On a higher-order bounded discretization scheme

✍ Scribed by B. Song; G. R. Liu; K. Y. Lam; R. S. Amano

• Publisher: John Wiley and Sons
• Year: 2000
• Tongue: English
• Weight: 288 KB
• Volume: 32
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/(sici)1097-0363(20000415)32:7<881::aid-fld2>3.0.co;2-6

✦ Synopsis

This paper presents a new higher-order bounded scheme, weighted-average coefficient ensuring boundedness (WACEB), for approximating the convective fluxes in solving transport equations with the finite volume difference method (FVDM). 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) constraints 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 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 comparison with other schemes.