On a higher-order bounded discretization scheme

• Published in: International journal for numerical methods in fluids 2000-04, Vol.32 (7), p.881-897
• Main Authors: Song, B., Liu, G. R., Lam, K. Y., Amano, R. S.
• Format: Article
• Language: English
• Subjects: boundedness; Cavitation; Computational methods in fluid dynamics; Constraint theory; discretization scheme; Exact sciences and technology; Finite difference method; Finite volume method; Fluid dynamics; Fundamental areas of phenomenology (including applications); Interpolation; Physics; Transport properties; Variational techniques; weighted-average
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/(SICI)1097-0363(20000415)32:7<881::AID-FLD2>3.0.CO;2-6

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. Copyright © 2000 John Wiley & Sons, Ltd.