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  • 1
    Electronic Resource
    Electronic Resource
    Complex transition to chaotic flow in a periodic array of cylinders (1991)
    Springer
    Theoretical and computational fluid dynamics 3 (1991), S. 79-93 
    Details
    ISSN: 1432-2250
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract This paper presents a numerical study of the transition to chaos of the flow of a Newtonian fluid in a periodic array of cylinders between two parallel walls. Using tools from dynamical system theory, we identify and characterize the different solutions to the Navier-Stokes equations at different values of the Reynolds number. We show that a very complex transition to chaos occurs for this problem where we first observe two incommensurate frequencies and then a frequency locking followed by a few period doublings following Feigenbaum's route to turbulence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00271618
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  • 2
    Electronic Resource
    Electronic Resource
    Localization of Hopf bifurcations in fluid flow problems (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 1185-1210 
    Details
    ISSN: 0271-2091
    Keywords: Hopf bifurcation ; hydrodynamic stability ; Navier-Stokes equations ; eigenproblem ; direct simulation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper is concerned with the precise localization of Hopf bifurcations in various fluid flow problems. This is when a stationary solution loses stability and often becomes periodic in time. The difficulty is to determine the critical Reynolds number where a pair of eigenvalues of the Jacobian matrix crosses the imaginary axis. This requires the computation of the eigenvalues (or at least some of them) of a large matrix resulting from the discretization of the incompressible Navier-Stokes equations. We thus present a method allowing the computation of the smallest eigenvalues, from which we can extract the one with the smallest real part. From the imaginary part of the critical eigenvalue we can deduce the fundamental frequency of the time-periodic solution. These computations are then confirmed by direct simulation of the time-dependent Navier-Stokes equations. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 27 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 3
    Electronic Resource
    Electronic Resource
    SOME EXPERIMENTS WITH STABILITY ANALYSIS OF DISCRETE INCOMPRESSIBLE FLOWS IN THE LID-DRIVEN CAVITY (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 477-492 
    Details
    ISSN: 0271-2091
    Keywords: finite element ; continuation ; Hopf bifurcation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We present results of a stability analysis of the lid-driven cavity flow based on classical C0 finite element discretizations of the Navier-Stokes system. Using arc length continuation and subspace iteration to compute the eigenvalues of the tangent operator, we study the dependence of the bifurcation diagram and of the spectrum on the chosen discretization. © 1997 by John Wiley & Sons, Ltd.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.500
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    Paper (German National Licenses)
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