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Matem. Mod., 2020, Volume 32, Number 12, Pages 65–80 (Mi mm4244)  

Difference scheme with a symmetry analizer for equations of magnetohydrodynamics

G. V. Ustyugovaa, A. V. Koldobab

a Keldysh Institute of Applied Mathematics RAS
b Moscow Institute of Physics and Technology (NSU)

Abstract: The paper proposes a computational algorithm for the numerical simulation of twodimensional MHD flows using a symmetry analyzer as an element of the numerical method. The algorithm is based on a finite-volume Godunov-type scheme with an approximate solution of the Riemann problem for calculating flows. A polar grid is used, but the equations of momentum and magnetic induction are approximated in a Cartesian coordinate system. It is assumed that the flows are either predominantly homogeneous plane-symmetric, or predominantly axisymmetric relative to the grid axis. To reconstruct vector variables in the computational cells, a symmetry analyzer is used, which makes it possible to locally classify the flow as one of the indicated types. Depending on what type the vector field will be assigned to, the corresponding components are used for its reconstruction.

Keywords: magnetohydrodynamics, Godunov-type difference scheme, symmetry analyzer.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-02-00907


DOI: https://doi.org/10.20948/mm-2020-12-06

Full text: PDF file (601 kB)
First page: PDF file
References: PDF file   HTML file

Received: 27.08.2020
Revised: 27.08.2020
Accepted:21.09.2020

Citation: G. V. Ustyugova, A. V. Koldoba, “Difference scheme with a symmetry analizer for equations of magnetohydrodynamics”, Matem. Mod., 32:12 (2020), 65–80

Citation in format AMSBIB
\Bibitem{UstKol20}
\by G.~V.~Ustyugova, A.~V.~Koldoba
\paper Difference scheme with a symmetry analizer for equations of magnetohydrodynamics
\jour Matem. Mod.
\yr 2020
\vol 32
\issue 12
\pages 65--80
\mathnet{http://mi.mathnet.ru/mm4244}
\crossref{https://doi.org/10.20948/mm-2020-12-06}


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