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  • 1
    Digitale Medien
    Digitale Medien
    Spectral Galerkin methods for the primary two-point boundary value problem in modelling viscoelastic flows (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 647-662 
    Details
    ISSN: 0029-5981
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: 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.
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nme.1620260309
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  • 2
    Digitale Medien
    Digitale Medien
    Spectral collocation methods for the primary two-point boundary value problem in modelling viscoelastic flows (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 805-813 
    Details
    ISSN: 0029-5981
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: 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.
    Zusätzliches Material: 4 Tab.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nme.1620260404
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  • 3
    Digitale Medien
    Digitale Medien
    Discontinuous spectral element approximations for the velocity-pressure-stress formulation of the Stokes problem (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 43 (1998), S. 1401-1419 
    Details
    ISSN: 0029-5981
    Schlagwort(e): Stokes problem ; discontinuous approximations ; compatible approximation spaces ; mixed formulation ; spectral element methods ; Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: 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.
    Zusätzliches Material: 10 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 4
    Digitale Medien
    Digitale Medien
    STEADY VISCOELASTIC FLOW PAST A SPHERE USING SPECTRAL ELEMENTS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 1517-1534 
    Details
    ISSN: 0029-5981
    Schlagwort(e): spectral elements ; viscoelasticity ; time-splitting method ; drag factor ; Uzawa algorithm ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: 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.
    Zusätzliches Material: 25 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 5
    Digitale Medien
    Digitale Medien
    Pseudospectral method for transient viscoelastic flow in an axisymmetric channel (1993)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 9 (1993), S. 691-710 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics ; Numerical Methods
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: 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.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/num.1690090606
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  • 6
    Digitale Medien
    Digitale Medien
    Three-dimensional spectral approximations to Stokes flow between eccentrically rotating cylinders (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 217-233 
    Details
    ISSN: 0271-2091
    Schlagwort(e): Spectral methods ; Journal bearing problem ; Stokes flow ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Maschinenbau
    Notizen: 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.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/fld.1650130206
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