Discrete approximation to the global spectrum of the tangent operator for flow past a circular cylinder

Tipo
Artigo
Data de publicação
2008
Periódico
Applied Numerical Mathematics
Citações (Scopus)
2
Autores
Lopez J.I.H.
Meneghini J.R.
Saltara F.
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Resumo
This paper deals with the calculation of the discrete approximation to the full spectrum for the tangent operator for the stability problem of the symmetric flow past a circular cylinder. It is also concerned with the localization of the Hopf bifurcation in laminar flow past a cylinder, when the stationary solution loses stability and often becomes periodic in time. The main problem is to determine the critical Reynolds number for which a pair of eigenvalues crosses the imaginary axis. We thus present a divergence-free method, based on a decoupling of the vector of velocities in the saddle-point system from the vector of pressures, allowing the computation of eigenvalues, from which we can deduce the fundamental frequency of the time-periodic solution. The calculation showed that stability is lost through a symmetry-breaking Hopf bifurcation and that the critical Reynolds number is in agreement with the value presented in reported computations. © 2007 IMACS.
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Assuntos Scopus
Global spectrum , Symmetric flow
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