Skip to main content
SpringerLink
Log in

Difference Scheme with a Symmetry Analyzer for Equations of Gas Dynamics

  • Published:
Mathematical Models and Computer Simulations Aims and scope

Abstract

The paper proposes a symmetry analyzer as an element of the computational algorithm for the numerical integration of two-dimensional equations of ideal gas dynamics. A symmetry analyzer is an algorithm that allows using grid data to give a preference to a component (in the present work, Cartesian or polar) of a vector field for its reconstruction on the cell interfaces of a computational grid and subsequent calculation of fluxes of conservative variables. A computational algorithm is constructed using a polar-type computational grid and including a symmetry analyzer. The algorithm is easily transferred to the three-dimensional cylindrical type of computational grids.

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

Access this article

Log in via an institution

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.

Similar content being viewed by others

REFERENCES

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

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

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

  4. E. F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics. A Practical Introduction (Springer, Berlin, 1997).

    Book  Google Scholar 

  5. P. V. Breslavski and V. I. Mazhukin, “Modeling of shock waves interaction on dynamically adapting grids,” Mat. Model. 19 (11), 83–85 (2007).

    MathSciNet  MATH  Google Scholar 

  6. V. A. Gasilov and S. V. Diachenko, “Quasimonotonous 2D MHD scheme for unstructured meshes,” Mat. Model. 17 (12), 87–109 (2005).

    MathSciNet  MATH  Google Scholar 

  7. I. V. Popov and I. V. Fryazinov, “Finite-difference method for computation of the gas dynamics equations with artificial viscosity,” Math. Models Comput. Simul. 1, 493–502 (2009).

    Article  Google Scholar 

  8. M. E. Ladonkina, O. A. Nekliudova, and V. F. Tishkin, “Construction of the limiter based on averaging of solutions for discontinued Galerkin method,” Mat. Model. 30 (5), 99–116 (2018).

    Google Scholar 

  9. O. B. Bocharova, M. G. Lebedev, I. V. Popov, V. V. Sitnik, and I. V. Fryazinov, “Shock wave reflection from the axis of symmetry in a nonuniform flow with the formation of a circulatory flow zone,” Math. Models Comput. Simul. 6, 142–154 (2014).

    Article  MathSciNet  Google Scholar 

  10. A. Harten, P. D. Lax, and B. van Leer, “Upstream differencing and Godunov-type schemes for hyperbolic conservation laws,” SIAM Rev. 25, 35–61 (1983).

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

Download references

Funding

The study was financially supported by the Russian Foundation for Basic Research (project no. 18-02-00907).

Author information

Authors and Affiliations

  1. Moscow Institute of Physics and Technology, Moscow, Russia

    A. V. Koldoba & G. V. Ustyugova

  2. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

    G. V. Ustyugova

Authors
  1. A. V. Koldoba
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. V. Ustyugova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Koldoba, A.V., Ustyugova, G.V. Difference Scheme with a Symmetry Analyzer for Equations of Gas Dynamics. Math Models Comput Simul 12, 125–132 (2020). https://doi.org/10.1134/S2070048220020076

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S2070048220020076

Keywords:

Search

Navigation