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  • 1
    Electronic Resource
    Electronic Resource
    The simultaneous use of 4×4 and 2×2 bilinear stress elements for viscoelastic flows (1993)
    Springer
    Computational mechanics 11 (1993), S. 341-354 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Mixed finite elements for viscoelastic flows based on a 4×4 sub-linear interpolation for the extra stress components satisfy the Babuska-Brezzi condition and are highly stable. They have been proved to be quite satisfactory in solving problems with strong stress boundary layers. In this work, we examine the simultaneous use of 4×4 and 2×2 bilinear stress elements in an attempt to reduce the computational cost without sacrificing the accuracy. The 4×4 bilinear elements are employed in regions where the stress field is anticipated to be steep while the 2×2 elements carry the burden elsewhere with a much smaller number of stress nodes. Additional constraints along the sides shared by different elements are necessary in order to preserve conformity. The method is applied to the creeping flow of a Maxwell fluid around a sphere falling along the axis of a cylindrical tube. Results are given for three mixed finite element formulations: the Galerkin method, the consistent streamline-upwind/Petrov-Galerkin method (SUPG) and the non-consistent streamline-upwind method (SU). Particular emphasis is given on the calculated drag correction factors. The effect of the sphere/cylinder diameter ratio is also examined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00350092
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On the stability of the shear flow of a viscoelastic fluid with slip along the fixed wall (1996)
    Springer
    Rheologica acta 35 (1996), S. 39-47 
    Details
    ISSN: 1435-1528
    Keywords: Shear flow ; Oldroyd-B model ; slip ; linear stability analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract In this paper we solve the time-dependent shear flow of an Oldroyd-B fluid with slip along the fixed wall. We use a non-linear slip model relating the shear stress to the velocity at the wall and exhibiting a maximum and a minimum. We assume that the material parameters in the slip equation are such that multiple steady-state solutions do not exist. The stability of the steady-state solutions is investigated by means of a one-dimensional linear stability analysis and by numerical calculations. The instability regimes are always within or coincide with the negative-slope regime of the slip equation. As expected, the numerical results show that the instability regimes are much broader than those predicted by the linear stability analysis. Under our assumptions for the slip equation, the Newtonian solutions are stable everywhere. The interval of instability grows as one moves from the Newtonian to the upper-convected Maxwell model. Perturbing an unstable steady-state solution leads to periodic solutions. The amplitude and the period of the oscillations increase with elasticity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00366551
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Extrusion of a compressible Newtonian fluid with periodic inflow and slip at the wall (1996)
    Springer
    Rheologica acta 35 (1996), S. 531-544 
    Details
    ISSN: 1435-1528
    Keywords: Extrudate swell ; compressible Newtonian flow ; slip ; time-dependent flow
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract We explore a mechanism of extrusion instability, based on the combination of nonlinear slip and compressibility. We consider the time-dependent compressible Newtonian extrudate swell problem with slip at the wall. Steady-state solutions are unstable in regimes where the shear stress is a decreasing function of the velocity at the wall. Compressibility provides the means for the alternate storage and release of elastic energy, and, consequently, gives rise to periodic solutions. The added novelty in the present work is the assumption of periodic volumetric flow rate at the inlet of the die. This leads to more involved periodic responses and to free surface oscillations similar to those observed experimentally with the stick-slip instability. To numerically simulate the flow, we use finite elements in space and a fully-implicit scheme in time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00396505
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    A singular finite element for Stokes flow: The stick-slip problem (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1353-1367 
    Details
    ISSN: 0271-2091
    Keywords: Singular finite elements ; Stokes flow ; Stress singularity ; 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: Abrupt changes in boundary conditions in viscous flow problems give rise to stress singularities. Ordinary finite element methods account effectively for the global solution but perform poorly near the singularity. In this paper we develop singular finite elements, similar in principle to the crack tip elements used in fracture mechanics, to improve the solution accuracy in the vicinity of the singular point and to speed up the rate of convergence. These special elements surround the singular point, and the corresponding field shape functions embody the form of the singularity. Because the pressure is singular, there is no pressure node at the singular point. The method performs well when applied to the stick-slip problem and gives more accurate results than those from refined ordinary finite element meshes.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650091105
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Singular finite elements for the sudden-expansion and the die-swell problems (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 357-372 
    Details
    ISSN: 0271-2091
    Keywords: Singular finite elements ; Die swell ; Sudden expansion ; 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 singular finite element method is used to solve the sudden-expansion and the die-swell problems in order to improve the accuracy of the solution in the vicinity of the singularity and to speed up the convergence. The method requires minor modifications to standard finite element schemes, and even coarse meshes give more accurate results than refined ordinary finite element meshes. Improved normal stress results for the sudden-expansion problem have been obtained for various Reynolds numbers up to 100 using the singular elements constructed for the creeping flow problem. In addition, the normal stresses at the walls appear to be insensitive to the singularity powers used in the construction of the singular basis functions. The die-swell problem is solved using the singular elements constructed for the stick-slip problem. The singular elements accelerate the convergence of the free surface dramatically.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650100402
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    A singular function boundary integral method for the Laplace equation (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 127-134 
    Details
    ISSN: 1069-8299
    Keywords: Laplace equation ; singularities ; boundary integral method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The authors present a new singular function boundary integral method for the numerical solution of problems with singularities which is based on approximation of the solution by the leading terms of the local asymptotic expansion. The essential boundary conditions are weakly enforced by means of appropriate Lagrange multipliers. The method is applied to a benchmark Laplace-equation problem, the Motz problem, giving extremely accurate estimates for the leading singular coefficients. The method converges exponentially with the number of singular functions and requires a low computational cost. Comparisons are made to the analytical solution and other numerical methods.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
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