A locally modified second order upwind scheme for convection terms discretization

A finite difference scheme for convection term discretization, called BSOU (stands for Bounded Second Order Upwind), is developed and its performance is assessed against exact or benchmark solutions in linear and non‐linear cases. It employs a flux blending technique between first order upwind and second order upwind schemes only in those regions of the flow field where spurious oscillations are likely to occur. The blending factors are calculated with the aid of the convection boundedness criterion. In all cases the scheme performed very well, minimizing the numerical diffusion errors. The scheme is transportive, conservative, bounded, stable and accurate enough so as to be suitable for inclusion into a general purpose solution algorithm.