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Critical Evaluation of Four Differencing Schemes for A Steady Convection-Diffusion Problem

Author Affiliations

  • 1Department of Mathematics, Maharaja Agrasen Institute of Technology, Delhi, India

Res. J. Mathematical & Statistical Sci., Volume 4, Issue (2), Pages 6-12, March,12 (2016)

Abstract

A steady convection diffusion problem is taken to compare the behavior and accuracy of four discretization schemes namely, Central Differencing Scheme, Upwind Differencing scheme, Hybrid Differencing Scheme and QUICK scheme. This well-known problem is solved numerically and solutions are discussed graphically. It is known that false diffusion arises in multidimensional flow problems only. Hence discretization errors may be investigated only in one-dimensional problems. Thus, the model taken to compare four schemes is a one dimensional flow model. It is validated that central differencing scheme give fairly good results for small Peclet number only, whereas upwind differencing scheme may be used for both large and small Peclet number. Hybrid scheme gives better results than QUICK scheme which works very well with large Peclet number but not for small Peclet number.

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