Geodesic
Method of calculation of the magnetic field in magnetohydrodynamic models of the electric arc
Matematičeskoe modelirovanie, Tome 24 (2012) no. 10, pp. 40-50.

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The computing method of self-induced magnetic field in magnetohydrodynamic models of the electric arc, based on the equation for an induction of a magnetic field is proposed. At testing in a two-dimensional case higher computing efficiency of a method in comparison with other known computing methods of an induction under the law of Biot–Savart and through vector potential is shown. The method permits generalization on a three-dimensional case which is more effective than the method of vector potential.
Keywords: mathematical modelling, electric arc, MHD model, magnetic field. 
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E. B. Kulumbaev; T. B. Nikulicheva. Method of calculation of the magnetic field in magnetohydrodynamic models of the electric arc. Matematičeskoe modelirovanie, Tome 24 (2012) no. 10, pp. 40-50. http://geodesic.mathdoc.fr/item/MM_2012_24_10_a3/

[1] Zhukov M. F. (red.), Teoriya termicheskoi elektrodugovoi plazmy, v. 1, Nauka SO, Novosibirsk, 1987, 574 pp.

[2] Engelsht V. S., Gurovich V. Ts., Desyatkov G. A. i dr. (red.), Teoriya stolba elektricheskoi dugi, Nauka SO, Novosibirsk, 1990, 376 pp.

[3] Hippler R. et al. (eds.), Low temperature plasmas: fundamentals, technologies and techniques, v. 1, Wiley-VCH, Weinheim, 2008, 409 pp.

[4] Finkelburg V., Mekker G., Elektricheskie dugi i termicheskaya plazma, IL, M., 1961, 370 pp.

[5] Galanin M. P., Popov Yu. P., Kvazistatsionarnye elektromagnitnye polya v neodnorodnykh sredakh: Matematicheskoe modelirovanie, Nauka, Fizmatlit, M., 1995, 320 pp. | MR | Zbl

[6] Murphy A. B., “A self-consistent three-dimensional model of the arc, electrode and weld pool in gas-metal arc welding”, J. Phys. D: Appl. Phys., 44 (2011), 194009, 11 pp. | DOI

[7] Freton P., Gonzales J. J., Masquere M., Reichert F., “Magnetic field approaches in dc thermal plasma modeling”, J. Phys. D: Appl. Phys., 44 (2011), 345202, 16 pp. | DOI

[8] Brackbill J. U., Barnes D. C., “The Effect of nonzero $\nabla\cdot\mathrm{B}=0$ on the numerical solution of the magnetohydrodynamic equations”, J. Comput. Phys., 35 (1980), 426–430 | DOI | MR | Zbl

[9] Patankar S., Chislennye metody resheniya zadach teploobmena i dinamiki zhidkosti, Per. s angl., Energoatomizdat, M., 1984, 152 pp.

[10] Zheenbaev Zh., Engelsht V. S., Dvukhstruinyi plazmotron, In-t fiziki i matematiki AN Kirg. SSR, Frunze, 1983, 199 pp.

[11] Kalitkin H. H., Chislennye metody, BHV, SPb., 2011, 592 pp.