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)

Abstract

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.

Keywords

Reynolds Number Circular Cylinder Direct Numerical Simulation High Reynolds Number Recirculation Zone 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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