An assessment of flow oriented schemes for reducing ‘false diffusion’

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Abstract
An important limiting factor in the accurate modelling of fluid flow problems is the numerical representation of the convection terms in the Navier‐Stokes equations. This paper reviews several approaches used to approximate the convection terms and reduce the so‐called false‐diffusion errors, within the context of finite‐difference and finite‐volume methods. Numerical errors are characterized as those due to discretization of the differential terms and those due to the influence of the multidimensional nature of the flow. Necessary criteria are identified which a numerical scheme must satisfy, if it is to be a candidate, at least in terms of accuracy and practicality, for the successful solution of the Navier‐Stokes equations. One of the criteria is the need of the scheme to account explicitly for the multidimensionality of the flow in the transport of scalar variables. All schemes except Raithby's SKEW approximation are deficient in this respect. However, the SKEW scheme does not satisfy some of the other criteria and does not always perform well. A new scheme called CUPID (Corner UPwInDing), which is based on the ideas of the SKEW scheme, yet obeys more of the criteria identified above, is described. The scheme is tested on a series of discriminating test problems which, the authors contend, demonstrate its potential for practical use in solving accurately the Navier‐Stokes equations.

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