The Finite Volume Method in Computational Rheology

Afonso, A.M.; Oliveira, Mónica; Oliveira, Paulo J.; Alves, M.A.; Pinho, F.T.

doi:10.5772/38644

Cited by 9 publications

(11 citation statements)

References 61 publications

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“…[24,25]) and viscoelastic (e.g. [26][27][28][29]) flows individually, but not to EVP flows, to the best of our knowledge (a hybrid FE/FV method was used in [30]). In this paper a FVM for the simulation of EVP flows is described.…”

Section: Introductionmentioning

confidence: 99%

A finite volume method for the simulation of elastoviscoplastic flows and its application to the lid-driven cavity case

Syrakos

Dimakopoulos

Tsamopoulos

2020

Journal of Non-Newtonian Fluid Mechanics

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We propose a Finite Volume Method for the simulation of elastoviscoplastic flows, modelled after the extension to the Herschel-Bulkley model by Saramito [J. Non-Newton. Fluid Mech. 158 (2009) 154-161]. The method is akin to methods for viscoelastic flows. It is applicable to cell-centred grids, both structured and unstructured, and includes a novel pressure stabilisation technique of the "momentum interpolation" type. Stabilisation of the velocity and stresses is achieved through a "both sides diffusion" technique and the CUBISTA convection scheme, respectively. A second-order accurate temporal discretisation scheme with adaptive time step is employed. The method is used to obtain benchmark results of lid-driven cavity flow, with the model parameters chosen so as to represent Carbopol. The results are compared against those obtained with the classic Herschel-Bulkley model. Simulations are performed for various lid velocities, with slip and no-slip boundary conditions, and with different initial conditions for stress. Furthermore, we investigate the cessation of the flow, once the lid is suddenly halted.

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Section: Introductionmentioning

confidence: 99%

A finite volume method for the simulation of elastoviscoplastic flows and its application to the lid-driven cavity case

Syrakos

Dimakopoulos

Tsamopoulos

2020

Journal of Non-Newtonian Fluid Mechanics

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“…Gradient discretisation schemes are among the basic ingredients of Finite Volume Methods (FVMs) designed for grids of general geometry. They are used in the discretisation of diffusion [1,2] and convection [3] terms, terms of turbulence closure equations [4], terms of non-Newtonian constitutive equations [3,[5][6][7] etc. Despite the level of maturity that FVMs have reached after decades of development, it has not yet been possible to devise a single general-purpose gradient discretisation scheme that performs well under all circumstances.…”

Section: Introductionmentioning

confidence: 99%

A family of first-order accurate gradient schemes for finite volume methods

Oxtoby¹,

Syrakos²,

Varchanis³

et al. 2019

Preprint

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A new discretisation scheme for the gradient operator, suitable for use in second-order accurate Finite Volume Methods (FVMs), is proposed. The derivation of this scheme, which we call the Taylor-Gauss (TG) gradient, is similar to that of the least-squares (LS) gradients, whereby the values of the differentiated variable at neighbouring cell centres are expanded in truncated Taylor series about the centre of the current cell, and the resulting equations are summed after being weighted by chosen vectors. Unlike in the LS gradients, the TG gradients use vectors aligned with the face normals, resembling the Green-Gauss (GG) gradients in this respect. Thus, the TG and LS gradients belong in a general unified framework, within which other gradients can also be derived. The similarity with the LS gradients allows us to try different weighting schemes (magnitudes of the weighting vectors) such as weighting by inverse distance or face area. The TG gradients are tested on a variety of grids such as structured, locally refined, randomly perturbed, and with high aspect ratio. They are shown to be at least first-order accurate in all cases, and are thus suitable for use in second-order accurate FVMs. In many cases they compare favourably over existing schemes.

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“…In 2004, Fattal and Kupferman [17,18] observed that some numerical instabilities are caused by the failure of polynomial functions to approximate accurately the exponential growth of the stress tensor, due to the presence of the deformation as a source term in the tensor transport equation. The deformation source term takes its origin in the two last terms on the right-hand side of the tensor derivative (1). The solution proposed by these authors was a change of unknown that scale logarithmically with the stress tensor.…”

Section: Introductionmentioning

confidence: 99%

“…This idea was a new starting point and many improved numerical computations of viscoelastic flows were then performed (see e.g. [28,15,1] and [10] for a recent review).…”

Section: Introductionmentioning

confidence: 99%

On a modified non-singular log-conformation formulation for Johnson–Segalman viscoelastic fluids

Saramito

2014

Journal of Non-Newtonian Fluid Mechanics

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A modified log-conformation formulation of viscoelastic fluid flows is presented in this paper. This new formulation is non-singular for vanishing Weissenberg numbers and allows a direct steady numerical resolution by a Newton method. Moreover, an exact computation of all the terms of the linearized problem is provided. The use of an exact divergence-free finite element method for velocity-pressure approximation and a discontinuous Galerkin upwinding treatment for stresses leads to a robust discretization. A demonstration is provided by the computation of steady solutions at high Weissenberg numbers for the difficult benchmark case of the lid driven cavity flow. Numerical results are in good agreement, qualitatively with experiment measurements on real viscoelastic flows, and quantitatively with computations performed by others authors. The numerical algorithm is both robust and very efficient, as it requires a low mesh-invariant number of linear systems resolution to obtain solutions at high Weissenberg number. An adaptive mesh procedure is also presented: it alows representing accurately both boundary layers and the main and secondary vorties.

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The Finite Volume Method in Computational Rheology

Cited by 9 publications

References 61 publications

A finite volume method for the simulation of elastoviscoplastic flows and its application to the lid-driven cavity case

A finite volume method for the simulation of elastoviscoplastic flows and its application to the lid-driven cavity case

A family of first-order accurate gradient schemes for finite volume methods

On a modified non-singular log-conformation formulation for Johnson–Segalman viscoelastic fluids

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