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.
International Journal of Numerical Methods for Heat & Fluid Flow – Emerald Publishing
Published: May 1, 1992
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