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  • Articles: DFG German National Licenses  (9)
  • Engineering General  (9)
  • 1
    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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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Adaptive solutions for viscoelastic flows (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 643-655 
    Details
    ISSN: 1069-8299
    Keywords: viscoelastic flows ; sphere ; annular flow ; adaptive meshing ; finite elements ; error analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This work describes the implementation of an adaptive procedure for viscoelastic flows. Finite element simulations are conducted using a Taylor-Galerkin/pressure correction scheme. The constitutive equations considered are those for an Oldroyd-B and a Phan-Thien/Tanner model. The adaptive meshing technique is h-refined by grid remeshing, based on a Delaunay procedure. Results are presented for two benchmark problems, namely flow past a sphere in a cylindrical tube and flow in an annular converging tube. It is concluded from the results that the use of an adaptive procedure with mesh regeneration enables an optimized mesh to be devised and a predicted accuracy to be attained.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 3
    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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  • 4
    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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    Paper (German National Licenses)
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  • 5
    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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    Paper (German National Licenses)
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  • 6
    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)
  • 7
    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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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    The use of dynamic data structures in finite element applications (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 1795-1811 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The derivation of more efficient algorithms for finite element applications is not the primary goal of this article, but rather the efficient implementation of existing algorithms using dynamic data structures. In some cases the algorithms may be far from optimal, but serve to illustrate the advantages of dynamic data structures. In the first section, a tree data structure termed a PATRICIA tree is described and is shown to be suitable for storing data associated with finite element meshes. The manner in which the tree is constructed guarantees to provide rapid data retrieval times, competitive with those associated with static array data structures, whilst providing the added advantages of a dynamic data structure. The second section introduces a list of lists (LOL) data structure which is used to produce an efficient implementation of an example of a bandwidth reduction algorithm. Furthermore, the LOL data structure is also shown to be appropriate for implementing a novel method for extracting the domain boundary, with its orientation, from a given finite element connectivity matrix.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620330903
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    Paper (German National Licenses)
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  • 9
    Electronic Resource
    Electronic Resource
    A comparison of gradient recovery methods in finite-element calculations (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 7 (1991), S. 195-204 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we consider methods of gradient recovery in the context of primitive-variable finite-element solutions of viscous flow problems. Two methods are considered: a global method based on a Galerkin weighted residual procedure, and a direct method where gradients are recovered directly at individual nodes. The direct method has the benefit of utilizing the property of superconvergence as a natural consequence of its formulation, and furthermore requires no smoothing matrix to obtain the gradients at the nodal points. The two recovery schemes are considered with respect to two benchmark viscous flow problems of differing complexity. Both schemes are shown to produce comparable results, although the direct recovery method is found to be significantly more cost-effective than the global method.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630070304
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