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ULTRASHARP SOLUTION OF THE SMITHHUTTON PROBLEM

ULTRASHARP SOLUTION OF THE SMITHHUTTON PROBLEM In 1982, Smith and Hutton published comparative results of several different convectiondiffusion schemes applied to a specially devised test problem involving neardiscontinuities and strong streamline curvature. Firstorder methods showed significant artificial diffusion, whereas higherorder methods gave less smearing but had a tendency to overshoot and oscillate. Perhaps because unphysical oscillations are more obvious than unphysical smearing, the intervening period has seen a rise in popularity of loworder artificially diffusive schemes, especially in the numerical heattransfer industry. This paper presents an alternative strategy of using nonartificially diffusive higherorder methods, while maintaining strictly monotonic transitions through the use of simple fluxlimiter constraints. Limited thirdorder upwinding is usually found to be the most costeffective basic convection scheme. Tighter resolution of discontinuities can be obtained at little additional cost by using automatic adaptive stencil expansion to higher order in local regions, as needed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Numerical Methods for Heat & Fluid Flow Emerald Publishing

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Publisher
Emerald Publishing
Copyright
Copyright © Emerald Group Publishing Limited
ISSN
0961-5539
DOI
10.1108/eb017502
Publisher site
See Article on Publisher Site

Abstract

In 1982, Smith and Hutton published comparative results of several different convectiondiffusion schemes applied to a specially devised test problem involving neardiscontinuities and strong streamline curvature. Firstorder methods showed significant artificial diffusion, whereas higherorder methods gave less smearing but had a tendency to overshoot and oscillate. Perhaps because unphysical oscillations are more obvious than unphysical smearing, the intervening period has seen a rise in popularity of loworder artificially diffusive schemes, especially in the numerical heattransfer industry. This paper presents an alternative strategy of using nonartificially diffusive higherorder methods, while maintaining strictly monotonic transitions through the use of simple fluxlimiter constraints. Limited thirdorder upwinding is usually found to be the most costeffective basic convection scheme. Tighter resolution of discontinuities can be obtained at little additional cost by using automatic adaptive stencil expansion to higher order in local regions, as needed.

Journal

International Journal of Numerical Methods for Heat & Fluid FlowEmerald Publishing

Published: May 1, 1992

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