Modeling of problems in magnetohydrodynamics on high performance computational systems
Matematičeskoe modelirovanie, Tome 32 (2020) no. 12, pp. 3-13.

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The work presented here discusses an algorithm for solving problems of magnetic gas dynamics which is well adapted to the architecture of computer systems with extramaximal parallelism. The algorithm is based on a kinetic model describing the interaction of an ensemble of charged and neutral particles, as well as a magnetic field. As an illustration, the results of a 3D calculation of motion of molten sodium in a channel conjugated with a cavern are given.
Keywords: magnetohydrodynamics, kinetic algorithms, high-performance calculations.
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B. N. Chetverushkin; A. V. Saveliev; V. I. Saveliev. Modeling of problems in magnetohydrodynamics on high performance computational systems. Matematičeskoe modelirovanie, Tome 32 (2020) no. 12, pp. 3-13. http://geodesic.mathdoc.fr/item/MM_2020_32_12_a0/

[1] B. N. Chetverushkin, N. D'Ascenzo, A. V. Saveliev, V. I. Saveliev, “Simulation of Astrophysical Phenomena on the Basis of High-Performance Computations”, Doklady Mathematics, 95:1 (2017), 68–71 | DOI | MR | Zbl

[2] B. N. Chetverushkin, “Superkompiuternye tekhnologii: problemy i perspektivy blizhaishego budushchego”, Vestnik RAN, 88:12 (2018), 1083–1089

[3] B. N. Chetverushkin, N. D'Ascenzo, V. I. Saveliev, “Kinetically consistent magnetogasdynamics equations and their use in supercomputer computations”, Doklady Mathematics, 90:1 (2014), 495–498 | DOI | MR | Zbl

[4] B. Chetverushkin, N. D'Ascenzo, S. Ishanov, V. Saveliev, “Hyperbolic Type Explicit Kinetic Scheme of Magneto Gas Dynamics for High Performance Computing Systems”, Russian J. Num. Analys. Math. Modeling, 30:1 (2015), 27–36 | MR | Zbl

[5] M. A. Abramowicz, G. Björnsson, I. E. Pringle, Theory of Black Hole Accretion Discs, Cambridge University Press, Cambridge, 1999 | MR

[6] www.nasa.gov/chandra

[7] B. N. Chetverushkin, A. V. Saveliev, V. I. Saveliev, “Compact Quasi-Gasdynamic System for High-Performance Computations”, Comp. Math. Math. Phys, 59:3 (2019), 493–500 | DOI | MR | Zbl

[8] B. N. Chetverushkin, Kinetic Schemes and Quasi-Gas Dynamic System of Equations, CIMNE, Barcelona, 2008, 298 pp. | MR

[9] V. V. Vedeniapin, Kineticheskie uravneniya Boltzmanna i Vlasova, Fizmatlit, M., 2001, 112 pp.

[10] C. Cerignani, Theory and application of the Boltzmann Equation, Scottish Academic Press, Edinburgh, 1988 | MR

[11] B. N. Chetverushkin, A. V. Gulin, “Explicit Schemes and Numerical Simulation Using Ultra-high-Performance Computer Systems”, Doklady Mathematics, 86:2 (2012), 681–683 | DOI | MR | Zbl

[12] A.A. Samarskii, The Theory of Difference Schemes, Marcel Dekker, New York, 2001, 786 pp. | MR | MR | Zbl

[13] V. M. Novikov, “The Results of the investigations of Russian Research Center “Kurchatov Institute” on Molten Salt Applications to Problems of Nuclear Energy Systems”, Proc. AIP Conf., 346 (1995), 138–147 | DOI

[14] B. Wang, Russian MBIR Sodium Cooled Fast Reactor on Track to 2020 Completion, (Retrieved 8 September 2018) nextbigfuture.com

[15] J. K. Fink, L. Leibowitz, Thermodynamic and Transport Properties of Sodium Liquid and Vapor, ANL/RE-95/2

[16] U. Ghia, K. N. Ghia, C. T. Shin, “High Re Solutions for Incompressible Flow Using the Navier-Stokes Equations and a Multigrid Method”, J. Comp. Phys., 48:3 (1982), 387–411 | DOI | MR | Zbl

[17] L. G. Loitsianskii, Mekhanika zhidkosti i gaza, Nauka, M., 1978, 677 pp.