Identifying the Stationary Viscous Flows Around a Circular Cylinder at High Reynolds Numbers

  • Christo I. Christov
  • Rossitza S. Marinova
  • Tchavdar T. Marinov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4818)


We propose an approach to identifying the solutions of the steady incompressible Navier-Stokes equations for high Reynolds numbers. These cannot be obtained as initial-value problems for the unsteady system because of the loss of stability of the latter. Our approach consists in replacing the original steady-state problem for the Navier-Stokes equations by a boundary value problem for the Euler-Lagrange equations for minimization of the quadratic functional of the original equations. This technique is called Method of Variational Imbedding (MVI) and in this case it leads to a system of higher-order partial differential equations, which is solved by means of an operator-splitting method. As a featuring example we consider the classical flow around a circular cylinder which is known to lose stability as early as for Re= 40. We find a stationary solution with recirculation zone for Reynolds numbers as large as Re= 200. Thus, new information about the possible hybrid flow regimes is obtained.


Reynolds Number Circular Cylinder Direct Numerical Simulation High Reynolds Number Recirculation Zone 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Christo I. Christov
    • 1
  • Rossitza S. Marinova
    • 2
  • Tchavdar T. Marinov
    • 1
  1. 1.Dept. of Math.University of Louisiana at LafayetteUSA
  2. 2.Dept. of Math. & Computing Sci.Concordia Univ. College of AlbertaEdmontonCanada

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