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. © 2008 Springer.
CITATION STYLE
Christov, C. I., Marinova, R. S., & Marinov, T. T. (2008). Identifying the stationary viscous flows around a circular cylinder at high Reynolds numbers. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4818 LNCS, pp. 175–183). https://doi.org/10.1007/978-3-540-78827-0_18
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