ASSESSMENT OF HIGHER-ORDER UPWIND SCHEMES INCORPORATING FCT FOR CONVECTION-DOMINATEDPROBLEMS

Abstract

A new generalized formulation is suggested for four-point discretization schemes on nonuniform grids. The central difference scheme, the QUICK scheme, and the second-order upwind scheme fall into this formulation. A second-order hybrid scheme is also presented on nonuniform grids. The unbounded behavior of the generalized formulation is examined. A flux-corrected transport algorithm is then applied to the above four schemes on a uniform grid. Four two-dimensional convection-dominated problems are used to test the schemes. Incorporation of flux-corrected transport (FCT) into the high-order schemes improves the solution accuracy greatly. The unmodified multidimensional FCT limiter is found to be unable to completely suppress the small-scale oscillation of a velocity component which has discontinuities in a direction normal to the advection.

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Yuguo Li

Address correspondence to Yuguo Li, Division Building, Construction, and Engineering, CSIRO, Graham Road, P.O. Box 56, Highett, Victoria 3190, Australia.