1D–2D Coupled Numerical Model for Shallow-Water Flows
Publication: Journal of Hydraulic Engineering
Volume 138, Issue 2
Abstract
This paper presents a new method, the water stage prediction-correction (WSPC) method, based on the theory of characteristics to couple numerical models in the boundary-connected way for shallow-water flows. From the WSPC method, a one-dimensional (1D)–two-dimensional (2D) coupled numerical model is established, which incorporates the artificial porosity method and is thus capable of treating wetting and drying. Details of the 1D submodel and the 2D submodel are given, with special emphasis put on the coupling between the submodels. With the help of the WSPC method, the physically coupled submodels are executed separately and then coupled by means of prediction-correction of the water stages at the coupling units (i.e., where the submodels are linked) so that it is possible to make use of existing submodels with minimum modifications. The convergence of the WSPC method is proved, and the parameter identification is discussed, taking a flat-bottom channel with rectangular cross section as an example. The one-dimensional 1D–2D coupled model is applied to both a hypothetic case and a real-life case in central China, and the results show its validity, stability, and practical reliability.
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Acknowledgments
The authors gratefully acknowledge the financial support of the National Natural Science Foundation of China (No. NNSFC51039002 and No. NNSFC50823005), the State Key Laboratory of Hydroscience and Engineering (No. UNSPECIFIED2009-TC-2), and Major Projects on Control and Rectification of Water Pollution (UNSPECIFIED2008ZX07207-010-05).
References
Audusse, E., Bristeau, M. O., and Decoene, A. (2008). “Numerical simulations of 3D free surface flows by a multilayer Saint-Venant model.” Int. J. Numer. Methods Fluids, 56(3), 331–350.
Barton, I. E. (1998). “Comparison of SIMPLE- and PISO-type algorithms for transient flows.” Int. J. Numer. Methods Fluids, 26(4), 459–483.
Bates, P. D., and Hervouet, J. M. (1999). “A new method for moving-boundary hydrodynamic problems in shallow water.” Proc. R. Soc. London, Ser. A, 455(1988), 3107–3128.
Chippada, S., Dawson, C. N., Martinet, M. L., and Wheeler, M. F. (1998). “A Godunov-type finite volume method for the system of shallow water equations.” Comput. Methods Appl. Mech. Eng., 151(1–2), 105–129.
Cunge, J. A., Holly, F. M. Jr., and Verwey, A. (1980). Practical aspects of computational river hydraulics, Pitman, London.
D’Alpaos, L., and Defina, A. (2007). “Mathematical modeling of tidal hydrodynamics in shallow lagoons: A review of open issues and applications to the Venice lagoon.” Comput. Geosci., 33(4), 476–496.
Ferziger, J. H., and Peric, M. (1996). Computational methods for fluid dynamics, Springer, Berlin.
Fread, D. L., Jin, M., and Lewis, J. M. (1996). “An LPI numerical solution for unsteady mixed flow simulation.” North American Water and Environment Congress ’96, ASCE, Reston, VA, 22–28.
Gejadze, I. Y., and Monnier, J. (2007). “On a 2D ‘zoom’ for the 1D shallow water model: Coupling and data assimilation.” Comput. Methods Appl. Mech. Eng., 196(45–48), 4628–4643.
Horritt, M. S., and Bates, P. D. (2002). “Evaluation of 1D and 2D numerical models for predicting river flood inundation.” J. Hydrol. (Amsterdam), 268(1–4), 87–99.
Issa, R. I. (1986). “Solution of the implicitly discretized fluid flow equations by operator-splitting.” J. Comput. Phys., 62(1), 40–65.
Jasak, H. (1996). “Error analysis and estimation for the finite volume method with applications to fluid flows.” Ph.D. thesis, Imperial College of Science, Technology, and Medicine, London.
Kuiry, S. N., Sen, D., and Bates, P. D. (2010). “Coupled 1D-quasi-2D flood inundation model with unstructured grids.” J. Hydraul. Eng., 136(8), 493–506.
Lai, X. J., and Wang, D. G. (2002). “1-D and 2-D coupling numerical model of unsteady flow.” Hydro-Sci. Eng., (2), 48–51 (in Chinese).
Lai, Y. G. (2010). “Two-dimensional depth-averaged flow modeling with an unstructured hybrid mesh.” J. Hydraul. Eng., 136(1), 12–23.
Lin, B. L., and Chandler-Wilde, S. N. (1996). “A depth-integrated 2D coastal and estuarine model with conformal boundary-fitted mesh generation.” Int. J. Numer. Methods Fluids, 23(8), 819–846.
Lin, B. L., Wicks, J. M., Falconer, R. A., and Adams, K. (2006). “Integrating 1D and 2D hydrodynamic models for flood simulation.” Proc. Inst. Civ. Eng.: Water Manage., 159(1), 19–25.
Liu, Z. W., Chen, Y. C., Hu, H. M., and Zhu, D. J. (2009a). “A non-horizontal multilayer numerical model for the flow in natural rivers.” Int. J. Comput. Fluid, D., 23(1), 59–68.
Liu, Z. W., Chen, Y. C., Li, L., and Zheng, J. Y. (2009b). “Sigma-coordinate numerical model for side-discharge into natural rivers.” J. Hydrodyn. Ser. B, 21(3), 333–340.
Long, J., and Li, S. Y. (2007). “Finite element method combining the 1-D and 2-D hydrodynamic modeling of the Pearl River outlets.” J. Hydrodyn., Ser. A, 22(4), 512–519 (in Chinese).
Mao, J. Q., Chen, Q. W., and Chen, Y. C. (2008). “Three-dimensional eutrophication model and application to Thihu Lake, China.” J. Environ. Sci. (China), 20(3), 278–284.
Marin, J., and Monnier, J. (2009). “Superposition of local zoom models and simultaneous calibration for 1D–2D shallow water flows.” Math. Comput. Simul., 80(3), 547–560.
Miglio, E., Perotto, S., and Saleri, F. (2005). “Model coupling techniques for free-surface flow problems: Part I.” Nonlinear Anal. Theory Methods Appl., 63(5–7), e1885–e1896.
Patankar, S. V. (1981). Numerical heat transfer and fluid flow, Hemisphere, Washington, DC.
Sen, D. J., and Garg, N. K. (2002). “Efficient algorithm for gradually varied flows in channel networks.” J. Irrig. Drain. Eng., 128(6), 351–357.
Sobey, R. J. (2001). “Evaluation of numerical models of flood and tide propagation in channels.” J. Hydraul. Eng., 127(10), 805–824.
Steinebach, G., Rademacher, S., Rentrop, P., and Schulz, M. (2004). “Mechanisms of coupling in river flow simulation systems.” J. Comput. Appl. Math., 168(1–2), 459–470.
Twigt, D. J., De Goede, E. D., Zijl, F., Schwanenberg, D., and Chiu, A. Y. W. (2009). “Coupled 1D-3D hydrodynamic modelling, with application to the Pearl River Delta.” Ocean Dynam., 59(6), 1077–1093.
van’t Hof, B. V., and Vollebregt, E. A. H. (2005). “Modelling of wetting and drying of shallow water using artificial porosity.” Int. J. Numer. Methods Fluids, 48(11), 1199–1217.
Verwey, A. (2001). “Latest developments in floodplain modelling—1D/2D integration.” Proc., 6th Conf. on Hydraulics in Civil Engineering, The Institute of Engineers, Hobart, Australia, 13–24.
Vreugdenhil, C. B. (1994). Numerical methods for shallow-water flow, Kluwer, Boston, 81–82.
Weller, H. G., Tabor, G., Jasak, H., and Fureby, C. (1998). “A tensorial approach to computational continuum mechanics using object-oriented techniques.” Comput. Phys., 12(6), 620–631.
Xu, Z. X., and Yin, H. L. (2004). “Development of coupled 1D–2D mathematical models for tidal rivers.” J. Hydrodyn. Ser. B, 16(6), 767–776.
Zhu, D. J., Chen, Y. C., and Wang, Z. Y. (2009). “A novel method for gradually varied subcritical flow simulation in general channel networks.” Proc., 33rd. Int. Association of Hydraulic Engineering & Research (IAHR) Congress: Water Engineering for a Sustainable Environment (CD-ROM), IAHR, Madrid, Spain, 6327–6335.
Zhu, D., Chen, Y., Wang, Z., and Liu, Z. (2011). “Simple, robust, and efficient algorithm for gradually varied subcritical flow simulation in general channel networks.” J. Hydraul. Eng., 137(7), 766–774.
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© 2012 American Society of Civil Engineers.
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Received: Jan 31, 2011
Accepted: Jun 28, 2011
Published online: Jun 30, 2011
Published in print: Feb 1, 2012
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