Concurrent use of finite element and finite volume methods for shallow water flows in locally 1-D channel networks

• Published in: International journal for numerical methods in fluids 2012-05, Vol.69 (2), p.255-272
• Main Authors: Unami, K., Alam, A. H. M. Badiul
• Format: Article
• Language: English
• Subjects: Applied fluid mechanics; Applied sciences; Buildings. Public works; Computational methods in fluid dynamics; Dams and subsidiary installations; Exact sciences and technology; finite element method; finite volume method; Fluid dynamics; Fundamental areas of phenomenology (including applications); Hydraulic constructions; Hydrodynamics, hydraulics, hydrostatics; hydromorphic farmlands; Irrigation networks; multiply connected channels; Physics; shallow water flows; transcritical flows
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.2554

SUMMARY A numerical model is developed for shallow water equation in locally 1‐D channel networks. The model concurrently uses the standard Galerkin finite element method for the continuity equation and the finite volume method with an upwind scheme for the momentum equation. The surface gradient method is consistently employed. A minimum treatment is given for channel junctions so that application to multiply connected channels do not require any special consideration The model is capable of computing different types of transcritical flows, wet and dry flows, and flows with complex source terms. Standardized test problems and laboratory experimental data are used for verifying the model. Applicability of the models is validated in a multiply connected channel network draining hydromorphic farmlands located in a West African savanna, and Manning's roughness coefficient is identified, so that the steady solution is consistent with field observations. Unsteady simulation demonstrates that the model is capable of stably reproducing shifts of hydraulic jumps in flows of sub‐millimeter water depths. Copyright © 2011 John Wiley & Sons, Ltd.