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
Differential Equations 04/2012; 46(12):1794-1798. · 0.42 Impact Factor
Doklady Mathematics 04/2012; 82(1):659-662. · 0.29 Impact Factor
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.
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