1. Dimakopoulos, Y; Makrigiorgos, G; Georgiou, G C; Tsamopoulos, J

The PAL (Penalized Augmented Lagrangian) method for computing viscoplastic flows: A new fast converging scheme Journal Article

In: Journal of Non-Newtonian Fluid Mechanics, 256 , pp. 23-41, 2018, ISSN: 03770257, (cited By 13).

Abstract | Links | BibTeX | Tags: Augmented Lagrangian method, Bubble rise, Filament, Lid-driven cavity, Papanastasiou regularization; Penalty method, stretching, Viscoplastic fluids

@article{Dimakopoulos201823,

title = {The PAL (Penalized Augmented Lagrangian) method for computing viscoplastic flows: A new fast converging scheme},

author = {Y Dimakopoulos and G Makrigiorgos and G C Georgiou and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85044113517&doi=10.1016%2fj.jnnfm.2018.03.009&partnerID=40&md5=46144d6483fc39fdf658de1f3f65dd06},

doi = {10.1016/j.jnnfm.2018.03.009},

issn = {03770257},

year = {2018},

date = {2018-01-01},

journal = {Journal of Non-Newtonian Fluid Mechanics},

volume = {256},

pages = {23-41},

abstract = {Computation of viscoplastic fluid flows has always been a challenging task. Viscoplastic models are intrinsically discontinuous at the yielded-unyielded interface, which leads to numerical difficulties, because of the singularity in the Jacobian matrix of the resulting discretized equations. For this reason, several modeling or numerical approaches have been proposed, the most popular being the Papanastasiou regularization (PR) and the Augmented Lagrangian (AL) methods, respectively. Recently, studies on AL methods have focused on developing accelerated algorithms, since the required computational cost of using AL is extremely high. In the present work, a fast converging and efficient algorithm is proposed for tracking the yield surface and predicting the flow field of viscoplastic fluids accurately. The numerical procedure is the Penalized Augmented Lagrangian (PAL) method, which is based on a monolithic Newton solver for AL, where the governing equations of the Lagrange-multiplier tensor for both the rate-of-strain projection and the extra-stress tensors are penalized. To test the efficiency of our algorithm, five benchmark flow-problems with fixed, free and moving boundaries are studied. First, the problem of the steady rise of a bubble in a viscoplastic medium is addressed validating the new algorithm with the findings by Dimakopoulos et al. (2013). Then the entrance flow in a rectangular channel is solved, where a primary unyielded region is found around the centerline in the developed part of the flow and secondary unyielded regions near the entrance. In addition, the lid-driven cavity problem is solved, which is an often used test for various numerical algorithms and the results are compared to relevant studies for viscoplastic fluids such as those of Syrakos et al. (2013, 2014) and Treskatis et al. (2016). Furthermore, the developed flow in a square duct is examined, similarly to Saramito (2016). Finally, the transient filament stretching of a shear-thinning, yield stress fluid is examined, and the results are compared to those by Balmforth et al. (2010). In all cases, either steady or transient, the algorithm captures the yield surfaces correctly, while maintaining a low computational cost, because the convergence of the method requires only a few (i.e. 5–30) Newton iterations. Based on these extensive tests, PAL is found to be superior combining accuracy and speed to all existing solution methods for viscoplastic fluids. © 2018 Elsevier B.V.},

note = {cited By 13},

keywords = {Augmented Lagrangian method, Bubble rise, Filament, Lid-driven cavity, Papanastasiou regularization; Penalty method, stretching, Viscoplastic fluids},

pubstate = {published},

tppubtype = {article}

}

Computation of viscoplastic fluid flows has always been a challenging task. Viscoplastic models are intrinsically discontinuous at the yielded-unyielded interface, which leads to numerical difficulties, because of the singularity in the Jacobian matrix of the resulting discretized equations. For this reason, several modeling or numerical approaches have been proposed, the most popular being the Papanastasiou regularization (PR) and the Augmented Lagrangian (AL) methods, respectively. Recently, studies on AL methods have focused on developing accelerated algorithms, since the required computational cost of using AL is extremely high. In the present work, a fast converging and efficient algorithm is proposed for tracking the yield surface and predicting the flow field of viscoplastic fluids accurately. The numerical procedure is the Penalized Augmented Lagrangian (PAL) method, which is based on a monolithic Newton solver for AL, where the governing equations of the Lagrange-multiplier tensor for both the rate-of-strain projection and the extra-stress tensors are penalized. To test the efficiency of our algorithm, five benchmark flow-problems with fixed, free and moving boundaries are studied. First, the problem of the steady rise of a bubble in a viscoplastic medium is addressed validating the new algorithm with the findings by Dimakopoulos et al. (2013). Then the entrance flow in a rectangular channel is solved, where a primary unyielded region is found around the centerline in the developed part of the flow and secondary unyielded regions near the entrance. In addition, the lid-driven cavity problem is solved, which is an often used test for various numerical algorithms and the results are compared to relevant studies for viscoplastic fluids such as those of Syrakos et al. (2013, 2014) and Treskatis et al. (2016). Furthermore, the developed flow in a square duct is examined, similarly to Saramito (2016). Finally, the transient filament stretching of a shear-thinning, yield stress fluid is examined, and the results are compared to those by Balmforth et al. (2010). In all cases, either steady or transient, the algorithm captures the yield surfaces correctly, while maintaining a low computational cost, because the convergence of the method requires only a few (i.e. 5–30) Newton iterations. Based on these extensive tests, PAL is found to be superior combining accuracy and speed to all existing solution methods for viscoplastic fluids. © 2018 Elsevier B.V.2. Mitsoulis, E; Tsamopoulos, J

Numerical simulations of complex yield-stress fluid flows Journal Article

In: Rheologica Acta, 56 (3), pp. 231-258, 2017, ISSN: 00354511, (cited By 36).

Abstract | Links | BibTeX | Tags: Bingham plastics, Elastoviscoplastic fluids, Herschel-Bulkley fluids, Simulations, unyielded regions, Viscoplastic fluids, Viscoplastic models, Yield stress, Yielded

@article{Mitsoulis2017231,

title = {Numerical simulations of complex yield-stress fluid flows},

author = {E Mitsoulis and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85001022076&doi=10.1007%2fs00397-016-0981-0&partnerID=40&md5=78c8b6500b006f7b3ca82c4182414f3f},

doi = {10.1007/s00397-016-0981-0},

issn = {00354511},

year = {2017},

date = {2017-01-01},

journal = {Rheologica Acta},

volume = {56},

number = {3},

pages = {231-258},

abstract = {Viscoplasticity is characterized by a yield stress, below which the materials will not deform and above which they will deform and flow according to different constitutive relations. Viscoplastic models include the Bingham plastic, the Herschel-Bulkley model and the Casson model. All of these ideal models are discontinuous. Analytical solutions exist for such models in simple flows. For general flow fields, it is necessary to develop numerical techniques to track down yielded/unyielded regions. This can be avoided by introducing into the models a regularization parameter, which facilitates the solution process and produces virtually the same results as the ideal models by the right choice of its value. This work reviews several benchmark problems of viscoplastic flows, such as entry and exit flows from dies, flows around a sphere and a bubble and squeeze flows. Examples are also given for typical processing flows of viscoplastic materials, where the extent and shape of the yielded/unyielded regions are clearly shown. The above-mentioned viscoplastic models leave undetermined the stress and elastic deformation in the solid region. Moreover, deviations have been reported between predictions with these models and experiments for flows around particles using Carbopol, one of the very often used and heretofore widely accepted as a simple “viscoplastic” fluid. These have been partially remedied in very recent studies using the elastoviscoplastic models proposed by Saramito. © 2016, Springer-Verlag Berlin Heidelberg.},

note = {cited By 36},

keywords = {Bingham plastics, Elastoviscoplastic fluids, Herschel-Bulkley fluids, Simulations, unyielded regions, Viscoplastic fluids, Viscoplastic models, Yield stress, Yielded},

pubstate = {published},

tppubtype = {article}

}

Viscoplasticity is characterized by a yield stress, below which the materials will not deform and above which they will deform and flow according to different constitutive relations. Viscoplastic models include the Bingham plastic, the Herschel-Bulkley model and the Casson model. All of these ideal models are discontinuous. Analytical solutions exist for such models in simple flows. For general flow fields, it is necessary to develop numerical techniques to track down yielded/unyielded regions. This can be avoided by introducing into the models a regularization parameter, which facilitates the solution process and produces virtually the same results as the ideal models by the right choice of its value. This work reviews several benchmark problems of viscoplastic flows, such as entry and exit flows from dies, flows around a sphere and a bubble and squeeze flows. Examples are also given for typical processing flows of viscoplastic materials, where the extent and shape of the yielded/unyielded regions are clearly shown. The above-mentioned viscoplastic models leave undetermined the stress and elastic deformation in the solid region. Moreover, deviations have been reported between predictions with these models and experiments for flows around particles using Carbopol, one of the very often used and heretofore widely accepted as a simple “viscoplastic” fluid. These have been partially remedied in very recent studies using the elastoviscoplastic models proposed by Saramito. © 2016, Springer-Verlag Berlin Heidelberg.