Skip to main content
SpringerLink
Log in

An efficient numerical algorithm for simulating a two-dimensional glow discharge

  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

Abstract

A numerical algorithm of the second approximation order with respect to the space variables for simulating a two-dimensional elevated pressure glow discharge in the framework of the drift-diffusion approximation is presented. A specific feature of this algorithm is the use of the Laplace resolving operator for the solution of the system of grid equations. This makes it possible to ensure the convergence of the solution in strong grid norms. Mathematical aspects of the statement of the differential-difference and finite difference problems (solvability, nonnegativity, approximation, stability, and convergence) are discussed, and bounds on the norms of the corresponding differential and difference operators that are required for constructing an optimal iterative process are obtained.

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. G. G. Gladush and A. A. Samokhin, “Effect of Initial Plasma Density on the Duration of the Uniform Stage of a Glow Discharge,” Fiz. Plazmy 11, 230–235 (1985) [Sov. J. Plasma Phys. 11, No. 2, 136–139 (1985)].

    Google Scholar 

  2. Yu. P. Raizer and S. T. Surzhikov, “Two-Dimensional Structure in a Normal Glow Discharge and Diffusion Effects in Cathode and Anode Spot Formation,” Teplofiz. Vysokikh Temp. 26, 428–435 (1988) [High Temp. 26, 304–311 (1988)].

    Google Scholar 

  3. R. Sh. Islamov, “Numerical Study of Transition from Dark Townsend to Anomalous Glowing Discharge,” Izv. Ross. Akad. Nauk, Ser. Fiz. 64, 1407–1410 (2000) [Bull. Russ. Acad. Sci. Phys. 64, 1130–1132 (2000)].

    Google Scholar 

  4. R. Sh. Islamov, “Global Solutions of the Drift-Diffusion Approximation Equations in Gas Discharge Theory,” Differ. Uravn. 39, 1662–1676 (2003) [Differ. Equations 39, 1750–1766 (2003)].

    MATH  MathSciNet  Google Scholar 

  5. R. Sh. Islamov, “On the Regularity of Solutions to the Drift-Diffusion Approximation Equations in Gas Discharge Theory,” Zh. Vychisl. Mat. Mat. Fiz. 46, 131–147 (2006) [Comput. Math. Math. Phys. 46, 125–140 (2006)].

    MathSciNet  Google Scholar 

  6. R. Sh. Islamov and E. N. Gulamov, “Numerical Simulation of Axisymmetric Anode Spot Formation in Glow Discharge at Elevated Pressure,” IEEE Trans. Plasma Sci. 26(1), 7–13 (1998).

    Article  Google Scholar 

  7. R. Sh. Islamov, Simulation of Current Self-Organization in the Glowing Discharge,” Izv. Ross. Akad. Nauk, Ser. Fiz. 64, 1402–1406 (2000) [Bull. Russ. Acad. Sci. Physics 64, 1126–1129 (2000)].

    Google Scholar 

  8. R. Sh. Islamov, O. A. Novodvorskii, and R. Ya. Sagdeev, “Stratification of Current Near the Anode Surface in a Glow Discharge in a Gas Flow and Effect of Doubling the Stratification Period,” Fiz. Plazmy 23, 970–976 (1997) [Plasma Phys. Rep. 23, 895–901 (1997)].

    Google Scholar 

  9. A. A. Samarskii, Theory of Finite Difference Schemes (Nauka, Moscow, 1977; Marcel Dekker, New York, 2001).

    Google Scholar 

  10. A. A. Samarskii and A. V. Gulin, Stability of Finite Difference Schemes (Nauka, Moscow, 1973) [in Russian].

    Google Scholar 

  11. A. A. Samarskii and P. N. Vabishchevich, Numerical Methods for Convection-Diffusion Problems (Editorial URSS, Moscow, 1999) [in Russian].

    Google Scholar 

  12. A. A. Samarskii and E. S. Nikolaev, Methods for Solving Grid Equations (Nauka, Moscow, 1978) [in Russian].

    Google Scholar 

  13. D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order (Springer, New York, 2001; Fizmatlit, Moscow, 1989).

    Google Scholar 

  14. R. Hockney, “The Potential Calculation and Some Applications,” in Methods in Computational Physics (Academic, New York, 1970; Mir, Moscow, 1974), vol. 9.

    Google Scholar 

  15. V. P. Il’in, Numerical Methods for Solving Electrophysics Problems (Nauka, Moscow, 1985) [in Russian].

    Google Scholar 

  16. R. Sh. Islamov, “Self-Organization of Current Structures in a Gas Discharge,” in Modern Laser and Information Technologies, Ed. by V. Ya Panchenko and V. S. Golubev Interkontakt Nauka, Moscow, 2005); http://www.laser.ru/science/pdf/select42.pdf [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Laser and Information Technologies, Russian Academy of Sciences, ul. Svyatoozerskaya 1, Shatura, Moscow oblast, 140700, Russia

    R. Sh. Islamov

Authors
  1. R. Sh. Islamov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © R.Sh. Islamov, 2006, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2006, Vol. 46, No. 11, pp. 2065–2080.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Islamov, R.S. An efficient numerical algorithm for simulating a two-dimensional glow discharge. Comput. Math. and Math. Phys. 46, 1972–1987 (2006). https://doi.org/10.1134/S0965542506110121

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542506110121

Keywords

Search

Navigation