A semi-staggered dilation-free finite volume method for the numerical solution of viscoelastic fluid flows on all-hexahedral elements

Mehmet Sahin; Helen J. Wilson

doi:10.1016/j.jnnfm.2007.06.008

A semi-staggered dilation-free finite volume method for the numerical solution of viscoelastic fluid flows on all-hexahedral elements

Mehmet Sahin^*, Helen J. Wilson

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

37 Citations (Scopus)

Abstract

The dilation-free semi-staggered finite volume method presented in Sahin [M. Sahin, A preconditioned semi-staggered dilation-free finite volume method for the incompressible Navier-Stokes equations on all-hexahedral elements, Int. J. Numer. Methods Fluids 49 (2005) 959-974] has been extended for the numerical solution of viscoelastic fluid flows on all-quadrilateral (2D) / hexahedral (3D) meshes. The velocity components are defined at element node points, while the pressure term and the extra stress tensor are defined at element centroids. The continuity equation is satisfied exactly within each element. An upwind least square method is employed for the calculation of the extra stresses at control volume faces in order to maintain stability for hyperbolic constitutive equations. The time stepping algorithm used decouples the calculation of the extra stresses from the evaluation of the velocity and pressure fields by solving a generalised Stokes problem. The resulting linear systems are solved using the GMRES method provided by the PETSc library with an ILU(k) preconditioner obtained from the HYPRE library. We apply the method to both two- and three-dimensional flow of an Oldroyd-B fluid past a confined circular cylinder in a channel with blockage ratio 0.5. Crown

Original language	English
Pages (from-to)	79-91
Number of pages	13
Journal	Journal of Non-Newtonian Fluid Mechanics
Volume	147
Issue number	1-2
DOIs	https://doi.org/10.1016/j.jnnfm.2007.06.008
Publication status	Published - 15 Nov 2007
Externally published	Yes

Funding

This work was supported in part by EPSRC Grant GR/T11807/01. The authors acknowledge the use of UCL Research Computing facilities (Altix) and the EPFL Pleiades Linux Cluster.

Funders	Funder number
Engineering and Physical Sciences Research Council	GR/T11807/01

Keywords

Finite volume
Iterative methods
Three-dimensional
Unstructured methods
Viscoelastic fluid flow

Access to Document

10.1016/j.jnnfm.2007.06.008

Cite this

@article{a8ae927f6858408a9285412c35373dc8,

title = "A semi-staggered dilation-free finite volume method for the numerical solution of viscoelastic fluid flows on all-hexahedral elements",

abstract = "The dilation-free semi-staggered finite volume method presented in Sahin [M. Sahin, A preconditioned semi-staggered dilation-free finite volume method for the incompressible Navier-Stokes equations on all-hexahedral elements, Int. J. Numer. Methods Fluids 49 (2005) 959-974] has been extended for the numerical solution of viscoelastic fluid flows on all-quadrilateral (2D) / hexahedral (3D) meshes. The velocity components are defined at element node points, while the pressure term and the extra stress tensor are defined at element centroids. The continuity equation is satisfied exactly within each element. An upwind least square method is employed for the calculation of the extra stresses at control volume faces in order to maintain stability for hyperbolic constitutive equations. The time stepping algorithm used decouples the calculation of the extra stresses from the evaluation of the velocity and pressure fields by solving a generalised Stokes problem. The resulting linear systems are solved using the GMRES method provided by the PETSc library with an ILU(k) preconditioner obtained from the HYPRE library. We apply the method to both two- and three-dimensional flow of an Oldroyd-B fluid past a confined circular cylinder in a channel with blockage ratio 0.5. Crown",

keywords = "Finite volume, Iterative methods, Three-dimensional, Unstructured methods, Viscoelastic fluid flow",

author = "Mehmet Sahin and Wilson, {Helen J.}",

year = "2007",

month = nov,

day = "15",

doi = "10.1016/j.jnnfm.2007.06.008",

language = "English",

volume = "147",

pages = "79--91",

journal = "Journal of Non-Newtonian Fluid Mechanics",

issn = "0377-0257",

publisher = "Elsevier B.V.",

number = "1-2",

}

TY - JOUR

T1 - A semi-staggered dilation-free finite volume method for the numerical solution of viscoelastic fluid flows on all-hexahedral elements

AU - Sahin, Mehmet

AU - Wilson, Helen J.

PY - 2007/11/15

Y1 - 2007/11/15

N2 - The dilation-free semi-staggered finite volume method presented in Sahin [M. Sahin, A preconditioned semi-staggered dilation-free finite volume method for the incompressible Navier-Stokes equations on all-hexahedral elements, Int. J. Numer. Methods Fluids 49 (2005) 959-974] has been extended for the numerical solution of viscoelastic fluid flows on all-quadrilateral (2D) / hexahedral (3D) meshes. The velocity components are defined at element node points, while the pressure term and the extra stress tensor are defined at element centroids. The continuity equation is satisfied exactly within each element. An upwind least square method is employed for the calculation of the extra stresses at control volume faces in order to maintain stability for hyperbolic constitutive equations. The time stepping algorithm used decouples the calculation of the extra stresses from the evaluation of the velocity and pressure fields by solving a generalised Stokes problem. The resulting linear systems are solved using the GMRES method provided by the PETSc library with an ILU(k) preconditioner obtained from the HYPRE library. We apply the method to both two- and three-dimensional flow of an Oldroyd-B fluid past a confined circular cylinder in a channel with blockage ratio 0.5. Crown

AB - The dilation-free semi-staggered finite volume method presented in Sahin [M. Sahin, A preconditioned semi-staggered dilation-free finite volume method for the incompressible Navier-Stokes equations on all-hexahedral elements, Int. J. Numer. Methods Fluids 49 (2005) 959-974] has been extended for the numerical solution of viscoelastic fluid flows on all-quadrilateral (2D) / hexahedral (3D) meshes. The velocity components are defined at element node points, while the pressure term and the extra stress tensor are defined at element centroids. The continuity equation is satisfied exactly within each element. An upwind least square method is employed for the calculation of the extra stresses at control volume faces in order to maintain stability for hyperbolic constitutive equations. The time stepping algorithm used decouples the calculation of the extra stresses from the evaluation of the velocity and pressure fields by solving a generalised Stokes problem. The resulting linear systems are solved using the GMRES method provided by the PETSc library with an ILU(k) preconditioner obtained from the HYPRE library. We apply the method to both two- and three-dimensional flow of an Oldroyd-B fluid past a confined circular cylinder in a channel with blockage ratio 0.5. Crown

KW - Finite volume

KW - Iterative methods

KW - Three-dimensional

KW - Unstructured methods

KW - Viscoelastic fluid flow

UR - http://www.scopus.com/inward/record.url?scp=35348837291&partnerID=8YFLogxK

U2 - 10.1016/j.jnnfm.2007.06.008

DO - 10.1016/j.jnnfm.2007.06.008

M3 - Article

AN - SCOPUS:35348837291

SN - 0377-0257

VL - 147

SP - 79

EP - 91

JO - Journal of Non-Newtonian Fluid Mechanics

JF - Journal of Non-Newtonian Fluid Mechanics

IS - 1-2

ER -

A semi-staggered dilation-free finite volume method for the numerical solution of viscoelastic fluid flows on all-hexahedral elements

Abstract

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this