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.
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Christov, C.I., Marinova, R.S., Marinov, T.T. (2008). Identifying the Stationary Viscous Flows Around a Circular Cylinder at High Reynolds Numbers. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2007. Lecture Notes in Computer Science, vol 4818. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78827-0_18
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DOI: https://doi.org/10.1007/978-3-540-78827-0_18
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