Application of the trajectory method and the finite element method to the modeling of viscous heat-conductive gas motion

Authors

  • V.V. Shaidurov
  • G.I. Shchepanovskaya
  • M.V. Yakubovich

Keywords:

Navier-Stokes equations
viscous heat-conductive gas
numerical modeling
trajectory method
finite element method

Abstract

An algorithm for the numerical solution of the modified Navier-Stokes equations is proposed for the case of one-dimensional motion of a viscous heat-conductive gas. The results of test computations are discussed. The problem on the propagation of heat impulse in the gas is solved. The proposed numerical model is used to study a number of one-dimensional geodynamic processes.


Published

2011-06-03

Issue

Section

Section 1. Numerical methods and applications

Author Biographies

V.V. Shaidurov

Institute of Computational Modeling of SB RAS (ICM SB RAS)
• Corresponding Member of RAS, Director

G.I. Shchepanovskaya

Institute of Computational Modeling of SB RAS (ICM SB RAS)
• Associate Professor, Senior Researcher

M.V. Yakubovich


References

  1. Ушакова О.А., Шайдуров В.В., Щепановская Г.И. Метод конечных элементов для уравнений Навье-Стокса в сферической системе координат // Вестник КрасГУ. 2006. N 4. 151-156.
  2. Флетчер К. Численные методы на основе метода Галеркина. М.: Мир, 1988.
  3. Pironneau O. On the transport-diffusion algorithm and its applications to the Navier-Stokes equations // Numerische Mathematik. 1982. 38. 309-332.
  4. Anderson D., Tannehill J., Pletcher R. Computational fluid mechanics and heat transfer. New York: Hemisphere Publ. Corp., 1984.
  5. Самарский А.А., Николаев Е.С. Методы решения сеточных уравнений. М.: Наука, 1978.
  6. Шайдуров В.В., Щепановская Г.И., Якубович М.В. Одномерная модель динамики вязкого теплопроводного газа // Материалы XIV международной научной конференции «Решетневские чтения». Красноярск: СибГАУ, 2010. 440-441.
  7. Шайдуров В.В, Щепановская Г.И. Газодинамическая модель внутреннего строения Земли // Вестник СибГАУ. 2008. N 1. 79-83.
  8. Vyatkin A.V., Shaidurov V.V., Shchepanovskaya G.I. Numerical spherically-symmetric simulation of deep-seated geodynamics // J. of Applied and Industrial Mathematics. 2010. 4, N 2. 290-297.
  9. Jeffreys H. The Earth: its origin, history, and physical constitution. Cambridge: Cambridge Univ. Press, 2008.

 How to cite   
Berendeev E.A., Snytnikov A.V., Berendeev E.A. and Lazareva G.G. Supercomputer simulation of plasma electron dynamics in a magnetic trap with inverse magnetic mirrors and multipole magnetic walls // Numerical Methods and Programming. 2013. 14, No 1. 149–154.

TEX CODE:

Berendeev E. , Snytnikov A. , Berendeev E. et al., (2013) “Supercomputer simulation of plasma electron dynamics in a magnetic trap with inverse magnetic mirrors and multipole magnetic walls,” Numerical Methods and Programming, vol. 14, no. 1, pp. 149–154.

TEX CODE:

E. Berendeev, A. Snytnikov, E. Berendeev et al., “Supercomputer simulation of plasma electron dynamics in a magnetic trap with inverse magnetic mirrors and multipole magnetic walls,” Numerical Methods and Programming 14, no. 1 (2013): 149–154

TEX CODE:

Berendeev E. , Snytnikov A. , Berendeev E. et al. Supercomputer simulation of plasma electron dynamics in a magnetic trap with inverse magnetic mirrors and multipole magnetic walls. Numerical Methods and Programming. 2013;14(1):149–154.(In Russ.).

TEX CODE:



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