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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 3, Pages 505–528 (Mi zvmmf172)  
This article is cited in 38 scientific papers (total in 38 papers)

Piecewise parabolic method on a local stencil for ideal magnetohydrodynamics

M. V. Popov, S. D. Ustyugov

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia
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Abstract: A numerical scheme based on the piecewise parabolic method on a local stencil (PPML) is proposed for solving the ideal magnetohydrodynamic (MHD) equations. The method makes use of the conservation of Riemann invariants along the characteristics of the MHD equations. As a result, a local stencil can be used to construct a numerical solution. This approach improves the dissipative properties of the numerical scheme and is convenient in the case of adaptive grids. The basic stages in the design of the scheme are illustrated in the two-dimensional case. The conservation of the solenoidal property of the magnetic field is discussed. The scheme is tested using several typical MHD problems.
Key words: numerical methods for MHD problems, local stencil, Riemann invariants, PPM, PPML.
Received: 20.06.2007
English version:
Computational Mathematics and Mathematical Physics, 2008, Volume 48, Issue 3, Pages 477–499
DOI: https://doi.org/10.1007/s11470-008-3011-1
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: M. V. Popov, S. D. Ustyugov, “Piecewise parabolic method on a local stencil for ideal magnetohydrodynamics”, Zh. Vychisl. Mat. Mat. Fiz., 48:3 (2008), 505–528; Comput. Math. Math. Phys., 48:3 (2008), 477–499
Citation in format AMSBIB
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    • This publication is cited in the following 38 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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