Abstract
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 analog of a quasi-dynamic 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.
Similar content being viewed by others
References
B. N. Chetverushkin, Kinetic Schemes and Quasi-Gas Dynamic System of Equations (CIMNE, Barcelona, 2008).
A. A. Davydov, B. N. Chetverushkin, and E. V. Shil’nikov, “Simulating flows of incompressible and weakly compressible fluids on multicore hybrid computer systems,” Comput. Math. Math. Phys. 50, 2157–2166 (2010).
B. N. Chetverushkin, “Kinetic models for solving continuum mechanics problems on supercomputers,” Math. Models Comput. Simul. 7, 531–539 (2015).
S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases (Cambridge Univ. Press, Cambridge, 1991).
B. N. Chetverushkin, N. D’Ascenzo, and V. I. Saveliev, “Kinetically consistent magnetogasdynamics equations and their use in supercomputer computations,” Dokl. Math. 90, 495–498 (2014).
B. Chetverushkin, N. D’Ascenzo, S. Ishanov, and V. Saveliev, “Hyperbolic type explicit kinetic scheme of magneto gas dynamics for high performance computing systems,” Russ. J. Num. Anal. Math. Model. 30, 27–36 (2015).
N. D’Ascenzo, V. I. Saveliev, and B. N. Chetverushkin, “On an algorithm for solving parabolic and elliptic equations,” Comput. Math. Math. Phys. 55, 1290–1297 (2015).
B. N. Chetverushkin, N. D’Ascenzo, and V. I. Saveliev, “Three-level scheme for solving parabolic and elliptic equations,” Dokl. Math. 91, 341–343 (2015).
A. G. Kulikovskii, N. V. Pogorelov, and A. Yu. Semenov, Mathematical Aspects of Numerical Solution of Hyperbolic Systems (Fizmatlit, Moscow, 2012; CRC, Boca Raton, FL, 2000).
B. N. Chetverushkin and V. I. Saveliev, “Kinetic models and high performance computing,” KIAM Preprint No. 79 (Keldysh Inst. Appl. Math. RAS, Moscow, 2015).
S. M. Repin and 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, 417–420 (2013).
E. E. Myshetskaya and V. F. Tishkin, “Estimates of the hyperbolization effect on the heat equation,” Comput. Math. Math. Phys. 55, 1270–1275 (2015).
M. D. Surnachev, V. F. Tishkin, and B. N. Chetverushkin, “On conservation laws for hyperbolized equations,” Differ. Equations 52, 817–823 (2016).
D. Balsara, “Divergence-free adaptive mesh refinement for magnetohydrodynamics,” J. Comput. Phys. 174, 614 (2001).
T. G. Elizarova and M. V. Popov, “Numerical simulation of three-dimensional quasi-neutral gas flows based on smoothed magnetohydrodynamic equations,” Comput. Math. Math. Phys. 55, 1330–1345 (2015).
D. S. Balsara, “Divergence-free reconstruction of magnetic fields and WENO schemes for magnetohydrodynamics,” J. Comp. Phys. 228, 5040–5056 (2009).
S. A. Orszag and C.-M. Tang, “Small-scale structure of two-dimensional magnetohydrodynamic turbulence,” J. Fluid Mech. 90, 129–143 (1979).
J. M. Stone, T. A. Gardiner, P. Teuben, J. F. Hawley, and J. B. Simon, “Athena: a new code for astrophysical MHD,” Astrophys. J. Suppl. 178, 137 (2008).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © B. Chetverushkin, N. D’Ascenzo, A. Saveliev, V. Saveliev, 2017, published in Matematicheskoe Modelirovanie, 2017, Vol. 29, No. 3, pp. 3–15.
Rights and permissions
About this article
Cite this article
Chetverushkin, B., D’Ascenzo, N., Saveliev, A. et al. A kinetic model for magnetogasdynamics. Math Models Comput Simul 9, 544–553 (2017). https://doi.org/10.1134/S2070048217050039
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S2070048217050039