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  • 1
    Electronic Resource
    Electronic Resource
    Steady states and oscillatory instability of swirling flow in a cylinder with rotating top and bottom (1996)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 8 (1996), S. 2614-2625 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: In this study we present a numerical investigation of steady states, onset of oscillatory instability, and slightly supercritical oscillatory states of an axisymmetric swirling flow of a Newtonian incompressible fluid in a cylinder, with independently rotating top and bottom. The first part of the study is devoted to the influence of co- and counter-rotation of the bottom on the steady vortex breakdown, which takes place in the well-known problem of flow in a cylinder with a rotating top. It is shown that weak counter-rotation of the bottom may suppress the vortex breakdown. Stronger counter-rotation may induce a stable steady vortex breakdown at relatively large Reynolds numbers for which a vortex breakdown does not appear in the case of the stationary bottom. Weak corotation may promote the vortex breakdown at lower Reynolds numbers than in the cylinder with the stationary bottom. Stronger corotation leads to the detachment of the recirculation zone from the axis and the formation of an additional vortex ring. The second part of the study is devoted to the investigation of the onset of oscillatory instability of steady flows. It is shown that the oscillatory instability sets in due to a Hopf bifurcation. The critical Reynolds number and the critical frequency of oscillations were calculated as a function of the rotation ratio (ξ=Ωbottom/Ωtop) for a fixed value of the aspect ratio γ (height/radius) of the cylinder γ=1.5. The stability analysis showed that there are several most unstable linear modes of the perturbation that become successively dominant with a continuous change of ξ. It is shown that the oscillatory instability may lead to an appearance and coexistence of more than one oscillating separation vortex bubble. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869064
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  • 2
    Electronic Resource
    Electronic Resource
    Three-dimensional instability of a two-layer Dean flow (2001)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 13 (2001), S. 3185-3195 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Stability of a two-layer Dean flow in a cylindrical annulus with respect to three-dimensional perturbations is studied by a global Galerkin method. It is shown that for large inner radius of the annulus (i) the instability becomes three-dimensional if one of the fluid layers is thin, (ii) its onset is not affected by possible small deformations of the interface, and (iii) multiple three-dimensional flow states are expected in a slightly supercritical flow regime. Stability diagrams and patterns of the three-dimensional perturbations are reported. It is concluded that even when the axisymmetric perturbation is the most dangerous, the resulting supercritical flow is expected to be three-dimensional. Possible multiplicity of supercritical three-dimensional states is predicted. The basis functions of the global Galerkin method are constructed so as to satisfy analytically the boundary conditions on no-slip walls and at the liquid–liquid interface. A modification of the numerical approach, accounting for small deformations of the interface which is subject to the action of the capillary force, is proposed. The results are of potential importance for development of novel bioseparators employing Dean vortices for enhancement of mass transfer of a passive scalar (say, a protein) through the interface. The developed numerical approach can be used for stability analysis in other two-fluid systems. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1409967
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  • 3
    Electronic Resource
    Electronic Resource
    Multiple solutions and stability of confined convective and swirling flows - a continuing challenge (2004)
    Bradford : Emerald
    International journal of numerical methods for heat & fluid flow 14 (2004), S. 213-241 
    Details
    ISSN: 0961-5539
    Source: Emerald Fulltext Archive Database 1994-2005
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Our recent results on stability and multiplicity of flow states for confined flows of an incompressible Newtonian fluid are surveyed. The considered laminar flows are caused by either thermal, mechanical, or electromagnetic effects and beyond the stability limit exhibit multiplicity of stable, steady or oscillatory, asymptotic states. Stability diagrams as well as examples of multiple flow states are given. It is concluded that beyond the critical value of the characteristic non-dimensional parameter, and below the threshold to stochastic or turbulent state, multiple stable asymptotic flow states can be expected. This means that at such flow regimes, any computational (experimental) result may be strongly dependent on its initial condition and/or computational (experimental) path. Uncertainties of experimental and numerical modeling, which follow from this conclusion, are discussed. The global spectral Galerkin method using divergence free basis functions has been employed for the spatial approximation of the velocity and temperature fields. Several numerical experiments were performed comparing the present and other formulations, each of which confirmed the computational efficiency of the present approach over other classical numerical methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1108/09615530410513818
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  • 4
    Electronic Resource
    Electronic Resource
    Space-time spectral element methods for unsteady convection-diffusion problems (1997)
    Bradford : Emerald
    International journal of numerical methods for heat & fluid flow 7 (1997), S. 215-235 
    Details
    ISSN: 0961-5539
    Source: Emerald Fulltext Archive Database 1994-2005
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Deals with the formulation and application of temporal and spatial spectral element approximations for the solution of convection-diffusion problems. Proposes a new high-order splitting space-time spectral element method which exploits space-time discontinuous Galerkin for the first hyperbolic substep and space continuous-time discontinuous Galerkin for the second parabolic substep. Analyses this method and presents its characteristics in terms of accuracy and stability. Also investigates a subcycling technique, in which several hyperbolic substeps are taken for each parabolic substep; a technique which enables fast, cost-effective time integration with little loss of accuracy. Demonstrates, by a numerical comparison with other coupled and splitting space-time spectral element methods, that the proposed method exhibits significant improvements in accuracy, stability and computational efficiency, which suggests that this method is a potential alternative to existing schemes. Describes several areas for future research.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1108/09615539710163275
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  • 5
    Electronic Resource
    Electronic Resource
    New variational-asymptotic formulations for interlaminar stress analysis in laminated plates (1986)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 37 (1986), S. 305-321 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Eine neue Methode zur dreidimensionalen Spannungsanalyse von Verbundlaminaten wird dargelegt. Die Methode der gewünschten Entwicklungen zusammen mit dem Hellinger-Reissner'schen Variationsprinzip führt zur Herleitung des inneren Problems und des Grenzschichtproblems für höhere Näherungen. Eine neue Methode wird entwickelt, welche mit Hilfe von finiten Elementen, vom gemischt hybriden Verfahren ausgehend, das Grenzschichtproblem löst. Der Vergleich, der hier vorgeschlagenen Lösung mit einer klassischen, auf Verschiebungselementen beruhenden Lösung zeigt die Genauigkeits- und Effizienzvorteile der hier dargelegten neuen Methode.
    Notes: Abstract A new approach for the three-dimensional stress analyses in composite laminates is presented. The method of composite expansions along with Hellinger-Reissner variational formulation is employed to derive the interior and edge layer problems for high order approximations. A new method of finite element analysis for solving the edge layer problem is developed based on the modified mixed-hybrid method. Comparison of the present solution with an assumed displacement finite element solution is made to demonstrate the accuracy and efficiency of the present approach.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00946753
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  • 6
    Electronic Resource
    Electronic Resource
    New variational-asymptotic formulations for 3-D stress analyses of laminated composite shells with a circular hole (1988)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 39 (1988), S. 682-698 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A new approach for three-dimensional stress analyses in composite cylindrical shells is presented. The method of composite expansions along with Hellinger-Reissner variational formulation is employed to derive the interior and edge layer problems for high order approximations. Classical assumptions have been justified and new approximations have been established. These formulations are directed especially towards, new high integrity mixed-hybrid finite element schemes. The expository examples chosen are of cross-ply and angle-ply laminated shells. The circumferential location of the delamination failure initiation, for angle-ply laminates containing a circular hole, is within a sector located symmetrically around the perpendicular direction to the applied load.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00948730
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  • 7
    Electronic Resource
    Electronic Resource
    Nonlinear Modeling and Control of a Unicycle (1999)
    Springer
    Dynamics and control 9 (1999), S. 279-296 
    Details
    ISSN: 1573-8450
    Keywords: nonlinear dynamics ; unicycle ; time finite element
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A unicycle system is composed of a unicycle and a rider. This system is inherently unstable, but together with a skilled rider can be autonomously controlled and stabilized. A dynamical investigation, a control design and a numerical solution of a nonlinear unicycle autonomous model are presented. The use of a nonlinear model for the control design is shown in this paper to be of great importance. A three-rigid-body physical model was selected for the dynamical study of the system. In a linearized model important physical characteristics of the unicycle system disappear (e.g. interactions between the longitudinal and lateral systems are being neglected), and therefore it is not recommended to be used for the control design. A nonlinear control law, which replaces the rider in stabilizing the model, was derived in the present work, using a nonlinear unicycle model. A simulation study shows good performance of this controller. Time spectral element methods are developed and used for integrating the nonlinear equations of motion. The approach employs the time discontinuous Galerkin method which leads to A-stable high order accurate time integration schemes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1026481216262
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  • 8
    Electronic Resource
    Electronic Resource
    On the nature of the free edge stress singularity in composite laminated plates (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1507-1523 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The variational-asymptotic formulation for the edge layer problem is implemented by mixed-hybrid finite elements. This approach is used to analyse the stress singularity at the free edge in composite laminates. Results indicate that the stress singularity (as r → 0) is very closely approximated by log r instead of r-α.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260704
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  • 9
    Electronic Resource
    Electronic Resource
    On the generalized L2 Galerkin finite element method for linear hyperbolic equations (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 679-694 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this work, a Von Neumann analysis of the generalized L2 Galerkin method is described. The analysis is carried out on a linear scalar hyperbolic equation. The analysis shows both qualitatively and quantitatively the stability, dissipation and dispersion of the standard space-time discontinuous Galerkin finite element method, and of the space-time discontinuous streamline upwind Petrov Galerkin (SUPG) method. In addition a new special non-dissipative non-dispersive scheme is presented.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620360408
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  • 10
    Electronic Resource
    Electronic Resource
    Plate spectral elements based upon Reissner-Mindlin theory (1995)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 1341-1360 
    Details
    ISSN: 0029-5981
    Keywords: spectral elements ; plate finite elements ; Reissner-Mindlin plate theory ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Plate bending spectral elements based upon the Reissner-Mindlin theory is developed for a rectangular plate. Numerical comparison studies for static and eigenvalue problems, demonstrate the excellent performance and robustness of the present method. The improvement in accuracy and computational efficiency in comparison with low order plate bending elements is remarkable and suggests that the proposed approach is an alternative to existing schemes.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620380807
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