Effect of the angle of water entry of a body on the generated wave heights”, Fluid Dynamics, 51:2 (2016), 288–298 | DOI | DOI | MR | Zbl

[26] F. R. Menter, “Two-equation eddy-viscosity turbulence models for engineering applications”, AIAA J., 32:6 (1994), 1598–1605 | DOI

[27] OpenFOAM, http://openfoam.org/

[28] N. S. Bahvalov, N. P. Zhidkov, G. M. Kobel'kov, Chislennye metody, Laboratoriya Bazovyh Znanii, M., 2002 | MR

[29] U. Ghia, K. N. Ghia, C. T. Shin, “High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method”, J. Computational Physics, 48:3 (1982), 387–411 | DOI | MR | Zbl

[30] J. C. Vogel, J. K. Eaton, “Combined heat transfer and fluid dynamic measurements downstream of a backward-facing step”, J. Heat Transfer, 107:4 (1985), 922–929 | DOI

[31] D. S. Uotkins, Osnovy matrichnyh vychislenii, BINOM, M., 2009

[32] C. S. Woodward, SUNDIALS: Suite of Nonlinear and Differential/Algebraic Equation Solvers, UCRL-PRES-213978, Lawrence Livermore National Laboratory, Livermore

[33] D. A. Novaev, Yu. G. Bartenev, D. I. i dr. Lipov, “Programmnye sredstva STK dlya issledovaniya effektivnosti vypolneniya parallel'nyh prilozhenii”, Voprosy atomnoi nauki i tekhniki. Ser. Matematicheskoe modelirovanie fizicheskih processov, 4, 2011, 72–81

[34] M. Snir, S. Otto, S. Huss-Lederman, D. Walker, J. Dongarra, MPI: The Complete Reference, MIT Press, 1996

[35] A. S. Antonov, Parallel'noe programmirovanie s ispol'zovaniem tekhnologii OpenMP, Uchebnoe posobie, Izd-vo MGU, M., 2009