1. Syrakos, A; Dimakopoulos, Y; Tsamopoulos, J

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

In: Journal of Non-Newtonian Fluid Mechanics, 275 , 2020, ISSN: 03770257, (cited By 0).

Abstract | Links | BibTeX | Tags: Benchmark problem, Carbopol, Elastoviscoplastic flow, Finite Volume method, Flow cessation, Lid-driven cavity

@article{Syrakos2020,

title = {A finite volume method for the simulation of elastoviscoplastic flows and its application to the lid-driven cavity case},

author = {A Syrakos and Y Dimakopoulos and J Tsamopoulos},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85076172172&doi=10.1016%2fj.jnnfm.2019.104216&partnerID=40&md5=91473f41ebd36091adf437a2da72f783},

doi = {10.1016/j.jnnfm.2019.104216},

issn = {03770257},

year = {2020},

date = {2020-01-01},

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

volume = {275},

abstract = {We propose a Finite Volume Method for the simulation of elastoviscoplastic (EVP) flows, modelled after the extension to the Herschel-Bulkley model by Saramito [J. Non-Newton. Fluid Mech. 158 (2009) 154–161]. The method is applicable to cell-centred grids of arbitrary geometry by the introduction of new stabilisation techniques of the “momentum interpolation” and “both sides diffusion” types, for pressure and velocity, respectively. Adaptive time stepping is employed. The method is used to perform benchmark simulations of lid-driven cavity flow, which also serve to explore certain aspects of this EVP constitutive equation in a two-dimensional setting. The model parameters are chosen so as to represent Carbopol, and simulations are performed for different lid velocities and with either slip or no-slip wall boundaries. The results are compared against those obtained with the classic Herschel-Bulkley model. It is noticed that different initial conditions for stress lead to different steady states. Furthermore, we investigate the cessation of the flow, once the lid is suddenly halted; it is found that, contrary to the classic Herschel-Bulkley predictions, the EVP flow does not cease in finite time. Rather, the flow decays very slowly while the material oscillates as kinetic energy is converted to elastic energy and vice versa. Flow decay is much faster under slip conditions due to the friction between the material and the walls. © 2019 Elsevier B.V.},

note = {cited By 0},

keywords = {Benchmark problem, Carbopol, Elastoviscoplastic flow, Finite Volume method, Flow cessation, Lid-driven cavity},

pubstate = {published},

tppubtype = {article}

}

We propose a Finite Volume Method for the simulation of elastoviscoplastic (EVP) flows, modelled after the extension to the Herschel-Bulkley model by Saramito [J. Non-Newton. Fluid Mech. 158 (2009) 154–161]. The method is applicable to cell-centred grids of arbitrary geometry by the introduction of new stabilisation techniques of the “momentum interpolation” and “both sides diffusion” types, for pressure and velocity, respectively. Adaptive time stepping is employed. The method is used to perform benchmark simulations of lid-driven cavity flow, which also serve to explore certain aspects of this EVP constitutive equation in a two-dimensional setting. The model parameters are chosen so as to represent Carbopol, and simulations are performed for different lid velocities and with either slip or no-slip wall boundaries. The results are compared against those obtained with the classic Herschel-Bulkley model. It is noticed that different initial conditions for stress lead to different steady states. Furthermore, we investigate the cessation of the flow, once the lid is suddenly halted; it is found that, contrary to the classic Herschel-Bulkley predictions, the EVP flow does not cease in finite time. Rather, the flow decays very slowly while the material oscillates as kinetic energy is converted to elastic energy and vice versa. Flow decay is much faster under slip conditions due to the friction between the material and the walls. © 2019 Elsevier B.V.2. 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.