Highly parallelisable simulations of time-dependent viscoplastic fluid flow with structured adaptive mesh refinement

Sverdrup, Knut; Nikiforakis, Nikolaos; Almgren, Ann

doi:10.1063/1.5049202

Highly parallelisable simulations of time-dependent viscoplastic fluid flow with structured adaptive mesh refinement

Journal Article · Tue Sep 11 00:00:00 EDT 2018 · Physics of Fluids

DOI:https://doi.org/10.1063/1.5049202· OSTI ID:1543883

^[1]; ^[1]; Almgren, Ann ^[2]

Univ. of Cambridge (United Kingdom). Cavendish Lab.
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

We present the extension of an efficient and highly parallelisable framework for incompressible fluid flow simulations to viscoplastic fluids. The system is governed by incompressible conservation of mass, the Cauchy momentum equation, and a generalised Newtonian constitutive law. In order to simulate a wide range of viscoplastic fluids, we employ the Herschel-Bulkley model for yield-stress fluids with nonlinear stress-strain dependency above the yield limit. We utilise Papanastasiou regularisation in our algorithm to deal with the singularity in apparent viscosity. The resulting system of partial differential equations is solved using the IAMR (Incompressible Adaptive Mesh Refinement) code, which uses second-order Godunov methodology for the advective terms and semi-implicit diffusion in the context of an approximate projection method to solve adaptively refined meshes. By augmenting the IAMR code with the ability to simulate regularised Herschel-Bulkley fluids, we obtain efficient numerical software for time-dependent viscoplastic flow in three dimensions, which can be used to investigate systems not considered previously due to computational expense. We validate results from simulations using this new capability against previously published data for Bingham plastics and power-law fluids in the two-dimensional lid-driven cavity. In doing so, we expand the range of Bingham and Reynolds numbers which have been considered in the benchmark tests. Moreover, extensions to time-dependent flow of Herschel-Bulkley fluids and three spatial dimensions offer new insights into the flow of viscoplastic fluids in this test case, and we provide missing benchmark results for these extensions.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)

Sponsoring Organization:: USDOE

OSTI ID:: 1543883

Journal Information:: Physics of Fluids, Journal Name: Physics of Fluids Journal Issue: 9 Vol. 30; ISSN 1070-6631

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (59)

A Conservative Adaptive Projection Method for the Variable Density Incompressible Navier–Stokes Equations Almgren, Ann S.; Bell, John B.; Colella, Phillip Journal of Computational Physics, Vol. 142, Issue 1 https://doi.org/10.1006/jcph.1998.5890	journal	May 1998
Bingham’s model in the oil and gas industry Frigaard, Ian A.; Paso, Kristofer G.; de Souza Mendes, Paulo R. Rheologica Acta, Vol. 56, Issue 3 https://doi.org/10.1007/s00397-017-0999-y	journal	February 2017
A 3rd order upwind finite volume method for generalised Newtonian fluid flows Neofytou, Panagiotis Advances in Engineering Software, Vol. 36, Issue 10 https://doi.org/10.1016/j.advengsoft.2005.03.011	journal	October 2005
Uzawa-like methods for numerical modeling of unsteady viscoplastic Bingham medium flows Muravleva, Larisa Applied Numerical Mathematics, Vol. 93 https://doi.org/10.1016/j.apnum.2014.06.001	journal	July 2015
A damped Newton algorithm for computing viscoplastic fluid flows Saramito, Pierre Journal of Non-Newtonian Fluid Mechanics, Vol. 238 https://doi.org/10.1016/j.jnnfm.2016.05.007	journal	December 2016
Flow of Bingham plastics in a lid-driven square cavity Mitsoulis, E.; Zisis, Th. Journal of Non-Newtonian Fluid Mechanics, Vol. 101, Issue 1-3 https://doi.org/10.1016/s0377-0257(01)00147-1	journal	November 2001
Yielding to Stress: Recent Developments in Viscoplastic Fluid Mechanics Balmforth, Neil J.; Frigaard, Ian A.; Ovarlez, Guillaume Annual Review of Fluid Mechanics, Vol. 46, Issue 1 https://doi.org/10.1146/annurev-fluid-010313-141424	journal	January 2014
p-version least squares finite element formulation for two-dimensional, incompressible, non-Newtonian isothermal and non-isothermal fluid flow Bell, Brent C.; Surana, Karan S. International Journal for Numerical Methods in Fluids, Vol. 18, Issue 2 https://doi.org/10.1002/fld.1650180202	journal	January 1994
A Cell-Centered Adaptive Projection Method for the Incompressible Euler Equations Martin, Daniel F.; Colella, Phillip Journal of Computational Physics, Vol. 163, Issue 2 https://doi.org/10.1006/jcph.2000.6575	journal	September 2000
Formal Metrics for Large-Scale Parallel Performance Moreland, Kenneth; Oldfield, Ron Lecture Notes in Computer Science https://doi.org/10.1007/978-3-319-20119-1_34	book	January 2015
Inequalities in Mechanics and Physics Duvaut, Georges; Lions, Jacques Louis Grundlehren der mathematischen Wissenschaften https://doi.org/10.1007/978-3-642-66165-5	book	January 1976
Multiplier and gradient methods Hestenes, Magnus R. Journal of Optimization Theory and Applications, Vol. 4, Issue 5 https://doi.org/10.1007/bf00927673	journal	November 1969
Konsistenzmessungen von Gummi-Benzollösungen Herschel, Winslow H.; Bulkley, Ronald Kolloid-Zeitschrift, Vol. 39, Issue 4 https://doi.org/10.1007/bf01432034	journal	August 1926
The effect of cholesterol and triglycerides on the steady state shear rheology of blood Apostolidis, Alex J.; Beris, Antony N. Rheologica Acta, Vol. 55, Issue 6 https://doi.org/10.1007/s00397-015-0889-0	journal	December 2015
Cessation of the lid-driven cavity flow of Newtonian and Bingham fluids Syrakos, Alexandros; Georgiou, Georgios C.; Alexandrou, Andreas N. Rheologica Acta, Vol. 55, Issue 1 https://doi.org/10.1007/s00397-015-0893-4	journal	December 2015
Numerical simulations of complex yield-stress fluid flows Mitsoulis, Evan; Tsamopoulos, John Rheologica Acta, Vol. 56, Issue 3 https://doi.org/10.1007/s00397-016-0981-0	journal	December 2016
Progress in numerical simulation of yield stress fluid flows Saramito, Pierre; Wachs, Anthony Rheologica Acta, Vol. 56, Issue 3 https://doi.org/10.1007/s00397-016-0985-9	journal	January 2017
Parallel edge-based solution of viscoplastic flows with the SUPG/PSPG formulation Elias, Renato N.; Martins, Marcos A. D.; Coutinho, Alvaro L. G. A. Computational Mechanics, Vol. 38, Issue 4-5 https://doi.org/10.1007/s00466-005-0012-y	journal	December 2005
A finite-element method for incompressible non-Newtonian flows Bercovier, Michel; Engelman, Michael Journal of Computational Physics, Vol. 36, Issue 3 https://doi.org/10.1016/0021-9991(80)90163-1	journal	July 1980
High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method Ghia, U.; Ghia, K. N.; Shin, C. T. Journal of Computational Physics, Vol. 48, Issue 3 https://doi.org/10.1016/0021-9991(82)90058-4	journal	December 1982
On creeping drag flow of a viscoplastic fluid past a circular cylinder: wall effects Mitsoulis, Evan Chemical Engineering Science, Vol. 59, Issue 4 https://doi.org/10.1016/j.ces.2003.09.041	journal	February 2004
Analysis of semi-staggered finite-difference method with application to Bingham flows Olshanskii, Maxim A. Computer Methods in Applied Mechanics and Engineering, Vol. 198, Issue 9-12 https://doi.org/10.1016/j.cma.2008.11.010	journal	February 2009
Advances in the simulation of viscoplastic fluid flows using interior-point methods Bleyer, Jeremy Computer Methods in Applied Mechanics and Engineering, Vol. 330 https://doi.org/10.1016/j.cma.2017.11.006	journal	March 2018
On the numerical simulation of Bingham visco-plastic flow: Old and new results Dean, Edward J.; Glowinski, Roland; Guidoboni, Giovanna Journal of Non-Newtonian Fluid Mechanics, Vol. 142, Issue 1-3 https://doi.org/10.1016/j.jnnfm.2006.09.002	journal	March 2007
Dimensionless non-Newtonian fluid mechanics de Souza Mendes, Paulo R. Journal of Non-Newtonian Fluid Mechanics, Vol. 147, Issue 1-2 https://doi.org/10.1016/j.jnnfm.2007.07.010	journal	November 2007
Multiple-relaxation-time lattice Boltzmann model for generalized Newtonian fluid flows Chai, Zhenhua; Shi, Baochang; Guo, Zhaoli Journal of Non-Newtonian Fluid Mechanics, Vol. 166, Issue 5-6 https://doi.org/10.1016/j.jnnfm.2011.01.002	journal	March 2011
Incomplete fluid–fluid displacement of yield stress fluids in near-horizontal pipes: Experiments and theory Taghavi, S. M.; Alba, K.; Moyers-Gonzalez, M. Journal of Non-Newtonian Fluid Mechanics, Vol. 167-168 https://doi.org/10.1016/j.jnnfm.2011.10.004	journal	January 2012
Solution of the square lid-driven cavity flow of a Bingham plastic using the finite volume method Syrakos, Alexandros; Georgiou, Georgios C.; Alexandrou, Andreas N. Journal of Non-Newtonian Fluid Mechanics, Vol. 195 https://doi.org/10.1016/j.jnnfm.2012.12.008	journal	May 2013
Performance of the finite volume method in solving regularised Bingham flows: Inertia effects in the lid-driven cavity flow Syrakos, Alexandros; Georgiou, Georgios C.; Alexandrou, Andreas N. Journal of Non-Newtonian Fluid Mechanics, Vol. 208-209 https://doi.org/10.1016/j.jnnfm.2014.03.004	journal	June 2014
Non-Newtonian effects in simulations of coronary arterial blood flow Apostolidis, Alex J.; Moyer, Adam P.; Beris, Antony N. Journal of Non-Newtonian Fluid Mechanics, Vol. 233 https://doi.org/10.1016/j.jnnfm.2016.03.008	journal	July 2016
Viscoplastic dimensionless numbers Thompson, Roney L.; Soares, Edson J. Journal of Non-Newtonian Fluid Mechanics, Vol. 238 https://doi.org/10.1016/j.jnnfm.2016.05.001	journal	December 2016
An accelerated dual proximal gradient method for applications in viscoplasticity Treskatis, Timm; Moyers-González, Miguel A.; Price, Chris J. Journal of Non-Newtonian Fluid Mechanics, Vol. 238 https://doi.org/10.1016/j.jnnfm.2016.09.004	journal	December 2016
The PAL (Penalized Augmented Lagrangian) method for computing viscoplastic flows: A new fast converging scheme Dimakopoulos, Y.; Makrigiorgos, G.; Georgiou, G. C. Journal of Non-Newtonian Fluid Mechanics, Vol. 256 https://doi.org/10.1016/j.jnnfm.2018.03.009	journal	June 2018
A survey of high level frameworks in block-structured adaptive mesh refinement packages Dubey, Anshu; Almgren, Ann; Bell, John Journal of Parallel and Distributed Computing, Vol. 74, Issue 12 https://doi.org/10.1016/j.jpdc.2014.07.001	journal	December 2014
HACC: Simulating sky surveys on state-of-the-art supercomputing architectures Habib, Salman; Pope, Adrian; Finkel, Hal New Astronomy, Vol. 42 https://doi.org/10.1016/j.newast.2015.06.003	journal	January 2016
Laminar unsteady flows of Bingham fluids: a numerical strategy and some benchmark results Vola, D.; Boscardin, L.; Latché, J. C. Journal of Computational Physics, Vol. 187, Issue 2 https://doi.org/10.1016/s0021-9991(03)00118-9	journal	May 2003
An adaptive finite element method for viscoplastic fluid flows in pipes Saramito, Pierre; Roquet, Nicolas Computer Methods in Applied Mechanics and Engineering, Vol. 190, Issue 40-41 https://doi.org/10.1016/s0045-7825(01)00175-x	journal	July 2001
Viscoplastic flow around a cylinder kept between parallel plates Zisis, Th; Mitsoulis, E. Journal of Non-Newtonian Fluid Mechanics, Vol. 105, Issue 1 https://doi.org/10.1016/s0377-0257(02)00025-3	journal	July 2002
Transient displacement of a viscoplastic material by air in straight and suddenly constricted tubes Dimakopoulos, Yannis; Tsamopoulos, John Journal of Non-Newtonian Fluid Mechanics, Vol. 112, Issue 1 https://doi.org/10.1016/s0377-0257(03)00060-0	journal	May 2003
Interactions of two rigid spheres translating collinearly in creeping flow in a Bingham material Liu, Benjamin T.; Muller, Susan J.; Denn, Morton M. Journal of Non-Newtonian Fluid Mechanics, Vol. 113, Issue 1 https://doi.org/10.1016/s0377-0257(03)00111-3	journal	July 2003
The yield stress—a review or ‘παντα ρει’—everything flows? Barnes, Howard A. Journal of Non-Newtonian Fluid Mechanics, Vol. 81, Issue 1-2 https://doi.org/10.1016/s0377-0257(98)00094-9	journal	February 1999
Locomotion over a viscoplastic film Pegler, Samuel S.; Balmforth, Neil J. Journal of Fluid Mechanics, Vol. 727 https://doi.org/10.1017/jfm.2013.224	journal	June 2013
Analysis of von Kármán’s swirling flow on a rotating disc in Bingham fluids Guha, Abhijit; Sengupta, Sayantan Physics of Fluids, Vol. 28, Issue 1 https://doi.org/10.1063/1.4937590	journal	January 2016
The rising motion of spheres in structured fluids with yield stress Mirzaagha, S.; Pasquino, R.; Iuliano, E. Physics of Fluids, Vol. 29, Issue 9 https://doi.org/10.1063/1.4998740	journal	September 2017
An Adaptive Projection Method for Unsteady, Low-Mach Number Combustion Pember, R. B.; Howell, L. H.; Bell, J. B. Combustion Science and Technology, Vol. 140, Issue 1-6 https://doi.org/10.1080/00102209808915770	journal	December 1998
Castro: a new Compressible Astrophysical Solver. i. Hydrodynamics and Self-Gravity Almgren, A. S.; Beckner, V. E.; Bell, J. B. The Astrophysical Journal, Vol. 715, Issue 2 https://doi.org/10.1088/0004-637x/715/2/1221	journal	May 2010
Nyx: A MASSIVELY PARALLEL AMR CODE FOR COMPUTATIONAL COSMOLOGY Almgren, Ann S.; Bell, John B.; Lijewski, Mike J. The Astrophysical Journal, Vol. 765, Issue 1 https://doi.org/10.1088/0004-637x/765/1/39	journal	February 2013
Numerical simulation of laminar reacting flows with complex chemistry Day, M. S.; Bell, J. B. Combustion Theory and Modelling, Vol. 4, Issue 4 https://doi.org/10.1088/1364-7830/4/4/309	journal	December 2000
Modeling of the blood rheology in steady-state shear flows Apostolidis, Alex J.; Beris, Antony N. Journal of Rheology, Vol. 58, Issue 3 https://doi.org/10.1122/1.4866296	journal	May 2014
Modeling of human blood rheology in transient shear flows Apostolidis, Alex J.; Armstrong, Matthew J.; Beris, Antony N. Journal of Rheology, Vol. 59, Issue 1 https://doi.org/10.1122/1.4904423	journal	January 2015
Flows of Materials with Yield Papanastasiou, Tasos C. Journal of Rheology, Vol. 31, Issue 5 https://doi.org/10.1122/1.549926	journal	July 1987
A Direct Eulerian MUSCL Scheme for Gas Dynamics Colella, Phillip SIAM Journal on Scientific and Statistical Computing, Vol. 6, Issue 1 https://doi.org/10.1137/0906009	journal	January 1985
A Numerical Method for the Incompressible Navier-Stokes Equations Based on an Approximate Projection Almgren, Ann S.; Bell, John B.; Szymczak, William G. SIAM Journal on Scientific Computing, Vol. 17, Issue 2 https://doi.org/10.1137/s1064827593244213	journal	March 1996
The FEniCS Project Version 1.5 Alnæs, Martin; Blechta, Jan; Hake, Johan University Library Heidelberg https://doi.org/10.11588/ans.2015.100.20553	text	January 2015
A Quantitative Model for the Adhesive Locomotion of The Terrestrial Slug, Ariolimax Columbianus Denny, Mark W. Journal of Experimental Biology, Vol. 91, Issue 1 https://doi.org/10.1242/jeb.91.1.195	journal	April 1981
HACC: Simulating Sky Surveys on State-of-the-Art Supercomputing Architectures Habib, Salman; Pope, Adrian; Finkel, Hal arXiv https://doi.org/10.48550/arxiv.1410.2805	text	January 2014
An Accelerated Dual Proximal Gradient Method for Applications in Viscoplasticity Treskatis, Timm; Moyers-Gonzalez, Miguel A.; Price, Chris J. arXiv https://doi.org/10.48550/arxiv.1509.05084	text	January 2015
Performance of the finite volume method in solving regularised Bingham flows: inertia effects in the lid-driven cavity flow Syrakos, Alexandros; Georgiou, Georgios C.; Alexandrou, Andreas N. arXiv https://doi.org/10.48550/arxiv.1605.00590	text	January 2016
An investigation of the laws of plastic flow Bingham, E. C. Bulletin of the Bureau of Standards, Vol. 13, Issue 2 https://doi.org/10.6028/bulletin.304	journal	August 1916

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