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  • Engineering  (4)
  • Hopf bifurcation  (1)
  • finite element method  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Rheologica acta 29 (1990), S. 342-351 
    ISSN: 1435-1528
    Keywords: Oldroyd-B fluids ; die flows ; stick-slip problem ; finite element method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract Two decoupled methods for the finite element solution of the planar stick-slip transition problem with Oldroyd-B fluids, namely the method of characteristics and the Lesaint-Raviart technique, are presented and compared. These procedures are used for the local treatment of the stress transport equation imbedded in the constitutive law and allow the approximation of stresses with discontinuous shape functions. Computations are carried out up to a Deborah number of 4 and the methods are shown to yield fairly similar results.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 911-928 
    ISSN: 0271-2091
    Keywords: Incompressible ; Finite Elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We present a numerical procedure to eliminate internal nodes from elements designed to approximate incompressible flow problems. We compare six elements in academic and industrial like flow problem and we discuss their relative qualities. A surprising conclusion is that richer elements may behave less well than simple ones if a good enforcement of incompressibility is not maintained.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 1185-1210 
    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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  • 4
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 20 (1995), S. 31-57 
    ISSN: 0271-2091
    Keywords: Coextrusion ; Film casting ; Finite element ; Pseudoconcentration ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In the first part of this paper a numerical strategy is developed for the numerical simulation of the coextrusion process. Coextrusion consists of extruding many polymers in the same die in order to combine their respective properties. The die is generally flat and quite large and consequently a two-dimensional approximation is sufficient. The main difficulty is to accurately predict the interfaces between the different layers of polymers. A finite element method based on a pseudoconcentration function is developed to calculate these fluid interfaces. Numerical results are presented for the coextrusion of up to five fluids.In the second part of the paper the above strategy is slightly modified to simulate the film-casting process. In this case a polymer is stretched (with a draw velocity UL) at the exit of the die in order to produce a very thin layer of polymer that is cooled in contact with a chill roll. Only one polymer-air interface has to be computed. The draw ratio is defined as Dr = UL/U, where U is the mean velocity of the polymer at the exit of the die. As the draw ratio is increased, instabilities appear and numerical results put in evidence the draw resonance phenomenon.
    Additional Material: 36 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 1 (1985), S. 205-208 
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Usawa's algorithm provides an efficient method for solving the divergence-free Stokes problem. On the other hand, the Newton-Raphson scheme is very popular for the solution of the nonlinear Navier-Stokes equations. We propose here a new method that combines these two algorithms and converges to a divergence-free solution of the nonlinear Navier-Stokes equations.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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