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  • 1
    Electronic Resource
    Electronic Resource
    The hole-pressure problem (1984)
    Springer
    Rheologica acta 23 (1984), S. 582-590 
    Details
    ISSN: 1435-1528
    Keywords: Hole-pressure ; first normal-stress difference ; viscoelasticity ; creeping flow ; finite difference method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract There is a need to unify present hypotheses of the nature and role of the hole-pressure,p e , and thus provide consolidation on which to base future research and understanding. This paper is intended to meet this need. Attention is directed towards the calculation ofp e from the velocity and stress fields for viscoelastic fluids flowingacross rectangular holes. The constitutive models used are the Newtonian, Second-order and Maxwell models, for values of Reynolds number up to 10 and Weissenberg number up to 0.1. The numerical complications involved are studied through an investigation of the constituent parts ofp e . Verification of present theory is then sought, from which justification may be derived for the estimation of elasticity fromp e measurements. Attention is directed towards the predictions of Higashitani and Pritchard and the extension to the Tanner and Pipkin theory for ‘Second-order’ fluids. The effects of variation of geometric dimensions and flow type uponp e are also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01438798
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  • 2
    Electronic Resource
    Electronic Resource
    Computation of viscoelastic cable coating flows (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 697-712 
    Details
    ISSN: 0271-2091
    Keywords: viscoelastic ; boundary conditions ; tube tooling ; cable-coating ; finite elements ; 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: A viscoelastic analysis is presented for model tube tooling, draw-down and combined geometry flows encountered in the cable coating industries. The work investigates the development of stress fields and studies the effect of varying entry flow stress boundary conditions. The analysis takes into account tube tooling and draw-down flow sections individually, and in combination. The flow behaviour of cable-coating grade low density polyethylene is studied assuming a viscoelastic, isothermal flow, and employing a Taylor-Petrov-Galerkin finite element scheme with an exponential Phan-Thien-Tanner constitutive model. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    A Taylor-Galerkin-based algorithm for viscous incompressible flow (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 327-351 
    Details
    ISSN: 0271-2091
    Keywords: Finite elements ; Taylor-Galerkin algorithm ; Fractional step method ; Cavity 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: In this paper the development and behaviour of a new finite element algorithm for viscous incompressible flow is presented. The stability and background theory are discussed and the numerical performance is considered for some benchmark problems. The Taylor-Galerkin approach naturally leads to a time-stepping algorithm which is shown to perform well for a wide range of Reynolds numbers (1 ≤ Re ≤ 400).A conventional definition for Re is assumed. Various modifications to the algorithm are investigated, particularly with respect to their effects on stability and accuracy.
    Additional Material: 23 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650100307
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  • 4
    Electronic Resource
    Electronic Resource
    THE SIMULATION OF SOME MODEL VISCOELASTIC EXTENSIONAL FLOWS (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 23 (1996), S. 691-710 
    Details
    ISSN: 0271-2091
    Keywords: viscoelastic ; extensional flow ; wirecoating ; Taylor-Galerkin ; finite elements ; pressure-correction ; 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: The numerical simulation of three model viscoelastic extensional flows is considered: sink flow, model draw-down and conical section draw-down. A transient finite element scheme with a pressure correction method is employed to analyse the numerical treatment of such problems for Oldroyd- Band Phan-Thien/Tanner constitutive models. Both decoupled and coupled formulations are compared for these highly convective flows and effective mechanisms are proposed for removing numerical oscillations in the temporally developing solution. In pure viscoelastic extensional flow from an initial stress-free state, the maximum stress level attained decreases with increase in material relaxation time. When this is followed by stress relaxation, as in conical section draw-down, increasing the relaxation time inhibits stress decay.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 5
    Electronic Resource
    Electronic Resource
    Simulation of particle settling in rotating and non-rotating flows of non-Newtonian fluids (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 851-874 
    Details
    ISSN: 0271-2091
    Keywords: finite elements ; Taylor-Galerkin/pressure correction ; particle settling ; drag ; rotating and non-rotating flows ; inelastic non-Newtonian fluids ; 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: Finite element solutions are presented for the flow of Newtonian and non-Newtonian fluids around a sphere falling along the centreline of a cylindrical tube. Both rotating and stationary tube scenarios are considered. Calculations are reported for three different inelastic constitutive models that manifest shear-thinning, extension-thickening and their combination. The influence of inertia and these various forms of viscous response are examined for their influence upon the drag on the settling particle and the structure of the flow. Simulations are performed by employing a semi-implicit time marching Taylor-Galerkin/pressure-correction finite element algorithm, a fractional-staged scheme of second-order-accuracy. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 6
    Electronic Resource
    Electronic Resource
    A numerical case study of a non-Newtonian flow problem (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 695-704 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper addresses some of the theoretical aspects involved in the numerical study of non-Newtonian flow problems. We consider the second-order Rivlin-Erickson constitutive model due to the simple differential form that emerges for the system of equations that govern the flow when expressed in stream function-vorticity variables. This model describes slightly elastic fluids that exhibit a constant viscosity behaviour. A steady two-dimensional flow is studied through a planar contraction geometry.An auxiliary variable is introduced into the problem formulation producing a non-linear system of differential equations comprising two elliptic equations and one hyperbolic equation. This system is discretized by finite difference methods and the resulting system of non-linear algebraic equations is solved iteratively by successive substitutions. The simple structure of this iteration permits a convergence analysis which is presented in Section 2. This analysis is performed prior to the spatial discretization and establishes the dependence of the iteration upon the material parameters. At the discrete linearized equation level a combination of inner iterations for elliptic equations and direct marching for the hyperbolic equation is used. The stability of the marching scheme is considered in Section 4.3 and a discussion on the results is given in Section 5.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260312
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  • 7
    Electronic Resource
    Electronic Resource
    The iterative solution of Taylor - Galerkin augmented mass matrix equations (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 241-253 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper investigates the convergence properties of iterative schemes for the solution of finite element mass matrix equations that arise through the application of a Taylor-Galerkin algorithm to solve instationary Navier-Stokes equations. This is a time-stepping algorithm that involves Galerkin mass matrix equations at fractional stages within each time-step. Plane Poiseuille flow and shear-driven cavity flow are selected as benchmark problems on which to investigate the effects of various choice of scheme and time-step dependency. The iterative convergence of each mass matrix equation for a single fractional stage is studied, both at the element and the system matrix level. The underlying theory is confirmed and it is shown how optimal iterative convergence rates may be achieved for a Jacobi scheme by employing an appropriate acceleration factor. Moreover, this factor is trivial to compute. The consequential effects on the convergence of the time-stepping procedure to reach steady-state are also considered where non-linear effects are present.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620350203
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  • 8
    Electronic Resource
    Electronic Resource
    A Taylor - Galerkin finite element method for non-Newtonian flows (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 34 (1992), S. 741-757 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Some recent results are reviewed that indicate the appropriate nature of Taylor-Galerkin based algorithms for solving model convection-diffusion problems accurately in time and for simulating more complex non-Newtonian flows, such as those arising in the polymer industry. Initially attention is given therefore to linear and non-linear convection-diffusion model problems in two space dimensions, and then to transient problems involving heating effects. Newtonian and generalized Newtonian models are considered for both power-law and Carreau models for various parameters. Effects of shear-rate changes and temperature variations through transient build up periods are discussed in relation to their influence on the viscosity and viscous heating for thermal Péclet numbers of 1 and 100.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620340304
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    Paper (German National Licenses)
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  • 9
    Electronic Resource
    Electronic Resource
    Flow past a cylinder with and without an appurtenance (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 3991-4008 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper constitutes a numerical study of flow around a cylinder for cases with and without an appurtenance, and throughout a range of Reynolds numbers. This is achieved by solving the two-dimensional evolutionary Navier-Stokes equations using a pressure-velocity finite element method. The particular form of scheme employed is a combination of Taylor-Galerkin and pressure-correction methods. This scheme delivers second-order accuracy in time and introduces three fractional stages within each time-step. One of the practical applications of this work is the prediction of flows around gas and oil platforms at sea, and of concern to off-shore engineers are the effects of adding a sacrificial anode to the cylindrical legs of a platform. Such an appurtenance added to the basic cylindrical shape induces different drag forces on the legs depending on the angle of attack of the motion of the sea relative to the appurtenance location. Unidirectional and oscillatory flow solutions are reported, concentrating on flow patterns and forces experienced on the body surface, and the vortex shedding process.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620362305
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  • 10
    Electronic Resource
    Electronic Resource
    Coarse grain parallel finite element simulations for incompressible flows (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 41 (1998), S. 1321-1337 
    Details
    ISSN: 0029-5981
    Keywords: distributed parallelization ; finite elements ; coarse-grain parallelism ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Parallel simulation of incompressible fluid flows is considered on networks of homogeneous workstations. Coarse-grain parallelization of a Taylor-Galerkin/pressure-correction finite element algorithm are discussed, taking into account network communication costs. The main issues include the parallelization of system assembly, and iterative and direct solvers, that are of common interest to finite element and general numerical computation. The parallelization strategies are implemented on a Sun workstation cluster using the Parallel Virtual Machine (PVM) message passing library. Test results are obtained with a maximum of nineteen workstations and various PVM configurations are exhibited. Parallel efficiency close to ideal has been achieved for some strategies adopted. It is suggested that load balancing may not always be beneficial on distributed platforms with broadcasting communication connection. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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