A convectively stable, third-order accurate finite-difference method for steady two-dimensional flow and heat transfer

The QUICK 2D method is applied to a vorticity-streamfunction formulation of the Navier-Stokes equation and to the simulation of scalar (mass or thermal) transport in steady two-dimensional flow. High-convection numerical stability is achieved by using an upstream bias in the convective terms. However, because the modelled convection is third-order accurate, stabilization is achieved without sacrificing accuracy - truncation error terms are equivalent to an added fourth-derivative in the transport equation, thus allowing accurate modelling of both convection and diffusion on practical grids. The explicit algorithm is similar to flux formulations of second-order schemes but with the addition of stabilizing upstream-weighted normal curvature terms and a small transverse curvature term in estimating control-volume face values. Consistent modelling of gradients is equivalent to that of second-order schemes. Results are presented for laminar driven cavity flows for a range of Reynolds and Peclet numbers.