Studies in numerical computations of recirculating flows

This paper considers the use of various finite differencing schemes for the computation of flows involving regions of recirculation. Standard first-order hybrid schemes, vector (or skew) schemes and second-order schemes are used to predict laminar flows in a channel containing a constriction and over a normal flat plate with a downstream splitter plate. In the former case the results are compared with those of other workers and with the implications of analytic theories for the viscous dominated flow around the sharp corner. Attention is concentrated on the effects of errors arising from the use of non-uniform grids and it is shown that higher-order differencing schemes are generally much less susceptible to these than the simpler schemes. The major conclusion is that for flows containing regions where pressure gradients largely balance the convective terms in the momentum equations, in addition to other regions where convection and diffusion balance, higher order differencing schemes are likely to be essential if accurate predictions are required on grids without excessive numbers of nodes. It is argued that similar conclusions must hold for high Reynolds number turbulent flows.