Higher-Order Discretization Method for Computations of Separated Flows

This paper presents a new higher-order bounded scheme, WACEB, for approximating the convective fluxes in the transport equations. The weighted-average formulation is used for interpolating the variables at cell faces and the weighted-average coefficient is determined from normalized variable formulation and total variation diminishing (TVD) constrains to ensure the boundedness of solution. The new scheme is tested by solving three problems: 1) a pure convection of a box-shaped step profile in an oblique velocity field; 2) a sudden expansion of an oblique velocity field in a cavity, and; 3) a laminar flow over a fence. The results obtained by the present WACEB were compared with the UPWIND and the QUICK schemes and showed that this scheme has at least the second-order accuracy while ensuring boundedness of solutions. Moreover, it was demonstrated that this scheme produces results that better agree with the experimental data in comparison with other schemes.