Geodesic
Numerical simulation of three-dimensional quasi-neutral gas flows based on smoothed magnetohydrodynamic equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 8, pp. 1363-1379 
T. G. Elizarova; M. V. Popov. Numerical simulation of three-dimensional quasi-neutral gas flows based on smoothed magnetohydrodynamic equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 8, pp. 1363-1379. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_8_a8/
@article{ZVMMF_2015_55_8_a8,
     author = {T. G. Elizarova and M. V. Popov},
     title = {Numerical simulation of three-dimensional quasi-neutral gas flows based on smoothed magnetohydrodynamic equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1363--1379},
     year = {2015},
     volume = {55},
     number = {8},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_8_a8/}
}
TY  - JOUR
AU  - T. G. Elizarova
AU  - M. V. Popov
TI  - Numerical simulation of three-dimensional quasi-neutral gas flows based on smoothed magnetohydrodynamic equations
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2015
SP  - 1363
EP  - 1379
VL  - 55
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_8_a8/
LA  - ru
ID  - ZVMMF_2015_55_8_a8
ER  - 
%0 Journal Article
%A T. G. Elizarova
%A M. V. Popov
%T Numerical simulation of three-dimensional quasi-neutral gas flows based on smoothed magnetohydrodynamic equations
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2015
%P 1363-1379
%V 55
%N 8
%U http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_8_a8/
%G ru
%F ZVMMF_2015_55_8_a8

Voir la notice de l'article provenant de la source Math-Net.Ru

A new finite-difference method for the numerical simulation of compressible MHD flows is presented, which is applicable to a broad class of problems. The method relies on the magnetic quasi-gasdynamic equations (referred to as quasi-MHD (QMHD) equations), which are, in fact, the system of Navier–Stokes equations and Faraday’s laws averaged over a short time interval. The QMHD equations are discretized on a grid with the help of central differences. The averaging procedure makes it possible to stabilize the numerical solution and to avoid additional limiting procedures (flux limiters, etc.). The magnetic field is ensured to be free of divergence by applying Stokes’ theorem. Numerical results are presented for 3D test problems: a central blast in a magnetic field, the interaction of a shock wave with a cloud, and the three-dimensional Orszag–Tang vortex. Additionally, preliminary numerical results for a magnetic pinch in plasma are demonstrated.

[1] Elizarova T. G., Kvazigazodinamicheskie uravneniya i metody rascheta vyazkikh techenii, Nauchnyi mir, M., 2007

[2] Chetverushkin B. N., Kineticheskie skhemy i kvazigazodinamicheskaya sistema uravnenii, Maks Press, M., 2004

[3] Sheretov Yu. V., Dinamika sploshnykh sred pri prostranstvenno-vremennóm osrednenii, NITs “Regulyarnaya i khaoticheskaya dinamika”, Izhevsk, 2009

[4] Elizarova T. G., Kalachinskaya I. S., Sheretov Yu. V., Shirokov I. A., “Chislennoe modelirovanie techenii elektroprovodnoi zhidkosti vo vneshnem magnitnom pole”, Zh. radiotekhn. i elektronika, 50:2 (2005), 245–251

[5] Elizarova T. G., Ustyugov S. D., “Kvazigazodinamicheskii algoritm resheniya uravnenii magnitnoi gidrodinamiki. Odnomernyi sluchai”, Preprinty IPM im. M. V. Keldysha, 2011, 001, 20 pp.

[6] Elizarova T. G., Ustyugov S. D., “Kvazigazodinamicheskii algoritm resheniya uravnenii magnitnoi gidrodinamiki. Mnogomernyi sluchai”, Preprinty IPM im. M. V. Keldysha, 2011, 030, 24 pp.

[7] Ducomet B., Zlotnik A., “On a regularization of the magnetic gas dynamics system of equations”, Kinetic and Related Models, 6:3 (2013), 533–543 | DOI | MR | Zbl

[8] Kulikovskii A. G., Pogorelov N. V., Semenov A. Yu., Matematicheskie voprosy chislennogo resheniya giperbolicheskikh sistem uravnenii, Fizmatlit, M., 2001 | MR

[9] Elizarova T. G., “Osrednenie po vremeni kak priblizhennyi sposob postroeniya kvazigazodinamicheskikh i kvazigidrodinamicheskikh uravnenii”, Zh. vychisl. matem. i matem. fiz., 51:11 (2011), 2096–2105 | MR | Zbl

[10] Gardiner T. A., Stone J. M., “An unsplit Godunov method for ideal MHD via constained transport in three dimensions”, J. Comput. Phys., 227 (2008), 4123–4141 | DOI | MR | Zbl

[11] Ustyugov S. D., Popov M. V., Kritsuk A. F., Norman M. L., “Piecewise parabolic method on a local stencil for magnetized supersonic turbulence simulation”, J. Comput. Phys., 228 (2009), 7614–7633 | DOI | MR | Zbl

[12] Dai W., Woodward P., “A simple finite difference scheme for multidimensional magnetohydrodynamical equations”, J. Comput. Phys., 142 (1998), 331–369 | DOI | MR | Zbl

[13] Tóth G., “The $\nabla\cdot\mathbf{B}=0$ constraint in shocik-capturing magnetohydrodynamics codes”, J. Comput. Phys., 161 (2000), 605–652 | DOI | MR | Zbl

[14] Orszag S. A., Tang C./M., “Small-scale structure of two-dimensional magnetohydrodynamic trubulence”, J. Fluid Mech., 90 (1979), 129–143 | DOI

[15] Vedenov A. A., Velikhov E. P., Sagdeev R. Z., “Ustoichivost plazmy”, Uspekhi fiz. nauk, 73:4 (1961), 701–766 | DOI | MR

[16] Golant V. E., Zhilinskii A. P., Sakharov I. E., Osnovy fiziki plazmy, Atomizdat, M., 1977