On the simulation of highly elastic complex flows

Baloch, A.; Townsend, Peter; Webster, M.F.

doi:10.1016/0377-0257(95)01369-7

Cited by 28 publications

(54 citation statements)

References 20 publications

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“…With further increase in 4, Baloch et al's [16] predictions show that the salient corner vortex tends to finger towards the re-entrant corner, a feature not observed in the present study (c.f. [16] for Re 1, showing that the apparent`finger pattern' is rather a flattening of the salient corner vortex as it is being pushed towards the contraction wall by inertial forces. This is accompanied by a decrease in the strength of the vortex to a maximum normalised value of the stream function of 1.00104.…”

Section: Resultscontrasting

confidence: 32%

“…This eddy becomes less concave and stronger when 4 is raised to 0.25. The streamline plots of Baloch et al [16] are for a higher value of the Reynolds number, namely Re 1, but have a shape similar to those in Fig. 5 (b).…”

Section: Resultsmentioning

confidence: 80%

“…The next step was the utilisation of more realistic constitutive equations, and fortunately, it has been found that, in spite of their higher complexity, these models are less stringent from a numerical point of view [16]. Hence UCM and Oldroyd-B models are deemed adequate for the development and the improvement of methods that may evolve at a later stage to more realistic and numerically less demanding constitutive equations.…”

Section: Introductionmentioning

confidence: 99%

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Plane contraction flows of upper convected Maxwell and Phan-Thien–Tanner fluids as predicted by a finite-volume method

Oliveira

Pinho

1999

Journal of Non-Newtonian Fluid Mechanics

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A finite-volume (FV) procedure is applied to the prediction of two-dimensional (2-D) laminar flow through a 4 : 1 planar contraction of upper convected Maxwell (UCM) and simplified Phan-Thien±Tanner (SPTT) fluids. The method incorporates general coordinates, indirect addressing for easy mapping of complex domains, and is based on the collocated mesh arrangement. Calculations with the UCM model at a Reynolds number of 0.01 were carried out with three consecutively refined meshes which enabled the estimation of the accuracy of the predictions of the main vortex characteristics through Richardson's extrapolation. Converged solutions with the first-order upwind differencing scheme for the convective terms were obtained up to at least De 8 in the finest mesh, but were limited to De 1, De 3 and De 5 for the fine, medium and coarse meshes, respectively, when using the second-order linear upwind scheme. The predicted flow patterns for increasing Deborah numbers with the UCM model resemble the well known lip vortex enhancement mechanism reported in the literature for constant-viscosity fluids in axisymmetric contractions and shear-thinning fluids in planar contraction, but very fine meshes were required in order to capture the described vortex activity. Predictions with the SPTT model also compared well with the behaviour reported in the literature. #

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Section: Resultscontrasting

confidence: 32%

Section: Resultsmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 99%

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Plane contraction flows of upper convected Maxwell and Phan-Thien–Tanner fluids as predicted by a finite-volume method

Oliveira

Pinho

1999

Journal of Non-Newtonian Fluid Mechanics

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“…Baaijens [53]) or other upwind schemes that are of sufficient accuracy such as the third order accurate upwind technique of Singh and Leal [29] or Taylor-Galerkin based methods (i.e. Baloch et al [77]). The use of streamline upwind (SU) techniques or low order interpolation in combination with the DG method yields overly diffusive algorithms that are too inaccurate for practical calculations despite their robustness.…”

Section: Discussionmentioning

confidence: 99%

“…Carew et al [75], [76] and [77] have developed a Taylor-Petrov-Galerkin algorithm that also decouples the set of equations at each fractional time step.…”

Section: Time Dependent Flowsmentioning

confidence: 99%

Mixed finite element methods for viscoelastic flow analysis: a review

Baaijens

1998

Journal of Non-Newtonian Fluid Mechanics

271

150

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The progress made during the past decade in the application of mixed finite element methods to solve viscoelastic flow problems using differential constitutive equations is reviewed. The algorithmic developments are discussed in detail. Starting with the classical mixed formulation, the elastic viscous stress splitting (EVSS) method as well as the related discrete EVSS and the so-called EVSS-G method are discussed among others. Furthermore, stabilization techniques such as the streamline upwind PetrovGalerkin (SUPG) and the discontinuous Galerkin (DG) are reviewed. The performance of the numerical schemes for both smooth and non-smooth benchmark problems is discussed. Finally, the capabilities of viscoelastic flow solvers to predict experimental observations are reviewed.

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Temporal acceleration techniques for viscoelastic flows

Matallah

Townsend

Webster

1998

Commun. Numer. Meth. Engng.

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SUMMARYThis paper presents a ®nite element study based on a technique associated with time extrapolation to accelerate the convergence rate to the steady state for viscoelastic¯ows. The approach adopted is a local extrapolation method attributed to Neville. Temporal extrapolation is embedded within a time-marching Taylor±Galerkin/pressure-correction scheme as applied to the solution of model channel¯ow, 4 : 1 plane contraction¯ow and¯ow past a circular cylinder. In particular, consideration is given to obtaining steadystate solutions for an Oldroyd-B model. When extrapolation is performed for stress and velocity or pressure, then stress and velocity overshoot, which consequently leads to divergence. In contrast, a stable numerical scheme emerges when only the stress is extrapolated. #

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On the simulation of highly elastic complex flows

Cited by 28 publications

References 20 publications

Plane contraction flows of upper convected Maxwell and Phan-Thien–Tanner fluids as predicted by a finite-volume method

Plane contraction flows of upper convected Maxwell and Phan-Thien–Tanner fluids as predicted by a finite-volume method

Mixed finite element methods for viscoelastic flow analysis: a review

Temporal acceleration techniques for viscoelastic flows

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