Geodesic
Numerical investigation of high-energy plasmoid behavior in the upper ionosphere. Part~2. Development of the three-dimensional model
Matematičeskoe modelirovanie, Tome 16 (2004) no. 8, pp. 3-23.

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We develop a new modification for the monotone conservative variant of the grid-characteristic method of 2-3 order of approximation. The general algorithm of the transition from the known state at $t=t^n$ to the desired one at the instant $t=t^{n+1}$ includes the splitting in spatial variables. If there are discontinuities of great intensity, it includes the splitting in “the physical processes” as well (the “gas-dynamic” stage, the “magnetic” stage, and the stage of calculating the magnetic field diffusion). We carry out the numerical investigations of the evolution of the strong plasma disturbances in the near-Earth space to times of the order of 6 sec. We demonstrate the considerable influence of the nonhomogeneity of the exponential atmosphere and the geomagnetic field on the structure of the plasma flow. 
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     title = {Numerical investigation of high-energy plasmoid behavior in the upper ionosphere. {Part~2.} {Development} of the three-dimensional model},
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A. S. Kholodov; Ya. A. Kholodov; E. L. Stupitsky; A. J. Repin. Numerical investigation of high-energy plasmoid behavior in the upper ionosphere. Part~2. Development of the three-dimensional model. Matematičeskoe modelirovanie, Tome 16 (2004) no. 8, pp. 3-23. http://geodesic.mathdoc.fr/item/MM_2004_16_8_a0/

[1] Stupitskii E. L., Repin A. M., Kholodov A. S., Kholodov Ya. A., “Chislennoe issledovanie povedeniya vysokoenergetichnogo plazmennogo sgustka v verkhnei ionosfere. Chast 1. Nachalnaya stadiya razleta i tormozheniya plazmennogo sgustka”, Matemat. modelir., 16:7 (2004), 43–58

[2] Repin A. Yu., Stupitskii E. L., Shapranov A. V., “Chislennoe modelirovanie povedeniya plazmennoi strui v geomagnitnom pole”, Geomagnetizm i aeronomiya, 43:3 (2003)

[3] Kulikovskii A. G., Pogoreloe N. V., Semenov A. Yu., Matematicheskie voprosy chislennogo resheniya giperbolicheskikh sistem uravnenii, Fizmatlit, M., 2001, 607 pp. | Zbl

[4] Vorobev O. V., Kholodov Ya. A., “Ob odnom metode chislennogo integrirovaniya odnomernykh zadach gazovoi dinamiki”, Matemat. modelir., 8:1 (1996), 77–92 | MR

[5] Kholodov Ya. A., A monotone high-order accuracy schemes for hyperbolic CFD problems, APS$53^{rd}$ Meeting of the Division of Fluid Dynamics, Washington, 2000

[6] Magomedov K. M., Kholodov A. S., Setochno-kharakteristicheskie chislennye metody, Nauka, M., 1988, 287 pp. | MR

[7] Kholodov A. S., “O postroenii raznostnykh skhem s polozhitelnoi approksimatsiei dlya uravnenii giperbolicheskogo tipa”, Zh. vychisl. matem. i matem. fiz., 18:6 (1978), 1476–1492 | MR | Zbl

[8] Kholodov A. S., “O postroenii raznostnykh skhem povyshennogo poryadka tochnosti dlya uravnenii giperbolicheskogo tipa”, Zh. vychisl. matem. i matem. fiz., 20:6 (1980), 1601–1620 | MR | Zbl

[9] Godunov S. K., “Raznostnyi metod chislennogo rascheta razryvnykh reshenii uravnenii gidrodinamiki”, Mat. sb., 47(89):3 (1959), 271–306 | MR | Zbl

[10] Roe P. L., “Approximate Riemann problem solvers, parameter vectors, and difference schemes”, J. Copput. Phys., 43:2 (1981), 357–372 | DOI | MR | Zbl

[11] Osher S., “Numerical solution of singular perturbation problems and hyperbolic systems of conservatioin laws”, North Holland Mathematical Studies, 47 (1981), 179–205 | DOI | MR

[12] Fizika yadernogo vzryva, t. 1, Nauka, M., 1997, 526 pp.

[13] D. K. Bhadra, “Expansion of a Resistive Plasmoid in a Magnetic Field”, The Physics of Fluids, 11:1 (1968), 234–239 | DOI

[14] Bakhrakh S. M., Gubkov E. V., Zhmailo V. A., Terekhin V. A., “Razlet plazmennogo oblaka v odnorodnom magnitnom pole”, PMTF, 1974, no. 4, 146–148