Skip to main content
SpringerLink
Log in

Analysis of Splitting Algorithms in Convection–Diffusion Problems

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

The mathematical modeling of the propagation of pollution from point sources in the air is considered. An approach that uses the idea of splitting and point-to-point computing is proposed for the numerical solution of multi-dimensional convection–diffusion equations. The construction of difference splitting schemes, approximation, and stability with respect to initial data is analyzed.

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

Similar content being viewed by others

References

  1. Design Procedure for Atmospheric Concentration of Harmful Substances in Emissions of Enterprises. An All-Union Regulatory Document (OND-86) [in Russian], Gidrometeoizdat, Leningrad (1987).

  2. Yu. A. Izrael’, Ecology and Environmental Monitoring [in Russian], Gidrometeoizdat, Leningrad (1984).

    Google Scholar 

  3. N. F. Tishchenko, Atmospheric Air Protection. Calculation of the Content of Harmful Substances and their Distribution in Air [in Russian], Khimiya, Moscow (1991).

    Google Scholar 

  4. M. Z. Zgurovsky V. V. Skopetsky, V. K. Khrushch, and N. N. Belyaev, Numerical Modeling of the Propagation of Environmental Pollutants [in Russian], Naukova Dumka, Kyiv (1997).

    Google Scholar 

  5. F. T. M. Nieuwstadt and H. van Dop (eds.), Atmospheric Turbulence and Atmospheric Pollution Modeling: A Course Held in The Hague, 21–25 September, 1981, Springer Netherlands (1982).

    Google Scholar 

  6. A. E. Aloyan, Modeling the Dynamics and Kinetics of Gas Impurities and Aerosols in the Atmosphere [in Russian], Nauka, Moscow (2008).

    Google Scholar 

  7. V. K. Arguchintsev and A. V. Arguchintseva, Models and Methods to Solve Atmosphere, Hydrosphere, and Underlying Terrain Protection Problems [in Russian], IGU, Irkutsk (2001).

    Google Scholar 

  8. G. I. Marchuk, Mathematical Modeling in the Environment Problem [in Russian], Nauka, Moscow (1982).

    Google Scholar 

  9. A. S. Grinin, N. A. Orekhov, and V. N. Novikov, Mathematical Modeling in Ecology [in Russian], YuNITI Moscow (2003).

    Google Scholar 

  10. A. E. Aloyan, V. V. Penenko, and V. V. Kozoderov, “Mahtematical modeling in the environmental problem,” in: Modern Problems of Calculus Mathematics and Mathematical Modeling [in Russian], Vol. 2, Nauka, Moscow (2005), pp. 279–351.

    Google Scholar 

  11. A. V. Gladkii, I. V. Sergienko, V. V. Skopetskii, and Yu. A. Gladka, Fundamentals of the Mathematical Modeling in Ecology [in Ukrainian], NTUU “KPI,” Kyiv (2009).

    Google Scholar 

  12. A. A. Samarskii, and P. N. Vabishchevich, Numerical Methods of the Solution of Convection–Diffusion Problems [in Russian], Editorial URSS, Moscow (2004).

    Google Scholar 

  13. A. A. Samarskii and P. N. Vabishchevich, Computational Heat Transfer [in Russian], Editorial URSS, Moscow (2003).

    Google Scholar 

  14. G. I. Marchuk, Splitting Methods [in Russian], Nauka, Moscow (1988).

    Google Scholar 

  15. A. A. Samarskii and E. S. Nikolaev, Methods to Solve Finite-Difference Equations [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  16. V. K. Saul’ev, “A technique for numerical integration of diffusion equations,” DAN, 115, No. 6, 1077–1080 (1957).

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    A. V. Gladky

Authors
  1. A. V. Gladky
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. V. Gladky.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 4, July–August, 2014, pp. 76–88.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gladky, A.V. Analysis of Splitting Algorithms in Convection–Diffusion Problems. Cybern Syst Anal 50, 548–559 (2014). https://doi.org/10.1007/s10559-014-9643-3

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-014-9643-3

Keywords

Search

Navigation