Numerical simulations of cessation flows of a Bingham plastic with the augmented Lagrangian method

Muravleva, Larisa; Muravleva, Ekaterina; Georgiou, Georgios C.; Mitsoulis, Evan

doi:10.1016/j.jnnfm.2010.02.002

Cited by 36 publications

(15 citation statements)

References 25 publications

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“…In a series of papers, Frigaard and coworkers pointed out some drawbacks of the regularization approach (Moyers- Gonzalez and Frigaard, 2004;Frigaard and Nouar, 2005;Putz et al, 2009). Finally, the augmented Lagrangian algorithm became the most popular way to solve viscoplastic flow problems because of its accuracy (Muravleva et al, 2010;Dimakopoulos et al, 2013), despite the fact that the regularization approach runs in general faster. The Rheolef library, a free software developed by one of the authors of this review article and supporting both the augmented Lagrangian algorithm and an autoadaptive mesh technique, is now widely used for various flow applications (Putz and Frigaard, 2010;Roustaei and Frigaard, 2013;Wachs and Frigaard, 2016;Boujlel et al, 2016).…”

Section: Overviewmentioning

confidence: 99%

“…For the Couette flow, there is no motionless unyielded region anymore and the position of the yielded surface is difficult to determine. Finally, with this modified problem, return to rest in finite time and quiescent state (Muravleva et al, 2010) cannot be captured: the flow never fully stops when the load is lower than the critical value. The finite time decay, quiescent state and limit load analysis can not be established clearly.…”

Section: The Regularization Approachmentioning

confidence: 99%

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Progress in numerical simulation of yield stress fluid flows

2017

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Numerical simulations of viscoplastic fluid flows have provided a better understanding of fundamental properties of yield stress fluids in many applications relevant of natural and engineering sciences. In the first part of this paper, we review the classical numerical methods for the solution of the non-smooth viscoplastic mathematical models, highlight their advantages and drawbacks, and discuss more recent numerical methods that show promises for fast algorithms and accurate solutions. In the second part, we present and analyze a variety of applications and extensions involving viscoplastic flow simulations: yield slip at the wall, heat transfer, thixotropy, granular materials, combining elasticity, with multiple phases and shallow flow approximations. We illustrate from a physical viewpoint how fascinating the corresponding rich phenomena pointed out by these simulations are.

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Section: Overviewmentioning

confidence: 99%

Section: The Regularization Approachmentioning

confidence: 99%

Progress in numerical simulation of yield stress fluid flows

2017

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“…Another important computation issue is the accurate tracking of the yield surfaces. Compared to the regularization method, the augmented Lagrangian method yields superior results regarding the location of the yield surface and explorations of the plastic limit, for example, in simulation of the flow cessation [38], [41] or no-flow limit [35]. According to [30], "pragmatically, the choice between augmented Lagrangian and regularization is related to whether one needs to determine the position of the yield surface, or whether a reasonable approximation to the velocity field is sufficient".…”

Section: Introductionmentioning

confidence: 99%

Squeeze plane flow of viscoplastic Bingham material

Muravleva

2015

Journal of Non-Newtonian Fluid Mechanics

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“…Undoubtedly, the subject matter of viscoplasticity/viscoelastoplasticity remains a hotly debated and challenging topic, which has provoked more than a thousand papers prior to 2005 (see Mitsoulis 2007). In addition, some authors have employed the augmented Lagrangian approach and applied it to problems of viscoplasticity (see, for example, Roquet and Saramito 2001, Huilgol and You 2005and Muravleva et al 2010). These authors have demonstrated the effectiveness of the augmented Lagrangian method for this type of problem.…”

Section: Introductionmentioning

confidence: 99%

Numerical modelling of thixotropic and viscoelastoplastic materials in complex flows

et al. 2014

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This study is concerned with the finite element/finite volume (fe/fv) simulation of thixotropic and viscoelastoplastic material systems through two model approaches: (i) a new micellar thixotropic constitutive model for wormlike micellar systems (that introduces viscoelasticity into the network structure construction/destruction kinetic equation) and (ii) adopting a Bingham-Papanastasiou model. The computational approach is based on a hybrid parent/subcell scheme, which is cast about a semi-implicit incremental pressure correction (ipc) scheme. The appearance of plastic behaviour arises through the micellar polymeric viscosity, by increasing the zero-shear viscosity (low solvent fractions), whilst the Bingham-Papanastasiou introduces plastic features through the solvent viscosity. The characteristics of thixotropic wormlike micellar systems are represented through the class of Bautista-Manero models. Correction is incorporated, based on physical arguments for fluidity, in which absolute values of the dissipation function are adopted in complex flow, thereby accessing low-solvent fractions and high-elasticity levels. Considering elastic and plastic influences separately, solutions are compared and contrasted for contraction-expansion flow, identifying such flow field features as vortex dynamics, stress field structure, yield front patterns and enhanced pressure drop. Particular attention is paid to the influence of enhanced strain hardening that is introduced through stronger thixotropic structural features. Vortex activity decreases as either We is increased at a fixed τ 0 or τ 0 is increased at a fixed We. Exaggerated strainhardening properties are observed to have a major impact on vortex activity. Patterns and trends in normal stress difference fields reflect those in re-entrant corner vortex patterns. Yield front patterns are significantly influenced with yield stress τ 0 variation and more so than elevation in elasticity. Findings on excess pressure drop (epd) versus increased yield stress (τ 0 ) follow a linear trend. Consistently, it is evident that any variation that leads to a more solid-like behaviour produces epd enhancement. In addition, relatively more structured fluids display distinctly larger epd values throughout the τ 0 range covered.

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Numerical simulations of cessation flows of a Bingham plastic with the augmented Lagrangian method

Cited by 36 publications

References 25 publications

Progress in numerical simulation of yield stress fluid flows

Progress in numerical simulation of yield stress fluid flows

Squeeze plane flow of viscoplastic Bingham material

Numerical modelling of thixotropic and viscoelastoplastic materials in complex flows

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