Third-order finite-difference method for steady two-dimensional convection

Under highly convective conditions, first-order upstream differencing in regions of the flow where convection dominates diffusion, the artificial numerical diffusion introduced by the truncation error may obscure accurate modeling of the process. In the present paper, a method is proposed which is practically free of numerical diffusion, while the inherent numerical convective stability is retained. This is achieved by means of a control-volume integral formulation, where cell face values are written in terms of a quadratic interpolation surface for steady two-dimensional flow. The truncation error is then merely of third order.