• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.6
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• pp.1179-1194
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• 1992

QUICKER scheme has several attractive properties. However, under highly convective conditions, it produces overshoots and possibly some oscillations on each side of steps in the dependent variable when the flow is convected at an angle oblique to the grid line. Fortunately, it is possible to modify the QUICKER scheme using non-linear and linear functional relationship. Details of the development of polynomial upwinding scheme are given in this paper, where it is seen that this non-linear scheme has also third order accuracy. This polynomial upwinding scheme is used as the basis for the SHARPER and SMARTER schemes. Another revised scheme was developed by partial modification of QUICKER scheme using CDS and UPWIND schemes(QUICKUP). These revised schemes are tested at the well known bench mark flows, Two-Dimensional Pure Convection Flows in Oblique-Step, Lid Driven Cavity Flows and Buoyancy Driven Cavity Flows. For pure convection oblique step flow test problem, QUICKUP, SMARTER and SHARPER schemes remain absolutely monotonic without overshoot and oscillation. QUICKUP scheme is more accurate than any other scheme in their relative accuracy. In high Reynolds number Lid Driven Cavity Flow, SMARTER and SHARPER schemes retain lower computational cost than QUICKER and QUICKUP schemes, but computed velocity values in the revised schemes produced less predicted values than QUICKER scheme which is strongly effected by overshoot and undershoot values. Also, in Buoyancy Driven Cavity Flow, SMARTER, SHARPER and QUICKUP schemes give acceptable results.