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  • 1
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 217-233 
    ISSN: 0271-2091
    Keywords: Spectral methods ; Journal bearing problem ; Stokes flow ; 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: A three-dimensional spectral algorithm for the solution of Stokes flow between eccentrically rotating cylinders is described. Included in the model are pressure boundary conditions at the two ends of the finite length cylinders and the effect of a fluid line source on the inner cylinder. A comparison of results for the load and couple on the inner cylinder is made with those available from lubrication theory in the absence of a line source. Good agreement is shown for long, short and finite journal bearings when the various geometrical assumptions inherent in the lubrication analysis are satisfied.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 647-662 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The essential character of the primary elliptic-hyperbolic operator encountered in the modelling of viscoelastic flows is encaptured in a non-linear fifth-order two-point boundary value problem in one dimension. Expansions in terms of beam functions and Chebyshev polynomials are used to compute solutions to the primary two-point boundary value problem within a spectral Galerkin formulation. An investigation of the performance of the methods with respect to the level of non-linearity is carried out. Accurate results are obtained with Chebyshev polynomials for high levels of non-linearity, whereas the behaviour of beam function expansions proves far more sensitive to the level of non-linearity.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 805-813 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Expansions in terms of beam functions and Chebyshev polynomials are used to compute solutions to the primary two-point boundary value problem within a spectral collocation formulation. The performance of the methods is analysed in terms of accuracy and robustness relative to the level of non-linearity. Accurate results are obtained with Chebyshev polynomials and the performance of these trial functions is insensitive to the level of non-linearity whereas the behaviour of the beam functions shows great sensitivity to the level of non-linearity. The use of Newton's method to solve the mixed linear-non-linear system for the Chebyshev coefficients is successful for highly non-linear problems without the need for parameter continuation.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 1517-1534 
    ISSN: 0029-5981
    Keywords: spectral elements ; viscoelasticity ; time-splitting method ; drag factor ; Uzawa algorithm ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The steady flow of a viscoelastic fluid past a sphere in a cylindrical tube is considered. A spectral element method is used to solve the system of coupled non-linear partial differential equations governing the flow. The spectral element method combines the flexibility of the traditional finite element method with the accuracy of spectral methods. A time-splitting algorithm is used to determine the solution to the steady problem. Results are presented for the Oldroyd B model. These show excellent agreement with the literature. The results converge with mesh refinement. A limiting Deborah number of approximately 0⋅6 is found, irrespective of the spatial resolution.
    Additional Material: 25 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 43 (1998), S. 1401-1419 
    ISSN: 0029-5981
    Keywords: Stokes problem ; discontinuous approximations ; compatible approximation spaces ; mixed formulation ; spectral element methods ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The discretization of the mixed velocity-pressure-stress formulation of the Stokes problem using the spectral element method is considered. The compatibility conditions between the discrete velocity and extra stress spaces are examined. A sufficient condition for compatibility, namely that the discrete extra stress space contains the gradient of the discrete velocity space, is satisfied provided one allows discontinuous approximations of the extra stress between elements. Numerical results are presented for smooth and non-smooth problems showing the consequences of satisfying or violating this condition. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 9 (1993), S. 691-710 
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new pseudospectral method for simulating transient viscoelastic flows is presented. The governing equations are a system of seven first-order equations of mixed type. The essential features of the method are (i) all seven independent flow variables are represented on a common Chebyshev-Gauss-Lobatto grid; (ii) the pressure is treated in such a way as to give a globally divergence-free velocity field, i.e., the divergence of the velocity field vanishes globally within the region, and (iii) different time scales pertaining within the hyperbolic constitutive equations are treated using the splitting technique of LeVeque and Yee originally proposed in a finite-difference context. The method is applied to transient axisymmetric flow of an Oldroyd B fluid in a channel formulated in two ways: (I) as an initial boundary-value problem, and (II) as a body-force problem. © 1993 John Wiley & Sons, Inc.
    Additional Material: 3 Ill.
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  • 7
    Publication Date: 2013-02-01
    Print ISSN: 1070-6631
    Electronic ISSN: 1089-7666
    Topics: Physics
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  • 8
    Publication Date: 2011-11-24
    Description: The lattice Boltzmann method has been established as an efficient technique for solving a wide range of complex problems in fluid dynamics including multiphase flows. In this paper, the extension of the technique to the simulation of non-Newtonian fluids is described. Two classes of non-Newtonian fluids are considered: inelastic fluids characterized by a variable viscosity and viscoelastic fluids characterized by fluid elasticity. A comprehensive review is given of developments in this area and sample numerical results are presented in the case of inelastic fluids.
    Print ISSN: 0272-4960
    Electronic ISSN: 1464-3634
    Topics: Mathematics
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  • 9
    Publication Date: 2012-09-21
    Description: Multi-bubble dynamics is investigated in the presence of a rigid boundary. A simplified configuration is considered in which two bubbles, not necessarily of the same size, are positioned along an axis of symmetry. The problem is formulated in terms of a generalized Bernoulli equation for a velocity potential. A boundary element method is adopted to determine the normal velocity at the bubble surface. Viscoelastic effects are incorporated into the model through the normal stress balance across the bubble surface. The model predicts that bubble dynamics, and jet formation, in particular, is strongly influenced by the initial bubble sizes, the initial stand-off distances and on the fluid parameters. Viscoelastic effects are shown to be responsible for some interesting dynamics. Although inter-bubble interaction is shown to play an important role, it is not always dominant for viscoelastic fluids.
    Print ISSN: 0272-4960
    Electronic ISSN: 1464-3634
    Topics: Mathematics
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  • 10
    Publication Date: 2011-03-01
    Print ISSN: 0935-4964
    Electronic ISSN: 1432-2250
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Springer
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