Mathematical and physical requirements for successful computations with viscoelastic fluid models

Zanden, J. van der; Hulsen, Martien A.

doi:10.1016/0377-0257(88)85052-3

Cited by 34 publications

(12 citation statements)

References 18 publications

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“…(6)) and the FENE-CR (Eq. (7)) models only along inflow boundaries, as described by Zanden and Hulsen [18]. The reason is that both equations are hyperbolic and their characteritics in a steady flow are the streamlines.…”

Section: Boundary Conditions On the Differential Equationsmentioning

confidence: 97%

“…(17), (1), (24), (16) and (18) or (19), by weighting functions ψ m , ψ c , ψ x , ψ G and ψ τ p , integrating over the unknown flow domain (bounded by ), applying the divergence theorem to the terms with divergences and mapping the integrals onto the known reference domain¯ (bounded by¯ ):…”

Section: Solution Of the Equation System By Galerkin And Petro-galerkmentioning

confidence: 99%

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Slot coating of mildly viscoelastic liquids

Romero

Scriven

Carvalho

2006

Journal of Non-Newtonian Fluid Mechanics

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Section: Boundary Conditions On the Differential Equationsmentioning

confidence: 97%

Section: Solution Of the Equation System By Galerkin And Petro-galerkmentioning

confidence: 99%

Slot coating of mildly viscoelastic liquids

Romero

Scriven

Carvalho

2006

Journal of Non-Newtonian Fluid Mechanics

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“…For the Giesekus model we first linearize the right-hand side and compute the eigenvalues of coefficient matrix of the perturbed system. The eigenvalues are derived in [11,12] and the result shows that for two-dimensional flows a single eigenvalue becomes positive when det C < 0,…”

Section: A Stability Criterion For Exponential Profilesmentioning

confidence: 99%

Flow of viscoelastic fluids past a cylinder at high Weissenberg number: Stabilized simulations using matrix logarithms

Hulsen

Fattal

Kupferman

2005

Journal of Non-Newtonian Fluid Mechanics

324

332

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The log conformation representation proposed in [1] has been implemented in a fem context using the DEVSS/DG formulation for viscoelastic fluid flow. We present a stability analysis in 1D and attribute the high Weissenberg problem to the failure of the numerical scheme to balance exponential growth. A slightly different derivation of the log based evolution equation than in [1] is also presented. We show numerical results for the flow around a cylinder for an Oldroyd-B and a Giesekus model. We provide evidence that the numerical instability identified in the 1D problem is also the actual reason for the failure of the standard fem implementation of the problem. With the log conformation representation we are able to obtain solutions far beyond the limiting Weissenberg numbers in the standard scheme. However it turns out that, although in large parts of the flow the solution converges, we have not been able to obtain convergence in localized regions of the flow. Possible reasons for this are: artefacts of the model (Oldroyd-B) or unresolved small scales (Giesekus). However, more work is necessary, including the use of more refined meshes and/or higher-order schemes, before any conclusion can be made on the local convergence problems.

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“…(7) is a tensor equation, tensor boundary conditions must be imposed. The only exception is the flow of polymer solutions whose stress is purely elastic (τ = 0), where only the normal and tangential components of the conformation dyadic must be specified at the inflow boundaries [37,38].…”

Section: Boundary Conditions On Transport Equationsmentioning

confidence: 99%