skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Abstract

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 consideredmore » 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.« less

Authors:
ORCiD logo [1]; ORCiD logo [1];  [2]
  1. Univ. of Cambridge (United Kingdom). Cavendish Lab.
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
Sponsoring Org.:
USDOE
OSTI Identifier:
1543883
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Fluids
Additional Journal Information:
Journal Volume: 30; Journal Issue: 9; Journal ID: ISSN 1070-6631
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; Mechanics; Physics

Citation Formats

Sverdrup, Knut, Nikiforakis, Nikolaos, and Almgren, Ann. Highly parallelisable simulations of time-dependent viscoplastic fluid flow with structured adaptive mesh refinement. United States: N. p., 2018. Web. doi:10.1063/1.5049202.
Sverdrup, Knut, Nikiforakis, Nikolaos, & Almgren, Ann. Highly parallelisable simulations of time-dependent viscoplastic fluid flow with structured adaptive mesh refinement. United States. doi:10.1063/1.5049202.
Sverdrup, Knut, Nikiforakis, Nikolaos, and Almgren, Ann. Tue . "Highly parallelisable simulations of time-dependent viscoplastic fluid flow with structured adaptive mesh refinement". United States. doi:10.1063/1.5049202. https://www.osti.gov/servlets/purl/1543883.
@article{osti_1543883,
title = {Highly parallelisable simulations of time-dependent viscoplastic fluid flow with structured adaptive mesh refinement},
author = {Sverdrup, Knut and Nikiforakis, Nikolaos and Almgren, Ann},
abstractNote = {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.},
doi = {10.1063/1.5049202},
journal = {Physics of Fluids},
number = 9,
volume = 30,
place = {United States},
year = {2018},
month = {9}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

A damped Newton algorithm for computing viscoplastic fluid flows
journal, December 2016


Bingham’s model in the oil and gas industry
journal, February 2017

  • Frigaard, Ian A.; Paso, Kristofer G.; de Souza Mendes, Paulo R.
  • Rheologica Acta, Vol. 56, Issue 3
  • DOI: 10.1007/s00397-017-0999-y

Viscoplastic dimensionless numbers
journal, December 2016


A survey of high level frameworks in block-structured adaptive mesh refinement packages
journal, December 2014

  • Dubey, Anshu; Almgren, Ann; Bell, John
  • Journal of Parallel and Distributed Computing, Vol. 74, Issue 12
  • DOI: 10.1016/j.jpdc.2014.07.001

A Cell-Centered Adaptive Projection Method for the Incompressible Euler Equations
journal, September 2000

  • Martin, Daniel F.; Colella, Phillip
  • Journal of Computational Physics, Vol. 163, Issue 2
  • DOI: 10.1006/jcph.2000.6575

Laminar unsteady flows of Bingham fluids: a numerical strategy and some benchmark results
journal, May 2003


On the numerical simulation of Bingham visco-plastic flow: Old and new results
journal, March 2007

  • Dean, Edward J.; Glowinski, Roland; Guidoboni, Giovanna
  • Journal of Non-Newtonian Fluid Mechanics, Vol. 142, Issue 1-3
  • DOI: 10.1016/j.jnnfm.2006.09.002

An Adaptive Projection Method for Unsteady, Low-Mach Number Combustion
journal, December 1998

  • Pember, R. B.; Howell, L. H.; Bell, J. B.
  • Combustion Science and Technology, Vol. 140, Issue 1-6
  • DOI: 10.1080/00102209808915770

Interactions of two rigid spheres translating collinearly in creeping flow in a Bingham material
journal, July 2003

  • Liu, Benjamin T.; Muller, Susan J.; Denn, Morton M.
  • Journal of Non-Newtonian Fluid Mechanics, Vol. 113, Issue 1
  • DOI: 10.1016/s0377-0257(03)00111-3

Modeling of the blood rheology in steady-state shear flows
journal, May 2014

  • Apostolidis, Alex J.; Beris, Antony N.
  • Journal of Rheology, Vol. 58, Issue 3
  • DOI: 10.1122/1.4866296

The yield stress—a review or ‘παντα ρει’—everything flows?
journal, February 1999


HACC: Simulating sky surveys on state-of-the-art supercomputing architectures
journal, January 2016


Flows of Materials with Yield
journal, July 1987

  • Papanastasiou, Tasos C.
  • Journal of Rheology, Vol. 31, Issue 5
  • DOI: 10.1122/1.549926

Performance of the finite volume method in solving regularised Bingham flows: Inertia effects in the lid-driven cavity flow
journal, June 2014

  • Syrakos, Alexandros; Georgiou, Georgios C.; Alexandrou, Andreas N.
  • Journal of Non-Newtonian Fluid Mechanics, Vol. 208-209
  • DOI: 10.1016/j.jnnfm.2014.03.004

The rising motion of spheres in structured fluids with yield stress
journal, September 2017

  • Mirzaagha, S.; Pasquino, R.; Iuliano, E.
  • Physics of Fluids, Vol. 29, Issue 9
  • DOI: 10.1063/1.4998740

The effect of cholesterol and triglycerides on the steady state shear rheology of blood
journal, December 2015


p-version least squares finite element formulation for two-dimensional, incompressible, non-Newtonian isothermal and non-isothermal fluid flow
journal, January 1994

  • Bell, Brent C.; Surana, Karan S.
  • International Journal for Numerical Methods in Fluids, Vol. 18, Issue 2
  • DOI: 10.1002/fld.1650180202

An adaptive finite element method for viscoplastic fluid flows in pipes
journal, July 2001

  • Saramito, Pierre; Roquet, Nicolas
  • Computer Methods in Applied Mechanics and Engineering, Vol. 190, Issue 40-41
  • DOI: 10.1016/s0045-7825(01)00175-x

On creeping drag flow of a viscoplastic fluid past a circular cylinder: wall effects
journal, February 2004


Parallel edge-based solution of viscoplastic flows with the SUPG/PSPG formulation
journal, December 2005

  • Elias, Renato N.; Martins, Marcos A. D.; Coutinho, Alvaro L. G. A.
  • Computational Mechanics, Vol. 38, Issue 4-5
  • DOI: 10.1007/s00466-005-0012-y

The PAL (Penalized Augmented Lagrangian) method for computing viscoplastic flows: A new fast converging scheme
journal, June 2018

  • Dimakopoulos, Y.; Makrigiorgos, G.; Georgiou, G. C.
  • Journal of Non-Newtonian Fluid Mechanics, Vol. 256
  • DOI: 10.1016/j.jnnfm.2018.03.009

Modeling of human blood rheology in transient shear flows
journal, January 2015

  • Apostolidis, Alex J.; Armstrong, Matthew J.; Beris, Antony N.
  • Journal of Rheology, Vol. 59, Issue 1
  • DOI: 10.1122/1.4904423

Non-Newtonian effects in simulations of coronary arterial blood flow
journal, July 2016

  • Apostolidis, Alex J.; Moyer, Adam P.; Beris, Antony N.
  • Journal of Non-Newtonian Fluid Mechanics, Vol. 233
  • DOI: 10.1016/j.jnnfm.2016.03.008

Dimensionless non-Newtonian fluid mechanics
journal, November 2007


Multiple-relaxation-time lattice Boltzmann model for generalized Newtonian fluid flows
journal, March 2011

  • Chai, Zhenhua; Shi, Baochang; Guo, Zhaoli
  • Journal of Non-Newtonian Fluid Mechanics, Vol. 166, Issue 5-6
  • DOI: 10.1016/j.jnnfm.2011.01.002

Cessation of the lid-driven cavity flow of Newtonian and Bingham fluids
journal, December 2015

  • Syrakos, Alexandros; Georgiou, Georgios C.; Alexandrou, Andreas N.
  • Rheologica Acta, Vol. 55, Issue 1
  • DOI: 10.1007/s00397-015-0893-4

Viscoplastic flow around a cylinder kept between parallel plates
journal, July 2002


Uzawa-like methods for numerical modeling of unsteady viscoplastic Bingham medium flows
journal, July 2015


An investigation of the laws of plastic flow
journal, August 1916


An accelerated dual proximal gradient method for applications in viscoplasticity
journal, December 2016

  • Treskatis, Timm; Moyers-González, Miguel A.; Price, Chris J.
  • Journal of Non-Newtonian Fluid Mechanics, Vol. 238
  • DOI: 10.1016/j.jnnfm.2016.09.004

A 3rd order upwind finite volume method for generalised Newtonian fluid flows
journal, October 2005


Incomplete fluid–fluid displacement of yield stress fluids in near-horizontal pipes: Experiments and theory
journal, January 2012

  • Taghavi, S. M.; Alba, K.; Moyers-Gonzalez, M.
  • Journal of Non-Newtonian Fluid Mechanics, Vol. 167-168
  • DOI: 10.1016/j.jnnfm.2011.10.004

Analysis of semi-staggered finite-difference method with application to Bingham flows
journal, February 2009

  • Olshanskii, Maxim A.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 198, Issue 9-12
  • DOI: 10.1016/j.cma.2008.11.010

A Direct Eulerian MUSCL Scheme for Gas Dynamics
journal, January 1985

  • Colella, Phillip
  • SIAM Journal on Scientific and Statistical Computing, Vol. 6, Issue 1
  • DOI: 10.1137/0906009

Solution of the square lid-driven cavity flow of a Bingham plastic using the finite volume method
journal, May 2013

  • Syrakos, Alexandros; Georgiou, Georgios C.; Alexandrou, Andreas N.
  • Journal of Non-Newtonian Fluid Mechanics, Vol. 195
  • DOI: 10.1016/j.jnnfm.2012.12.008

Analysis of von Kármán’s swirling flow on a rotating disc in Bingham fluids
journal, January 2016

  • Guha, Abhijit; Sengupta, Sayantan
  • Physics of Fluids, Vol. 28, Issue 1
  • DOI: 10.1063/1.4937590

Progress in numerical simulation of yield stress fluid flows
journal, January 2017


Locomotion over a viscoplastic film
journal, June 2013

  • Pegler, Samuel S.; Balmforth, Neil J.
  • Journal of Fluid Mechanics, Vol. 727
  • DOI: 10.1017/jfm.2013.224

A Conservative Adaptive Projection Method for the Variable Density Incompressible Navier–Stokes Equations
journal, May 1998

  • Almgren, Ann S.; Bell, John B.; Colella, Phillip
  • Journal of Computational Physics, Vol. 142, Issue 1
  • DOI: 10.1006/jcph.1998.5890

Transient displacement of a viscoplastic material by air in straight and suddenly constricted tubes
journal, May 2003


A finite-element method for incompressible non-Newtonian flows
journal, July 1980


Numerical simulations of complex yield-stress fluid flows
journal, December 2016


Advances in the simulation of viscoplastic fluid flows using interior-point methods
journal, March 2018


Yielding to Stress: Recent Developments in Viscoplastic Fluid Mechanics
journal, January 2014


Numerical simulation of laminar reacting flows with complex chemistry
journal, December 2000


High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
journal, December 1982


The FEniCS Project Version 1.5
text, January 2015