An evaluation of higher-order upwind differencing for elliptic flow problems

The development of higher-order discretization methods is often a balance between accuracy and ancillary requirements such as resistance to spurious numerical oscillations and ease of solution. In turbulent flow computations these two effects become increasingly important. In this paper, the high-order upwind difference scheme is presented which is robust and which can easily be solved using a 'pseudo-deferred correction' method. Applications of this method to laminar and turbulent flows over a backward facing step show significant reductions in errors per unit cost in comparison with hybrid differencing. It is important to note that it was not necessary to use excessive under-relaxation nor an especially good initial approximation for the new scheme.