On the Numerical Simulation of Viscoplastic Fluid Flow

Glowinski, Roland; Wachs, Anthony

doi:10.1016/b978-0-444-53047-9.00006-x

Cited by 96 publications

(86 citation statements)

References 121 publications

(264 reference statements)

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“…Regularized models have first been proposed to replace the non-smooth viscoplastic constitutive law by a smooth purely viscous model [3,4]. Augmented Lagrangian (AL) approaches have then emerged as an interesting alternative to the use of regularized models to solve viscoplastic fluid flows, it is now one of the most popular method to solve such problems [5][6][7][8][9]. However, it still suffers from a slow convergence rate so that three-dimensional simulations are still extremely expensive.…”

Section: Introductionmentioning

confidence: 99%

Advances in the simulation of viscoplastic fluid flows using interior-point methods

Bleyer

2018

Computer Methods in Applied Mechanics and Engineering

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We present a primal-dual interior point algorithm for the resolution of steady-state viscoplastic fluid flows formulated as a conic optimization problem. We give a complete description of the algorithm including some advanced aspects such as a predictor-corrector and scaling scheme to improve its efficiency. Our interior-point approach is shown to be largely more efficient than Augmented Lagrangian (AL) approaches which are traditionally used to solve such problems. In particular, the interior-point approach is roughly 5 times faster than the modern accelerated version of AL algorithms. The yield surfaces are shown to be accurately predicted and various examples ranging from channel flows to three-dimensional flows through a porous medium demonstrate its efficiency.

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Section: Introductionmentioning

confidence: 99%

Advances in the simulation of viscoplastic fluid flows using interior-point methods

Bleyer

2018

Computer Methods in Applied Mechanics and Engineering

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“…We refer to Glowinski and coworkers for details on this duality methodà la Uzawa: the book [22] and the article [23] for a recent review in the context of Bingham flows.…”

Section: Appendix Appendix a Derivation Of The Al Approachmentioning

confidence: 99%

“…While for BM( ) the optimal parameter opt is defined by (23), equals to 10.3 approximately for this test. Note that both, ω opt and opt are near to the optimal value obtained numerically, which are respectively 26 and 21.…”

Section: Well-balanced Tests Test 51a: Analytical Stationary Solutionmentioning

confidence: 99%

“…For the BM algorithm ω n i+1/2 is defined in terms of ω opt , following (22) or (23). Concretely, we can set…”

Section: Well-balanced Discretization With General Bed and Wet/dry Frmentioning

confidence: 99%

“…[34], [38,37], [25], [36], [26]) is that they use decomposition-coordination methods to solve the variational inequality associated to constitutive laws with a so-called plastic threshold (the most simple and iconic one being the Bingham model). This kind of approach takes its roots in the seminal works of Duvaut-Lions [15] and the series of papers of Glowinski and coworkers (see the recent book [23] for a detailed review), initiated at the end of the seventies and anchored in the Augmented Lagrangian formalism. One of the crucial advantage of these methods over regularized approaches (see e.g.…”

Section: Introductionmentioning

confidence: 99%

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Efficient numerical schemes for viscoplastic avalanches. Part 2: The 2D case

Fernández-Nieto

Gallardo

Vigneaux

2018

Journal of Computational Physics

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This paper deals with the numerical resolution of a shallow water viscoplastic flow model. Viscoplastic materials are characterized by the existence of a yield stress: below a certain critical threshold in the imposed stress, there is no deformation and the material behaves like a rigid solid, but when that yield value is exceeded, the material flows like a fluid. In the context of avalanches, it means that after going down a slope, the material can stop and its free surface has a non trivial shape, as opposed to the case of water (Newtonian fluid). The model involves variational inequalities associated to the yield threshold: finite-volume schemes are used together with duality methods (namely Augmented Lagrangian and Bermúdez-Moreno) to discretize the problem. To be able to accurately simulate the stopping behaviour of the avalanche, new schemes need to be designed, involving the classical notion of wellbalancing. In the present context, it needs to be extended to take into account the viscoplastic nature of the material as well as general bottoms with wet/dry fronts which are encountered in geophysical geometries. We derived such schemes and numerical experiments are presented to show their performances.

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Non‐Newtonian Fluids

Patel

Chhabra

2020

Kirk-Othmer Encyclopedia of Chemical Technology

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This chapter aims at introducing and demonstrating the ubiquitous nature of non‐Newtonian flow characteristics in a broad spectrum of industrial settings. Beginning with the definitions of a viscous fluid and an elastic material and a Newtonian fluid, different kinds of non‐Newtonian flow characteristic are introduced and briefly discussed. Next, each of these is illustrated by presenting experimental data for polymer solutions, suspensions, and so on. Most such complex materials exhibit nonlinear viscosity (shear‐thinning, shear‐thickening, yield stress, visco‐elasticity, etc), time‐dependent, and extensional flow characteristics under appropriate conditions, which are of great interest from their processing, manufacturing and the end‐user stand point. This is followed by a discussion of a few constitutive models, some of which are purely empirical in nature, while others are based on different combinations of a dashpot (viscous) and a spring (elastic) elements to capture varying blends of fluid‐like and solid‐like non‐Newtonian characteristics. Next, a range of selected applications including the steady flow of such fluids in ducts of circular and noncircular cross‐sections, in packed columns and in unconsolidated porous media, and boundary layer‐type external flows over a sphere and a long cylinder are briefly discussed. The chapter is concluded by mentioning the other important aspects of this class of fluids and their processing in wide‐ranging settings for interested readers to gain further insights into the fascinating world of non‐Newtonian fluids.

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On the Numerical Simulation of Viscoplastic Fluid Flow

Cited by 96 publications

References 121 publications

Advances in the simulation of viscoplastic fluid flows using interior-point methods

Advances in the simulation of viscoplastic fluid flows using interior-point methods

Efficient numerical schemes for viscoplastic avalanches. Part 2: The 2D case

Non‐Newtonian Fluids

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