On a higher-order bounded discretization scheme

This paper presents a new higher-order bounded scheme, weighted-average coe fficient ensuring boundedness (WACEB), for approximating the convective flu xes in solving transport equations with the finite volume difference method (FVDM). The weighted-average formulation is used for interpolating the var iables at cell faces and the weighted-average coefficient is determined fro m normalized variable formulation and total variation diminishing (TVD) con straints 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 velocit y field in a cavity, and (3) a laminar flow over a fence. The results obtai ned by the present WACEB are compared with the UPWIND and the QUICK schemes and it is shown that this scheme has at least second-order accuracy, while ensuring boundedness of solutions. Moreover, it is demonstrated that this scheme produces results that better agree with the experimental data in com parison with other schemes. Copyright (C) 2000 John Wiley & Sons, Ltd.