Geodesic
Difference scheme with a symmetry analizer for equations of magnetohydrodynamics
Matematičeskoe modelirovanie, Tome 32 (2020) no. 12, pp. 65-80

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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. 
@article{MM_2020_32_12_a5,
     author = {G. V. Ustyugova and A. V. Koldoba},
     title = {Difference scheme with a symmetry analizer for equations of magnetohydrodynamics},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {65--80},
     publisher = {mathdoc},
     volume = {32},
     number = {12},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2020_32_12_a5/}
}
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G. V. Ustyugova; A. V. Koldoba. Difference scheme with a symmetry analizer for equations of magnetohydrodynamics. Matematičeskoe modelirovanie, Tome 32 (2020) no. 12, pp. 65-80. http://geodesic.mathdoc.fr/item/MM_2020_32_12_a5/