A novel fully implicit finite volume method applied to the lid-driven cavity problem-Part I: High Reynolds number flow calculations

A novel implicit cell‐vertex finite volume method is described for the solution of the Navier–Stokes equations at high Reynolds numbers. The key idea is the elimination of the pressure term from the momentum equation by multiplying the momentum equation with the unit normal vector to a control volum...

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Published in:	International journal for numerical methods in fluids Vol. 42; no. 1; pp. 57 - 77
Main Authors:	Sahin, Mehmet, Owens, Robert G.
Format:	Journal Article
Language:	English
Published:	Chichester, UK John Wiley & Sons, Ltd 10.05.2003 Wiley
Subjects:	Computational methods in fluid dynamics direct solver Exact sciences and technology Fluid dynamics Fundamental areas of phenomenology (including applications) high Reynolds numbers implicit finite volume methods Laminar flows Laminar flows in cavities lid-driven cavity flow Physics Large Reynolds number Streamlines Computational fluid dynamics Digital simulation Vorticity Velocity distribution Unsteady flow Incompressible fluid Cavity flow Mesh generation Finite volume methods Moving wall
ISSN:	0271-2091, 1097-0363
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Abstract	A novel implicit cell‐vertex finite volume method is described for the solution of the Navier–Stokes equations at high Reynolds numbers. The key idea is the elimination of the pressure term from the momentum equation by multiplying the momentum equation with the unit normal vector to a control volume boundary and integrating thereafter around this boundary. The resulting equations are expressed solely in terms of the velocity components. Thus any difficulties with pressure or vorticity boundary conditions are circumvented and the number of primary variables that need to be determined equals the number of space dimensions. The method is applied to both the steady and unsteady two‐dimensional lid‐driven cavity problem at Reynolds numbers up to 10000. Results are compared with those in the literature and show excellent agreement. Copyright © 2003 John Wiley & Sons, Ltd.
AbstractList	A novel implicit cell‐vertex finite volume method is described for the solution of the Navier–Stokes equations at high Reynolds numbers. The key idea is the elimination of the pressure term from the momentum equation by multiplying the momentum equation with the unit normal vector to a control volume boundary and integrating thereafter around this boundary. The resulting equations are expressed solely in terms of the velocity components. Thus any difficulties with pressure or vorticity boundary conditions are circumvented and the number of primary variables that need to be determined equals the number of space dimensions. The method is applied to both the steady and unsteady two‐dimensional lid‐driven cavity problem at Reynolds numbers up to 10000. Results are compared with those in the literature and show excellent agreement. Copyright © 2003 John Wiley & Sons, Ltd.
Author	Owens, Robert G. Sahin, Mehmet
Author_xml	– sequence: 1 givenname: Mehmet surname: Sahin fullname: Sahin, Mehmet organization: FSTI-ISE-LMF, Ecole Polytechnique Fédérale de Lausanne, CH 1015 Lausanne, Switzerland – sequence: 2 givenname: Robert G. surname: Owens fullname: Owens, Robert G. email: robert.owens@epfl.ch organization: FSTI-ISE-LMF, Ecole Polytechnique Fédérale de Lausanne, CH 1015 Lausanne, Switzerland
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Keywords	Large Reynolds number Streamlines Computational fluid dynamics Digital simulation Vorticity Velocity distribution Unsteady flow Incompressible fluid Cavity flow Mesh generation Finite volume methods Moving wall
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Math. Anal. Numér. doi: 10.1051/m2an/1994280606991
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Snippet	A novel implicit cell‐vertex finite volume method is described for the solution of the Navier–Stokes equations at high Reynolds numbers. The key idea is the...
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SubjectTerms	Computational methods in fluid dynamics direct solver Exact sciences and technology Fluid dynamics Fundamental areas of phenomenology (including applications) high Reynolds numbers implicit finite volume methods Laminar flows Laminar flows in cavities lid-driven cavity flow Physics
Title	A novel fully implicit finite volume method applied to the lid-driven cavity problem-Part I: High Reynolds number flow calculations
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