In the present work, a three-dimensional mathematical model of the influence of electron concentration on the dynamics of the E-layer of the ionosphere under nonisothermal conditions is developed. The proposed method shows high computational efficiency and good quality estimates. To approximate the solution of the convective and diffusion terms of the intermediate velocity field, the finite difference method is used in combination with a five-diagonal matrix, which made it possible to achieve fourth-order accuracy in space and third-order accuracy in time. To solve the pressure, the Poisson equation is solved, which ensures the fulfillment of the continuity equation. The Poisson equation is transformed from physical space to spectral space using the Fourier transform. The equation for the temperature and electron concentration is solved using the Adams-Bashforth method. Before modeling the influence of the magnetic field on MHD turbulence, to test the adequacy of the numerical algorithm, the Taylor Green test problem was performed for various Reynolds numbers, where it agrees well with the reference spectral method and analytical solutions. As a result of the simulation, the temperature contours and turbulent flow isotherms for various Stuart numbers were obtained. The developed numerical algorithm can be used to model the attenuation of ionospheric turbulence at various Stuart numbers.


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How to Cite
ABDIBEKOVA, A.U.; ZHAKEBAYEV, D.B.; KARUNA, O.. MODELLING THE INFLUENCE OF ELECTRON CONCENTRATION ON MHD TURBULENCE BY LES. Journal of Mathematics, Mechanics and Computer Science, [S.l.], v. 106, n. 2, p. 91-103, june 2020. ISSN 2617-4871. Available at: <>. Date accessed: 23 sep. 2020. doi:
Keywords Ionosphere E-layer, concentration of electron, magnetohydrodynamics, Taylor-Green vortex problem, finite difference method