Skip to main content
Log in

Difference Scheme with a Symmetry Analyzer for Equations of Magnetohydrodynamics

  • Published:
Mathematical Models and Computer Simulations Aims and scope

Abstract

The paper proposes a computational algorithm for the numerical simulation of two-dimensional magnetohydrodynamic (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 mesh is used, but the momentum and magnetic induction equations are approximated in a Cartesian coordinate system. It is assumed that the flows are either predominantly homogeneous plane-symmetric, or predominantly axisymmetric with respect to the grid’s 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 the type of the vector field, the corresponding components are used for its reconstruction.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.

Similar content being viewed by others

REFERENCES

  1. S. K. Godunov, A. V. Zabrodin et al., Numerical Solution of Multidimensional Problems of Gas Dynamics (Nauka, Moscow, 1976) [in Russian].

    Google Scholar 

  2. A. G. Kulikovskii, N. V. Pogorelov, and A. Yu. Semenov, Mathematical Aspects of Numerical Solution of Hyperbolic Systems (Fizmatlit, Moscow, 2001; Chapman & Hall/CRC, Boca Raton, FL, 2001).

  3. V. M. Goloviznin and B. N. Chetverushkin, “New generation algorithms for computational fluid dynamics,” Comput. Math. Math. Phys. 58 (8), 1217–1225 (2018).

    Article  MathSciNet  Google Scholar 

  4. M. D. Bragin, Y. A. Kriksin, and V. F. Tishkin, “Discontinuous Galerkin method with an entropic slope limiter for Euler equations,” Math. Models Comput. Simul. 12 (5), 824–833 (2020).

    Article  MathSciNet  Google Scholar 

  5. A. V. Koldoba and G. V. Ustyugova, “Difference scheme with a symmetry analyzer for equations of gas dynamics,” Math. Models Comput. Simul. 12 (2), 125–132 (2020).

    Article  MathSciNet  Google Scholar 

  6. T. Miyoshi and K. J. Kusano, “A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics,” J. Comput. Phys. 208 (1), 315–344 (2005).

    Article  MathSciNet  Google Scholar 

  7. D. S. Balsara and D. S. Spicer, “A staggered mesh algorithm using high order Godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations,” J. Comput. Phys. 149 (2), 270–292 (1999).

    Article  MathSciNet  Google Scholar 

  8. I. B. Petrov and A. I. Lobanov, Lectures on Computational Mathematics (Internet-Univ. Inf. Tekhnol., Moscow, 2006) [in Russian].

    Google Scholar 

  9. V. A. Gasilov, A. S. Boldarev, S. V. Dyachenko et al., “Program package MARPLE3D for simulation of pulsed magnetically driven plasma using high performance computing,” Mat. Model. 24 (1), 55–87 (2012).

    MATH  Google Scholar 

Download references

Funding

This study was supported by the Russian Foundation for Basic Research, grant 18-02-00907.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to G. V. Ustyugova or A. V. Koldoba.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ustyugova, G.V., Koldoba, A.V. Difference Scheme with a Symmetry Analyzer for Equations of Magnetohydrodynamics. Math Models Comput Simul 13, 674–683 (2021). https://doi.org/10.1134/S2070048221040219

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S2070048221040219

Keywords:

Navigation