N. A. Magnitskii

Publications (4)1.13 Total impact

• Article: Nonlinear dynamics in the initial-boundary value problem on the fluid flow from a ledge for the hydrodynamic approximation to the boltzmann equations

  N. M. Evstigneev, N. A. Magnitskii
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  ABSTRACT: We numerically analyze the laminar-turbulent transition in the problem on the flow of a viscous incompressible fluid from a ledge. To model the fluid flow, we use the Boltzmann integro-differential equations expanded in the Knudsen number. For the fundamental analysis, we use a numerical method of increased accuracy for the integration of the initial-boundary value problem. By analyzing the phase portraits of the behavior of the system, we find that the transition from a stationary solution to an irregular chaotic one takes place in accordance with the Feigenbaum-Sharkovskii-Magnitskii scenario. Moreover, the transition process differs from the results obtained by using the Navier-Stokes equations for solving a similar initial-boundary value problem.
  Differential Equations 04/2012; 46(12):1794-1798. · 0.42 Impact Factor
• Article: On possible scenarios of the transition to turbulence in Rayleigh-Bénard convection

  N. M. Evstigneev, N. A. Magnitskii
  Doklady Mathematics 04/2012; 82(1):659-662. · 0.29 Impact Factor
• Article: Nonlinear Dynamics of Laminar‐Turbulent Transition in Back Facing Step Problem for Bolzmann Equations in Hydrodynamic Limit

  N. M. Evstigneev, N. A. Magnitskii
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  ABSTRACT: A numerical analysis of laminar‐turbulent transition regime for the back facing step problem is considered. The initial‐boundary problem is posed for Boltzmann integral‐differential equations for very small Knudsen number limit Ű hydrodynamic limit. In order to consider nonlinear high accuracy analysis a high order numerical method is used to solve Boltzmann equations. The analysis revealed that the formation of turbulent transition in the initial‐boundary value problem is represented by the Feigenbaum Sarkovskii Magnitskii scenario. However the transition process is different from the results of Navier‐Stokes equations solution of the same initial boundary value problem.
  AIP Conference Proceedings. 09/2010; 1281(1):896-900.
• Article: On the nature of turbulence in a problem on the motion of a fluid behind a ledge

  N. M. Evstigneev, N. A. Magnitskii, S. V. Sidorov
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  ABSTRACT: In the present paper, we suggest a numerical method for the analysis of the motion of a viscous incompressible fluid under the transition to the turbulent mode for an example of the numerical solution of a three-dimensional space problem on the fluid flow behind a ledge for various values of the Reynolds number. We show that, at the initial stages, the turbulence in the problem is developed via successive bifurcations of generation of a stable cycle, two-dimensional tori, and then three-dimensional tori in the infinite-dimensional phase space of the system.
  Differential Equations 12/2008; 45(1):68-72. · 0.42 Impact Factor