Browse > Article
http://dx.doi.org/10.3741/JKWRA.2022.55.10.811

Numerical analysis of shallow-water flow over the square-edged broad-crested weir  

Hwang, Seung-Yong (Korea Institute of Civil Engineering and Building Technology)
Publication Information
Journal of Korea Water Resources Association / v.55, no.10, 2022 , pp. 811-821 More about this Journal
Abstract
Accuracy of a numerical model with the Hwang's scheme of directly analyzing discontinuous topography could be enhanced by introducing a flux correction coefficient that accounted for the deviation of actual pressure from hydrostatic distribution acting on the front of discontinuous topography. The optimal coefficient was determined from 218 experimental runs for square-edged broad-crested weir and simulation with it showed good agreement with another two square-edged broad-crested weir experiments and an unsteady side-weir experiment. This enabled accurate numerical simulation of shallow-water flow over the discontinuous river structure, such as square-edged broad-crested weir, without alleviating discontinuous topography with refined meshes or imposing internal boundary conditions.
Keywords
Square-edged broad-crested weir; Discontinuous topography; Shallow-water flow; Numerical simulation; Hwang's scheme;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
연도 인용수 순위
1 Hwang, S.-Y. (2015). "A novel scheme to depth-averaged model for analyzing Shallow-water flows over discontinuous topography." KSCE Journal of Civil and Environmental Engineering Research, KSCE, Vol. 35, No. 6, pp. 1237-1246.
2 Hwang, S.-Y., and Kim, H.S. (2021). "Numerical simulation and laboratory experiment of flooding on a perpendicular floodplain with dam-break flows." KSCE Journal of Civil and Environmental Engineering Research, KSCE, Vol. 41, No. 3, pp. 219-227.   DOI
3 Kim, S. (2013). Analysis on flood-control effect of side-weir detention basin considering the flow pattern over the weir. Master's Thesis, Myongji University.
4 Lee, K.S., and Lee, S.-T. (1998). "Two-dimensional finite-volume unsteady-flow model for shocks." Journal of Korea Water Resources Association, KWRA, Vol. 31, No. 3, pp. 279-290.
5 Moss, W.D. (1970). Flow over a square-edged broad-crested weir. Doctoral dissertation, University of Surrey, Guildford Surrey, U.K.
6 Prokof'ev, V.A. (2005). "Two-dimensional horizontal numerical model of open flow over a bed with obstacles." Water Resources, Vol. 32, No. 3, pp. 252-264.   DOI
7 Sarker, M.A., and Rhodes, D.G. (2004). "Calculation of free-surface profile over a rectangular broad-crested weir." Flow Measurement and Instrumentation, Vol. 15, No. 4, pp. 215-219.   DOI
8 van Leer, B. (1979). "Towards the ultimate conservative difference scheme. V. a second-order sequel to Godunov's method." Journal of Computational Physics, Vol. 32, No. 1, pp. 101-136.   DOI
9 Willmott, C.J., Robeson, S.M., and Matsuura, K. (2012). "A refined index of model performance." International Journal of Climatology, Vol. 32, No. 13, pp. 2088-2094.   DOI
10 Doeringsfeld, H.A., and Barker, C.L. (1941). "Pressure-momentum theory applied to the broad-crested weir." Transactions of the American Society of Civil Engineers, ASCE, Vol. 106, No. 1, pp. 934-946.   DOI
11 Echeverribar, I., Morales-Hernandez, M., Brufau, P., and Garcia-Navarro, P. (2019). "Use of internal boundary conditions for levees representation: Application to river flood management." Environmental Fluid Mechanics, Vol. 19, No. 5, pp. 1253-1271.   DOI
12 Goodarzi, E., Farhoudi, J., and Shokri, N. (2012). "Flow characteristics of rectangular broad-crested weirs with sloped upstream face." Journal of Hydrology and Hydromechanics, Vol. 60, No. 2, pp. 87-100.
13 Hwang, S.-Y., and Lee, S.H. (2012). "An application of the HLLL approximate Riemann solver to the shallow water equations." KSCE Journal of Civil and Environmental Engineering Research, KSCE, Vol. 32, No. 1B, pp. 21-27.
14 Garcia-Alen, G., Garcia-Fonte, O., Cea, L., Pena, L., and Puertas, J. (2021). "Modelling weirs in two-dimensional shallow water models." Water, MDPI, Vol. 13, No. 16, 2152.   DOI
15 Govinda Rao, N.S., and Muralidhar, D. (1963). "Discharge characteristics of weirs of finite-crest width." La Houille Blanche, Vol. 49, No. 5, pp. 537-545.   DOI
16 Batten, P., Lambert, C., and Causon, D.M. (1996). "Positively conservative high-resolution convection schemes for unstructured elements." International Journal for Numerical Methods in Engineering, Vol. 39, No. 11, pp. 1821-1838.   DOI
17 Bureau of Reclamation (Reclamation) (2001). Water measurement manual. A Water Resources Technical Publication, United States Department of the Interior, Washington, D.C., U.S.
18 Henderson, F. (1966). Open channel flow, Macmillan Publishing Co., Inc., NY, U.S.
19 Hwang, S.-Y. (2019). "Flow resistance by discontinuous topography in simulating Shallow-water flow." KSCE Journal of Civil and Environmental Engineering Research, KSCE, Vol. 39, No. 1, pp. 175-181.
20 Hager, W., and Schwalt, M. (1994). "Broad-crested weir." Journal of Irrigation and Drainage Engineering, ASCE, Vol. 120, No. 1, pp. 13-26.   DOI
21 Jun, K.S. (1996). "A study on unsteady flow model including weir flow simulation." Journal of Korea Water Resources Association, KWRA, Vol. 29, No. 2, pp. 153-165.
22 Kirkgoz, M.S., Akoz, M.S., and Oner, A.A. (2008). "Experimental and theoretical analyses of two-dimensional flows upstream of broad-crested weirs." Canadian Journal of Civil Engineering, CSP, Vol. 35, No. 9, pp. 975-986.   DOI
23 Lee, H. (2020). "Implicit discontinuous Galerkin scheme for discontinuous bathymetry in shallow water equations." KSCE Journal of Civil Engineering, KSCE, Vol. 24, No. 9, pp. 2694-2705.   DOI
24 Linde, T. (2002). "A practical, general-purpose, two-state HLL Riemann solver for hyperbolic conservation laws." International Journal for Numerical Methods in Fluids, Vol. 40, No. 3-4, pp. 391-402.   DOI
25 Morales-Hernandez, M., Murillo, J., and Garcia-Navarro, P. (2013). "The formulation of internal boundary conditions in unsteady 2-d shallow water flows: Application to flood regulation." Water Resources Research, Vol. 49, No. 1, pp. 471-487.   DOI
26 Paik, J., and Lee, N.J. (2015). "Numerical modeling of free surface flow over a broad-crested rectangular weir." Journal of Korea Water Resources Association, KWRA, Vol. 48, No. 4, pp. 281-290.   DOI
27 Press, W.H., Flannery, B.P., Teukolsky, S.A., and Vetterling, W.T. (1992). Numerical recipes in c: The art of scientific computing, second edition, Cambridge University Press, NY, U.S.
28 Rafter, G.W. (1900). "On the flow of waer over dams." Transactions of the American Society of Civil Engineers, ASCE, Vol. 44, pp. 220-398.   DOI
29 Schubert, J.E., and Sanders, B.F. (2012). "Building treatments for urban flood inundation models and implications for predictive skill and modeling efficiency." Advances in Water Resources, Vol. 41, pp. 49-64.   DOI
30 Ramamurthy, A.S., Tim, U.S., and Rao, M.V.J. (1988). "Characteristics of square-edged and round-nosed broad-crested weirs." Journal of Irrigation and Drainage Engineering, ASCE, Vol. 114, No. 1, pp. 61-73.   DOI
31 Tracy, H.J. (1957). Discharge characteristics of broad-crested weirs. Geological Survey Circular 397, Geological Survey, United States Department of the Interior, Washington, D.C., U.S.
32 Vanden-Broeck, J.-M., and Keller, J.B. (1986). Weir flows. MRC Technical Summary Report, 2919, Mathematics Research Center, University of Wisconsin-Madison, WI, U.S.
33 Weiyan, T. (1992). Shallow water hydrodynamics, Elsevier Science Publishers, Amsterdam, The Netherland.
34 Zhou, J.G., Causon, D.M., Ingram, D.M., and Mingham, C.G. (2002). "Numerical solutions of the shallow water equations with discontinuous bed topography." International Journal for Numerical Methods in Fluids, Vol. 38, No. 8, pp. 769-788.   DOI
35 Zhou, J.G., Causon, D.M., Mingham, C.G., and Ingram, D.M. (2001). "The surface gradient method for the treatment of source terms in the shallow-water equations." Journal of Computational Physics, Vol. 168, No. 1, pp. 1-25.   DOI
36 Horton, R.E. (1907). Weir experiments, coefficients, and formulas. Water-Supply and Irrigation Paper No. 200, Geological Survey, United States Department of the Interior, Washington, D.C., U.S.
37 Hargreaves, D.M., Morvan, H.P., and Wright, N.G. (2007). "Validation of the volume of fluid method for free surface calculation: The broad-crested weir." Engineering Applications of Computational Fluid Mechanics, Taylor & Francis, Vol. 1, No. 2, pp. 136-146.   DOI