On the numerical simulation of Bingham visco-plastic flow: Old and new results

Dean, Edward; Glowinski, Roland; Guidoboni, Giovanna

doi:10.1016/j.jnnfm.2006.09.002

Cited by 141 publications

(172 citation statements)

References 20 publications

(57 reference statements)

Supporting

Mentioning

168

Contrasting

Order By: Relevance

“…By characterizing the subgradient of the objective function in (1), its solution u satisfies the following conditions [8,27]:…”

Section: Second-order Cone Programming Formulation and Optimality Conmentioning

confidence: 99%

“…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%

See 1 more Smart Citation

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

Bleyer

2018

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

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.

show abstract

“…By characterizing the subgradient of the objective function in (1), its solution u satisfies the following conditions [8,27]:…”

Section: Second-order Cone Programming Formulation and Optimality Conmentioning

confidence: 99%

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

View full text Add to dashboard Cite

show abstract

“…In the case of "multiplier" method, a result such as Lemma 2.2 is used to introduce a new unknown at the expense of removing the inequality. In this work we will present an algorithm based in two step namely [5,6]:…”

Section: Alternating Direction Methods Of Multipliersmentioning

confidence: 99%

“…The point of departure of this study is the work of J.K. Djoko and M. Mbehou [7], where the resulting formulation had been solved by making use of the "Lagrange multiplier" and application of Uzawa's algorithm. In this work, we solve the problem associated with the Stokes equations by exploiting the minimization structure of the variational formulation, and apply to it an alternating direction method reminiscent to those used in [6,18,20,22,37,38]. Next, we solve the stationary Navier Stokes equations in two steps.…”

Section: Introductionmentioning

confidence: 99%

Numerical methods for the Stokes and Navier–Stokes equations driven by threshold slip boundary conditions

Djoko

Koko

2016

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

In this article, we discuss the numerical solution of the Stokes and Navier-Stokes equations completed by nonlinear slip boundary conditions of friction type in two and three dimensions. To solve the Stokes system, we first reduce the related variational inequality into a saddle point-point problem for a well chosen augmented Lagrangian. To solve this saddle point problem we suggest an alternating direction method of multiplier together with finite element approximations. The solution of the Navier Stokes system combines finite element approximations, time discretization by operator splitting and augmented Lagrangian method. Numerical experiment results for two and three dimensional flow confirm the interest of these approaches.

show abstract

“…The mathematical analysis of Bingham fluid flows dates back to the work of Duvaut & Lions (1976), where the problems are formulated as variational inequalities in Sobolev spaces. The numerical aproximation of a Bingham fluid flow is usually treated with finite element techniques; we refer to Dean et al (2007) for a recent review.…”

mentioning

confidence: 99%

Convection and total variation flow

Bouchut¹,

Doyen²,

Eymard³

2013

IMA Journal of Numerical Analysis

View full text Add to dashboard Cite

We deal with a nonlinear hyperbolic scalar conservation law, regularized by the total variation flow operator (or 1-Laplacian). We give an entropy weak formulation, for which we prove the existence and the uniqueness of the solution. The existence result is established using the convergence of a numerical approximation (a splitting scheme where the hyperbolic flow is treated with finite volumes and the total variation flow with finite elements). Some numerical simulations are also presented.Keywords: Bingham fluid, hyperbolic scalar conservation law, total variation flow, 1-Laplacian, entropy formulation, finite volumes, finite elements A Bingham fluid, also called rigid viscoplastic fluid, is a material that behaves as a rigid solid below a certain stress yield and as a viscous fluid above this yield; a familiar example of such a material is the tooth paste. For a d-dimensional Bingham fluid, the relation between the stress tensor σ , seen as a d × d matrix, the pressure p and the velocity u is When the viscosity becomes negligible (ν = 0), the analytical and numerical framework described above is no longer suitable -let us mention however an existence result in 2D obtained by Lions (1972). Although the study of inviscid Bingham fluids has been initiated in Bouchut et al. (2012) with the case of an unsteady flow without convection term, the presence of a nonlinear convection term is naturally issued from the inertial term in the momentum conservation equation. Unfortunately, the study of this problem seems to be out of reach in the actual state of the art, and we only consider here a simplified model of unsteady Bingham flow with convection. This simplified model is scalar and consists in †

show abstract

On the numerical simulation of Bingham visco-plastic flow: Old and new results

Cited by 141 publications

References 20 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

Numerical methods for the Stokes and Navier–Stokes equations driven by threshold slip boundary conditions

Convection and total variation flow

Contact Info

Product

Resources

About