A comparison of four implementations of the log-conformation formulation for viscoelastic fluid flows

Kane, Arti; Guénette, R.; Fortin, A.

doi:10.1016/j.jnnfm.2009.08.003

Cited by 15 publications

(25 citation statements)

References 11 publications

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“…The main advantage of this transformation is on its numerical solution since it provides the possibility of using the logconformation technique, introduced by Fattal and Kupferman [22], which has been shown to lead to a significant increase of numerical stability [23][24][25][26][27]. In this technique a simple tensor-logarithmic transformation is performed on the conformation tensor for differential viscoelastic constitutive equations.…”

Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

Purely elastic instabilities in three-dimensional cross-slot geometries

Afonso

Alves

Pinho

2010

Journal of Non-Newtonian Fluid Mechanics

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Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

Purely elastic instabilities in three-dimensional cross-slot geometries

Afonso

Alves

Pinho

2010

Journal of Non-Newtonian Fluid Mechanics

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“…This technique, originally proposed by Fattal & Kupferman (2004) in the context of computational rheology, introduces a better polynomial interpolation of the stresses when these exhibit an exponential growth, such as near stagnation points, and has been tested in the recent past in a number of viscoelastic flow problems and shown to enable computations at higher Deborah numbers than usual. An additional benefit of the log-conformation formulation is that it preserves positive-definiteness of the conformation tensor (Kwon 2004(Kwon , 2006Hulsen, Fattal & Kupferman 2005;Yoon & Kwon 2005;Coronado et al 2007;Pan & Hao 2007;Afonso et al 2009;Kane, Guénette & Fortin 2009), thus avoiding a kind of Hadamard instability plaguing the numerical simulation once the flow becomes inherently unstable, which invariably leads to quick divergence of iterative numerical procedures.…”

mentioning

confidence: 99%

Dynamics of high-Deborah-number entry flows: a numerical study

et al. 2011

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High-elasticity simulations of flows through a two-dimensional (2D) 4 : 1 abrupt contraction and a 4 : 1 three-dimensional square-square abrupt contraction were performed with a finite-volume method implementing the log-conformation formulation, proposed by Fattal & Kupferman (J. Non-Newtonian Fluid Mech., vol. 123, 2004, p. 281) to alleviate the high-Weissenberg-number problem. For the 2D simulations of Boger fluids, modelled by the Oldroyd-B constitutive equation, local flow unsteadiness appears at a relatively low Deborah number (De) of 2.5. Predictions at higher De were possible only with the log-conformation technique and showed that the periodic unsteadiness grows with De leading to an asymmetric flow with alternate back-shedding of vorticity from pulsating upstream recirculating eddies. This is accompanied by a frequency doubling mechanism deteriorating to a chaotic regime at high De. The log-conformation technique provides solutions of accuracy similar to the thoroughly tested standard finite-volume method under steady flow conditions and the onset of a time-dependent solution occurred approximately at the same Deborah number for both formulations. Nevertheless, for Deborah numbers higher than the critical Deborah number, and for which the standard iterative technique diverges, the log-conformation technique continues to provide stable solutions up to quite (impressively) high Deborah numbers, demonstrating its advantages relative to the standard methodology. For the 3D contraction, calculations were restricted to steady flows of Oldroyd-B and Phan-Thien-Tanner (PTT) fluids and very high De were attained (De ≈ 20 for PTT with ε = 0.02 and De ≈ 10 000 for PTT with ε = 0.25), with prediction of strong vortex enhancement. For the Boger fluid calculations, there was inversion of the secondary flow at high De, as observed experimentally by Sousa et al.

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“…The parallel algorithm described in Section 2 is used to compute the two-dimensional viscoelastic flow past a confined circular cylinder in a channel [1,2,11,17,19,26,30,33,39,58]. For this flow problem, we consider a circular cylinder of radius R positioned symmetrically between two parallel plates separated by a distance 2H.…”

Section: Oldroyd-b Fluid Past a Confined Circular Cylindermentioning

confidence: 99%

“…Coronado et al [17] presented a simple alternate form of the log-conformation formulation in which the conformation tensor is replaced by the matrix exponential. Kane et al [30] compared four different implementation of the log-conformation formulation on the flow around a circular cylinder. The authors pointed out that the original log-conformation [22] is an excellent choice despite its complex implementation.…”

Section: Introductionmentioning

confidence: 99%

“…Then the method is applied to classical benchmark problem of the flow of a viscoelastic fluid past a confined circular cylinder in a channel. The viscoelastic fluid past a confined circular cylinder was investigated by many researchers [1,2,11,17,19,26,30,33,39,58]. It is known that the problem is very difficult due to the very thin extra stress boundary layer on the cylinder surface and in the wake behind the cylinder.…”

Section: Introductionmentioning

confidence: 99%

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