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Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 8, Pages 1363–1379 (Mi zvmmf10251)  

This article is cited in 2 scientific papers (total in 2 papers)

Numerical simulation of three-dimensional quasi-neutral gas flows based on smoothed magnetohydrodynamic equations

T. G. Elizarovaa, M. V. Popovb

a Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia
b École Normale Supérieure de Lyon, CRAL (UMR CNRS 5574), Université de Lyon 1, 46 allée d'Italie 69007 Lyon, France

Abstract: 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 FaradayТs 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 StokesТ 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.

Key words: magnetic quasi-gas dynamics, QMHD, MHD flows, finite-difference algorithm, central-difference approximation.

DOI: https://doi.org/10.7868/S0044466915080086

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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:8, 1330–1345

Bibliographic databases:

UDC: 519.634
Received: 26.01.2015

Citation: T. G. Elizarova, M. V. Popov, “Numerical simulation of three-dimensional quasi-neutral gas flows based on smoothed magnetohydrodynamic equations”, Zh. Vychisl. Mat. Mat. Fiz., 55:8 (2015), 1363–1379; Comput. Math. Math. Phys., 55:8 (2015), 1330–1345

Citation in format AMSBIB
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\vol 55
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. T. G. Elizarova, I. A. Shirokov, M. V. Popov, “O vozmozhnostyakh kvazigazodinamicheskoi modeli dlya chislennogo analiza sverkhzvukovogo turbulentnogo techeniya mezhzvezdnogo gaza”, Preprinty IPM im. M. V. Keldysha, 2017, 009, 21 pp.  mathnet  crossref
    2. B. Chetverushkin, N. D'Ascenzo, A. Saveliev, V. Saveliev, “A kinetic model for magnetogasdynamics”, Math. Models Comput. Simul., 9:5 (2017), 544–553  mathnet  crossref  elib
  • ∆урнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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