Geodesic
A kinetic model for magnetogasdynamics
Matematičeskoe modelirovanie, Tome 29 (2017) no. 3, pp. 3-15.

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In this work the equations of ideal magnetogasdynamics are derived based on the introduced local complex Maxwellian distribution function. Using this kinetic model we obtain the analogue of the quasidynamic system of equations for magnetogasdynamics including dissipative processes. The resulting model and the algorithm of its solution have been tested by applying them to a number of well-known problems. The given algorithm can be easily adapted to an architecture of high performance systems with extramassive parallelism.
Keywords: magnetogasdynamics, explicit kinetic schemes, high performance computing. 
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B. Chetverushkin; N. D'Ascenzo; A. Saveliev; V. Saveliev. A kinetic model for magnetogasdynamics. Matematičeskoe modelirovanie, Tome 29 (2017) no. 3, pp. 3-15. http://geodesic.mathdoc.fr/item/MM_2017_29_3_a0/

[1] B. N. Chetverushkin, Kinetic Schemes and Quasi-Gas Dynamic System of Equations, CIMNE, Barcelona, 2008

[2] A. A. Davydov, B. N. Chetverushkin, E. V. Shil'nikov, “Simulating flows of incompressible and weakly compressible fluids on multicore hybrid computer systems”, Comput. Math. and Math. Phys., 50:12 (2010), 2157–2166 | DOI | MR | Zbl

[3] B. N. Chetverushkin, “Kinetic models for solving continuum mechanics problems on supercomputers”, Math. Models and Comput. Simul., 7:6 (2015), 531–539 | DOI | MR | Zbl

[4] S. Chapman, T. G. Cowling, The mathematical theory of non-uniform gases, Cambridge University Press, Cambridge, 1991, 448 pp. | MR | Zbl

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

[6] B. Chetverushkin, N. D'Ascenzo, S. Ishanov, V. Saveliev, “Hyperbolic type explicit kinetic scheme of magneto gas dynamics for high performance computing systems”, Rus. J. Num. Anal. Math. Model., 30:1 (2015), 27–36 | MR | Zbl

[7] N. D'Ascenzo, V. I. Saveliev, B. N. Chetverushkin, “On an algorithm for solving parabolic and elliptic equations”, Comput. Math. and Math. Phys., 55:8 (2015), 1290–1297 | DOI | DOI | MR | Zbl

[8] B. N. Chetverushkin, N. D'Ascenzo, V. I. Saveliev, “Three-level scheme for solving parabolic and elliptic equations”, Dokl. Math., 91:3 (2015), 341–343 | DOI | DOI | MR | Zbl

[9] A. G. Kulikovskii, N. V. Pogorelov, A. Yu. Semenov, Mathematical aspects of numerical solution of hyperbolic systems, CRC Press, Boca Raton, 2000, 560 pp. | MR

[10] B. N. Chetverushkin, V. I. Saveliev, “Kineticheskie modeli i vysokoproizvoditelnye vychilsleniya”, Keldysh Institute preprints, 2015, 079, 31 pp.

[11] S. M. Repin, B. N. Chetverushkin, “Estimates of the difference between approximate solutions of the Cauchy problems for the parabolic diffusion equation and a hyperbolic equation with a small parameter”, Dokl. Math., 88:1 (2013), 417–420 | DOI | DOI | MR | Zbl

[12] E. E. Myshetskaya, V. F. Tishkin, “Estimates of the hyperbolization effect on the heat equation”, Comput. Math. and Math. Phys., 55:8 (2015), 1270–1275 | DOI | DOI | MR | Zbl

[13] M. D. Surnachev, V. F. Tishkin, B. N. Chetverushkin, “O zakonakh sokhraneniya dlya giperbolizirovannykh uravnenii”, Diff. Uravneniya, 2016

[14] D. Balsara, “Divergence-Free Adaptive Mesh Refinement for Magnetohydrodynamics”, J. Comput. Phys., 174 (2001), 614 | DOI | Zbl

[15] T. G. Elizarova, M. V. Popov, “Numerical simulation of three-dimensional quasi-neutral gas flows based on smoothed magnetohydrodynamic equations”, Comput. Math. and Math. Phys., 55:8 (2015), 1330–1345 | DOI | DOI | MR | Zbl

[16] D. S. Balsara, “Divergence-Free Reconstruction of Magnetic Fields and WENO Schemes for Magnetohydrodynamics”, J. Comp. Phys., 228 (2009), 5040–5056 | DOI | MR | Zbl

[17] S. A. Orszag, C.-M. Tang, “Small-Scale Structure of Two-Dimensional Magnetohydrodynamic Turbulence”, J. Fluid Mech., 90 (1979), 129–143 | DOI

[18] J. M. Stone, T. A. Gardiner, P. Teuben, J. F. Hawley, J. B. Simon, “Athena: A New Code for Astrophysical MHD”, Astrophys. J. Suppl., 178 (2008), 137 | DOI | MR