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A representation of curved boundaries for the solution of the Navier-Stokes equations on a staggered three-dimensional Cartesian grid

Citation

Kirkpatrick, MP and Armfield, SW and Kent, JH, A representation of curved boundaries for the solution of the Navier-Stokes equations on a staggered three-dimensional Cartesian grid, Journal of Computational Physics, 184, (1) pp. 1-36. ISSN 0021-9991 (2003) [Refereed Article]

DOI: doi:10.1016/S0021-9991(02)00013-X

Abstract

A method is presented for representing curved boundaries for the solution of the Navier-Stokes equations on a non-uniform, staggered, three-dimensional Cartesian grid. The approach involves truncating the Cartesian cells at the boundary surface to create new cells which conform to the shape of the surface. We discuss in some detail the problems unique to the development of a cut cell method on a staggered grid. Methods for calculating the fluxes through the boundary cell faces, for representing pressure forces and for calculating the wall shear stress are derived and it is verified that the new scheme retains second-order accuracy in space. In addition, a novel "cell-linking" method is developed which overcomes problems associated with the creation of small cells while avoiding the complexities involved with other cell-merging approaches. Techniques are presented for generating the geometric information required for the scheme based on the representation of the boundaries as quadric surfaces. The new method is tested for flow through a channel placed oblique to the grid and flow past a cylinder at Re = 40 and is shown to give significant improvement over a staircase boundary formulation. Finally, it is used to calculate unsteady flow past a hemispheric protuberance on a plate at a Reynolds number of 800. Good agreement is obtained with experimental results for this flow. © 2002 Elsevier Science B.V. All rights reserved.

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Numerical and Computational Mathematics
Research Field:Numerical Analysis
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Kirkpatrick, MP (Dr Michael Kirkpatrick)
ID Code:34542
Year Published:2003
Web of Science® Times Cited:89
Deposited By:Engineering
Deposited On:2005-08-01
Last Modified:2005-08-01
Downloads:0

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