A novel flow-oriented discretization scheme for reducing false diffusion in three-dimensional (3D) flows: An application in the indoor environment

Numerical approximation of the convection terms in the conservation equations is mainly responsible for false diffusion errors. One way to overcome this problem is to use an upwind approximation which essentially follows the streamlines. This approach was originally derived by Raithby (1976a). Patel et al. (1988) derived a different formulation trying to eliminate the shortcomings of the original scheme. The latter approach was formally called CUPID11Corner Upwinding. (Corner Upwinding) and it was then simplified for 2D flows by SUCCA22Skew Upwind Corner Convection Algorithm. (Skew Upwind Corner Convection Algorithm). The method outlined in this paper retains the features of CUPID and SUCCA schemes and extents the formulation of the convection terms in a finite volume approach appropriate for 3D flows, including the momentum equations. The new discretization scheme formally called SUPER33Skew Upwind and Corner Algorithm. (Skew Upwind and Corner Algorithm) is validated by modelling the indoor two-phase flow of air and particles in the three dimensional geometry of a scale-model room. Furthermore, the performance of the new scheme is compared with the conventional upwind scheme in the case of inclined inflow (θ = 45°). The numerical results indicate that the new scheme has the potential for minimizing false diffusion in three dimensional flows. ► Distribution of air and particles is modelled by a two-phase flow Euler–Euler method. ► A new flow-oriented discretization scheme is employed. ► The convection terms in three directions (3D) are reformulated. ► The performance of the numerical scheme is tested in case of inclined flow. ► The new discretization scheme leads to a significant reduction of false diffusion.