Application of high performance computing systems to simulate the Farley-Buneman instability


  • E.A. Kuksheva Boreskov Institute of Catalysis of SB RAS
  • V.N. Snytnikov Boreskov Institute of Catalysis of SB RAS


mathematical simulation, supercomputer, parallel programming, astrophysics


The Farley-Buneman instability is observed in the E-region of the Earth’s ionosphere at altitudes about 100 km. A mathematical model is used to describe this instability. The model includes the ion kinetic equation dependent on five independent variables (two space coordinates, two velocity coordinates, and time), the fluid equations for electron density and temperature (these equations depend on three independent variables: two space coordinates and time), and the two-dimensional Poisson equation for the potential of the turbulent electric field. The problem is solved numerically on multidimensional grids containing 109 points on average. A software package was designed to solve the problem on supercomputing systems. Computations were performed on the supercomputers SKIF MGU Chebyshev and IBM Blue Gene/P installed at the VMK faculty of Moscow State University. A comparative analysis of numerical results is given. A good scalability of the software package is shown. An almost linear acceleration is achieved for large data sets (about 100 Gb of memory is used) and for a number of computational nodes about 2000. The work was performed as a part of the SKIG GRID project and was supported by the state contracts No. P-958 (August 20, 2009) and No. 02.740.11.0196 of the Federal Special-Purpose Program «Scientific and scientific-educational personnel of innovative Russia» and by the Russian Foundation for Basic Research (project No. 08-01-00721).

Author Biographies

E.A. Kuksheva

V.N. Snytnikov

Boreskov Institute of Catalysis of SB RAS
• Senior Researcher, Docent


  1. Farley D.T. A plasma instability resulting in field-aligned irregularities in the ionosphere // J. Geophys. Res. 1963. 68. 6083-6097.
  2. Buneman O. Excitation of field aligned sound waves by electron streams // Phys. Rev. Lett. 1963. 10. 285-288.
  3. Kovalev D.V., Smirnov A.P., Dimant Y.S. Modeling of the Farley-Buneman instability in the E-region ionosphere: a new hybrid approach // Ann. Geophys. 2008. 26, N 9. 2853-2870.
  4. Dimant Y.S., Oppenheim M.M. Ion thermal effects on E-region instabilities: linear theory // J. Atmos. Terr. Phys. 2004. 66, N 17. 1639-1654.
  5. Ковалёв Д.В., Смирнов А.П., Димант Я.С. Моделирование нелинейного развития фарлей-бунемановской неустойчивости с учетом электронных тепловых эффектов // Физ. плазмы. 2009. 35, № 7. 657-664.
  6. Ковалёв Д.В., Смирнов А.П., Димант Я.С. Исследование кинетических эффектов, возникающих при моделировании фарлей-бунемановской неустойчивости // Физ. плазмы. 2009. 35, № 5. 465-471.
  7. Bhatnagar P.L., Gross E.P., Krook M. A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems // Phys. Rev. 1954. 94, N 3. 511-525.
  8. Ковалёв Д.В. Моделирование фарлей-бунемановской неустойчивости с использованием четырехмерного кинетического уравнения // Матем. моделирование. 2008. 20, № 12. 89-104.



How to Cite

Кукшева Э.А., Снытников В.Н. Application of High Performance Computing Systems to Simulate the Farley-Buneman Instability // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2010. 11. 168-175



Section 1. Numerical methods and applications

Most read articles by the same author(s)