Start-up flow in a three-dimensional lid-driven cavity by means of a massively parallel direction splitting algorithm

SUMMARY The purpose of this paper is to validate a new highly parallelizable direction splitting algorithm. The parallelization capabilities of this algorithm are illustrated by providing a highly accurate solution for the start‐up flow in a three‐dimensional impulsively started lid‐driven cavity of...

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Published inInternational journal for numerical methods in fluids Vol. 68; no. 7; pp. 856 - 871
Main Authors Guermond, J. L., Minev, P. D.
Format Journal Article
LanguageEnglish
Published Chichester, UK John Wiley & Sons, Ltd 10.03.2012
Wiley
Subjects
Computational methods in fluid dynamics
direction splitting
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
incompressible flow
Laminar flows
Laminar flows in cavities
lid-driven cavity
MAC stencil
parallel algorithm
Physics
three dimensional
unsteady flow
three dimensional
Computational fluid dynamics
incompressible flow
Digital simulation
parallel algorithm
direction splitting
Velocity distribution
lid-driven cavity
unsteady flow
Parallel algorithms
Cavity flow
Moving wall
Three dimensional flow
MAC stencil
Modelling
Incompressible fluid
Mesh generation
Online AccessGet full text
ISSN0271-2091
1097-0363
DOI10.1002/fld.2583

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Abstract SUMMARY The purpose of this paper is to validate a new highly parallelizable direction splitting algorithm. The parallelization capabilities of this algorithm are illustrated by providing a highly accurate solution for the start‐up flow in a three‐dimensional impulsively started lid‐driven cavity of aspect ratio 1 × 1 × 2 at Reynolds numbers 1000 and 5000. The computations are done in parallel (up to 1024 processors) on adapted grids of up to 2 billion nodes in three space dimensions. Velocity profiles are given at dimensionless times t = 4, 8, and 12; at least four digits are expected to be correct at Re = 1000. Copyright © 2011 John Wiley & Sons, Ltd.
AbstractList The purpose of this paper is to validate a new highly parallelizable direction splitting algorithm. The parallelization capabilities of this algorithm are illustrated by providing a highly accurate solution for the start‐up flow in a three‐dimensional impulsively started lid‐driven cavity of aspect ratio 1 × 1 × 2 at Reynolds numbers 1000 and 5000. The computations are done in parallel (up to 1024 processors) on adapted grids of up to 2 billion nodes in three space dimensions. Velocity profiles are given at dimensionless times t  = 4, 8, and 12; at least four digits are expected to be correct at Re  = 1000. Copyright © 2011 John Wiley & Sons, Ltd.
SUMMARY The purpose of this paper is to validate a new highly parallelizable direction splitting algorithm. The parallelization capabilities of this algorithm are illustrated by providing a highly accurate solution for the start‐up flow in a three‐dimensional impulsively started lid‐driven cavity of aspect ratio 1 × 1 × 2 at Reynolds numbers 1000 and 5000. The computations are done in parallel (up to 1024 processors) on adapted grids of up to 2 billion nodes in three space dimensions. Velocity profiles are given at dimensionless times t = 4, 8, and 12; at least four digits are expected to be correct at Re = 1000. Copyright © 2011 John Wiley & Sons, Ltd.
Author Guermond, J. L.
Minev, P. D.
Author_xml – sequence: 1
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  surname: Guermond
  fullname: Guermond, J. L.
  email: guermond@math.tamu.edu, Jean L. Guermond, Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA., guermond@math.tamu.edu
  organization: Department of Mathematics, Texas A&M University, TX, 77843-3368, College Station, USA
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  givenname: P. D.
  surname: Minev
  fullname: Minev, P. D.
  organization: Department of Mathematical and Statistical Sciences, University of Alberta, Alberta, T6G 2G1, Edmonton, Canada
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Cites_doi 10.1006/jcph.2002.7145
10.1002/fld.953
10.1016/j.cma.2011.02.007
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10.1016/j.compfluid.2004.12.004
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10.1016/0021-9991(82)90058-4
10.1016/j.crma.2010.03.009
10.1146/annurev.fluid.32.1.93
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Keywords three dimensional
Computational fluid dynamics
incompressible flow
Digital simulation
parallel algorithm
direction splitting
Velocity distribution
lid-driven cavity
unsteady flow
Parallel algorithms
Cavity flow
Moving wall
Three dimensional flow
MAC stencil
Modelling
Incompressible fluid
Mesh generation
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References Albensoeder S, Kuhlmann HC. Accurate three-dimensional lid-driven cavity flow. Journal of Computational Physics 2005; 206:536-558.
Tang L, Cheng T, Tsang T. Transient solution for three-dimensional lid-driven cavity flows by a least-squares finite element method. International Journal Numerical Methods in Fluids 1995; 21:413-432.
Douglas J Jr. Alternating direction methods for three space variables. Numerische Mathematik 1962; 4:41-63.
Baragy E, Carey GF. Stream function-vorticity driven cavity solutions using p finite elements. Computers & Fluids 1997; 26:453-468.
Shankar PN, Deshpande MD. Fluid mechanics in the driven cavity. Annual Review of Fluid Mechanics 2000; 32:93-136.
Botella O, Peyret R. Benchmark spectral results on the lid-driven cavity flow. Computers & Fluids 1998; 27(4):421-433.
Guermond JL, Shen J. On the error estimates for the rotational pressure-correction projection methods. Mathethamatics of Computation 2004; 73(248):1719-1737 (electronic).
Ramanan N, Homsy GM. Linear stability of lid-driven cavity flow. Physics of Fluids 1994; 6:2690-2701.
Auteri F, Parolini N, Quartapelle L. Numerical investigation on the stability of singular driven cavity flow. Journal of Computational Physics 2002; 183:1-25.
Bruneau C-H, Saad M. The 2D lid-driven cavity problem revisited. Computers & Fluids 2006; 35:326-348.
Guermond JL, Shen J. Velocity-correction projection methods for incompressible flows. SIAM Journal on Numerical Analysis 2003; 41(1):112-134.
Guermond J-L, Minev PD. A new class of fractional step techniques for the incompressible Navier-Stokes equations using direction splitting. Comptes Rendus Mathematique 2010; 348:581-585.
Ghia U, Ghia KN, Shin CT. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of Computational Physics 1982; 48(3):387-411.
Erturk E, Corke TC, Gokcol C. Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers. International Journal for Numerical Methods in Fluids 2005; 48:747-774.
Guermond J-L, Minev PD. A new class of splitting methods for the incompressible Navier-Stokes equations using direction splitting. Computer Methods in Applied Mechanics and Engineering 2011; 200:2083-2093.
Guermond J-L, Migeon C, Pineau G, Quartapelle L. Start-up flows in a three-dimensional rectangular driven cavity of aspect ratio 1:1:2 at Re = 1000. Journal of Fluid Mechanics 2002; 450:169-199.
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References_xml – reference: Bruneau C-H, Saad M. The 2D lid-driven cavity problem revisited. Computers & Fluids 2006; 35:326-348.
– reference: Guermond J-L, Minev PD. A new class of splitting methods for the incompressible Navier-Stokes equations using direction splitting. Computer Methods in Applied Mechanics and Engineering 2011; 200:2083-2093.
– reference: Ghia U, Ghia KN, Shin CT. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of Computational Physics 1982; 48(3):387-411.
– reference: Erturk E, Corke TC, Gokcol C. Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers. International Journal for Numerical Methods in Fluids 2005; 48:747-774.
– reference: Tang L, Cheng T, Tsang T. Transient solution for three-dimensional lid-driven cavity flows by a least-squares finite element method. International Journal Numerical Methods in Fluids 1995; 21:413-432.
– reference: Shankar PN, Deshpande MD. Fluid mechanics in the driven cavity. Annual Review of Fluid Mechanics 2000; 32:93-136.
– reference: Baragy E, Carey GF. Stream function-vorticity driven cavity solutions using p finite elements. Computers & Fluids 1997; 26:453-468.
– reference: Auteri F, Parolini N, Quartapelle L. Numerical investigation on the stability of singular driven cavity flow. Journal of Computational Physics 2002; 183:1-25.
– reference: Botella O, Peyret R. Benchmark spectral results on the lid-driven cavity flow. Computers & Fluids 1998; 27(4):421-433.
– reference: Albensoeder S, Kuhlmann HC. Accurate three-dimensional lid-driven cavity flow. Journal of Computational Physics 2005; 206:536-558.
– reference: Douglas J Jr. Alternating direction methods for three space variables. Numerische Mathematik 1962; 4:41-63.
– reference: Guermond J-L, Minev PD. A new class of fractional step techniques for the incompressible Navier-Stokes equations using direction splitting. Comptes Rendus Mathematique 2010; 348:581-585.
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– volume: 450
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  year: 2002
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  article-title: Start‐up flows in a three‐dimensional rectangular driven cavity of aspect ratio 1:1:2 at  = 1000
  publication-title: Journal of Fluid Mechanics
– volume: 26
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  year: 1997
  end-page: 468
  article-title: Stream function-vorticity driven cavity solutions using finite elements
  publication-title: Computers & Fluids
– volume: 41
  start-page: 112
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  article-title: Velocity‐correction projection methods for incompressible flows
  publication-title: SIAM Journal on Numerical Analysis
– volume: 206
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  article-title: Accurate three‐dimensional lid‐driven cavity flow
  publication-title: Journal of Computational Physics
– volume: 27
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  end-page: 585
  article-title: A new class of fractional step techniques for the incompressible Navier–Stokes equations using direction splitting
  publication-title: Comptes Rendus Mathematique
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  publication-title: Computers & Fluids
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  year: 2002
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  article-title: Numerical investigation on the stability of singular driven cavity flow
  publication-title: Journal of Computational Physics
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  issue: 3
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  publication-title: Journal of Computational Physics
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  start-page: 747
  year: 2005
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Snippet SUMMARY The purpose of this paper is to validate a new highly parallelizable direction splitting algorithm. The parallelization capabilities of this algorithm...
The purpose of this paper is to validate a new highly parallelizable direction splitting algorithm. The parallelization capabilities of this algorithm are...
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StartPage 856
SubjectTerms Computational methods in fluid dynamics
direction splitting
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
incompressible flow
Laminar flows
Laminar flows in cavities
lid-driven cavity
MAC stencil
parallel algorithm
Physics
three dimensional
unsteady flow
Title Start-up flow in a three-dimensional lid-driven cavity by means of a massively parallel direction splitting algorithm
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