Lattice Boltzmann Model for the Simulation of Flows in Open Channels with Application to Flows in a Submerged Sluice Gate
Publication: Journal of Irrigation and Drainage Engineering
Volume 136, Issue 12
Abstract
Numerical simulations of free-surface flows are important to provide a prediction tool for the optimal management of irrigation canals. Here, we consider an alternative to solving the shallow-water equations. We propose a free-surface model in which the vertical component of the water current is fully resolved. We believe that such a detailed description can be useful to model the flow around gates or in other situations where the vertical structure of the flow will be important such as in the case of sediment transport and deposition. Our approach is based on a two-fluid lattice Boltzmann model. We compare the predictions obtained from numerical simulation and experiments performed on a laboratory microcanal facility.
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Acknowledgments
The writers thank the Swiss National Science Foundation for financial support and the reviewers for their many corrections and useful suggestions that greatly improved the quality of this paper.NSF-CH
References
Ansumali, S., Karlin, I. V., Arcidiacono, S., Abbas, A., and Prasianakis, N. I. (2007). “Hydrodynamics beyond Navier-Stokes: Exact solution to the lattice Boltzmann hierarchy.” Phys. Rev. Lett., 98, 124502.
Axner, L., Bernsdorf, J., Zeiser, T., Lammers, P., Linxweiler, J., and Hoekstra, A. G. (2008). “Performance evaluation of a parallel sparse lattice Boltzmann solver.” J. Comput. Phys., 227(10), 4895–4911.
Bates, P. D., Lane, S. N., and Ferguson, R. (2005). Computational fluid dynamics: Applications in environmental hydraulics, Wiley, New York.
Baume, J. -P., Sau, J., and Malaterre, P. O. (1998). “Modeling of irrigation channel dynamics for controller design.” IEEE Int. Conf. on Systems, Man and Cybernetics (SMC’98), IEEE, Piscataway, N.J., 3856–3861.
Besançon, G., Dulhoste, J. F., and Georges, D. (2001). “A nonlinear backstepping-like controller for a three-point collocation model of water flow dynamics.” Proc., IEEE Conf. on Control Application CCA’2001, IEEE, Piscataway, N.J.
Bhatnager, P., Gross, E., and Krook, M. (1954). “A model for collision process in gases.” Phys. Rev., 94, 511–525.
Chartrand, R. (2005). “Numerical differentiation of noisy, nonsmooth data.” Technical Rep., Los Alamos National Laboratory, Los Alamos, N.M. ⟨http://math.lanl.gov/Research/Publications/Docs/chartrand-2007-numerical.pdf⟩ (Sept. 17, 2010).
Chaussinand, S. (2003). “Comparaison de lois de commande pour la gestion d’un micro-canal.” MS thesis, Grenoble Institute of Technology, Grenoble, France.
Chen, S., and Doolen, G. D. (1998). “Lattice Boltzmann method for fluid flows.” Annu. Rev. Fluid Mech., 30, 329–364.
Chopard, B. (2009). Lectures on lattice Boltzmann methods for complex fluid flows, Science4 Press, Pomigliano d'Arco, Italy.
Chopard, B., and Droz, M. (1998). Lattice-gas cellular automata and lattice Boltzmann models: An introduction, Cambridge University Press, Cambridge, England.
Chopard, B., Luthi, P., Masselot, A., and Dupuis, A. (2002). “Cellular automata and lattice Boltzmann techniques: An approach to model and simulate complex systems.” Adv. Complex Syst., 5(2–3), 103–246.
Chow, V. T. (1985). Open channel hydraulics, McGraw-Hill, New York.
Clemmens, A. J., Bautista, E., Wahlin, B. T., and Strand, R. J. (2005). “Simulation of automatic canal control systems.” J. Irrig. Drain. Eng., 131(4), 324–335.
Clemmens, A. J., Kacerek, T. F., Grawitz, B., and Schuurmans, W. (1998). “Test case for canal control algorithms.” J. Irrig. Drain. Eng., 124(1), 23–30.
Coron, J. M., d’Andra Novel, B., and Bastin, G. (1999). “A Lyapunov approach to control irrigation canals modeled by Saint-Venant equations.” Proc., European Control Conf. ECC’99, Karlsruhe, Germany, 3856–3861.
Cunge, J. A., Holloy, F. M., and Verwey, A. (1980). Practical aspects of computational river hydraulics, Oitman, London.
Donath, S., Iglberger, K., Wellein, G., Zeiser, T., Nitsure, A., and Rude, U. (2008). “Performance comparison of different parallel lattice Boltzmann implementations on multicore multisocket systems.” Int. J. Comput. Sci. Eng., 4(1), 3–11.
Dulhoste, J. F., Besançon, G., and Georges, D. (2001). “Nonlinear control of water flow dynamics by input-output linearization based on collocation model.” Proc., European Control Conf. ECC’2001, Porto, Portugal.
Dupuis, A., and Chopard, B. (2002). “Lattice gas modeling of scour formation under submarine pipelines.” J. Math. Phys., 178(1), 161–174.
Geller, S., Krafczyk, M., Tolke, J., Turek, S., and Hron, J. (2006). “Benchmark computations based on lattice-Boltzmann, finite element and finite volume methods for laminar flows.” Comput. Fluids, 35(8–9), 888–897.
Ginzburg, I. (2005). “Equilibrium-type and link-type lattice Boltzmann models for generic advection and anisotropic-dispersion equation.” Adv. Water Resour., 28(11), 1171–1195.
Ginzburg, I. (2007). “Lattice Boltzmann modeling with discontinuous collision components: Hydrodynamic and advection-diffusion equations.” J. Stat. Phys., 126(1), 157–206.
Ginzburg, I., and Steiner, K. (2003). “Lattice Boltzmann model for free-surface flow and its application to filling process in casting.” J. Comput. Phys., 185(1), 61–99.
Graf, W. H. (1993). Hydraulique fluviale, collection traité de genie civil, Presses Polytechniques et Universitaire Romandes, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland.
Guo, Z., Zheng, C., and Shi, B. (2002). “Discrete lattice effects on forcing terms in the lattice Boltzmann method.” Phys. Rev. E, 65, 046308.
Hamroun, B., Lefèvre, L., and Mendes, E. (2006). “Port-based modelling for open channel irrigation systems.” Transactions on Fluid Mechanics, 1(12), 995–1009.
Henderson, F. M. (1989). Open channel flow, Macmillan Publishing Company, New York.
Junk, M., Klar, A., and Luo, L. S. (2005). “Asymptotic analysis of the lattice Boltzmann equation.” J. Comput. Phys., 210(2), 676–704.
Kandhai, D. (1999). “Large scale lattice Boltzmann simulation: Computational methods and applications.” Ph.D. thesis, Univ. of Amsterdam, Amsterdam, The Netherlands.
Körner, C., Thies, M., Hoffmann, T., Thürey, N., and Rüde, U. (2005). “Lattice Boltzmann model for free surface flow for modeling foaming.” J. Stat. Phys., 121(1–2), 179–196.
Lätt, J. (2007). “Hydrodynamic limit of lattice Boltzmann equations.” Ph.D. thesis, Univ. of Geneva, Switzerland, ⟨http://www.unige.ch/cyberdocuments/theses2007/LattJ/meta.html⟩ (Sept. 17, 2010).
Lozano, D., Mateos, L., Merkley, G. P., and Clemmens, A. J. (2009). “Field calibration of submerged sluice gates in irrigation canals.” J. Irrig. Drain. Eng., 135(6), 763–772.
Malaterre, P. O., and Rodellar, J. (1997). “Multivariable predictive control of irrigation canals. Design and evaluation on a 2-pool model.” Int. Workshop on the Regulation of Irrigation Canals: State of the Art of Research and Applications, RIC97, Marrakech, Morocco, 230–238.
Malaterre, P. O., Rogers, D. C., and Schuurmans, J. (1998). “Classification of canal control algorithms.” J. Irrig. Drain. Eng., 124(1), 3–10.
Marcou, O., Chopard, B., and El Yacoubi, S. (2007). “Modeling of irrigation canals: A comparative study.” Int. J. Mod. Phys. C, 18(4), 739–748.
Marcou, O., El Yacoubi, S., and Chopard, B. (2006). “A bi-fluid lattice Boltzmann model for water flow in an irrigation channel.” ACRI 2006 Proc., Springer, New York, 373–382.
Martys, N. S., and Chen, H. (1996). “Simulation of multi-components fluids in complex three-dimensional geometries by the lattice Boltzmann method.” Phys. Rev. E, 53(1), 743–750.
Miller, W. A., and Cunge, J. A. (1975). Unsteady flow in open channels, Water Resources Publications, Fort Collins, Colo.
Ouarit, H., Lefèvre, L., and Georges, D. (2003). “Robust optimal control of one-reach open-channels.” Proc., European Control Conf. ECC’2003, University of Cambridge, U.K.
Pham, V. T. (2009). “Modélisation et commande des systèmes non-linéaire á paramètres distribués par la méthode de Boltzmann sur réseau: Application aux canaux d’irrigation.” MS thesis, Grenoble Institute of Technology, Grenoble, France.
Sawadogo, S., Malaterre, P. O., and Kosuth, P. (1995). “Multivariable optimal control for on-demand operation of irrigation canals.” Int. J. Syst. Sci., 26(1), 161–178.
Shan, X., and Chen, H. (1993). “Lattice Boltzmann model for simulating flows with multiple phases and components.” Phys. Rev. E, 47(3), 1815–1819.
Shan, X., and Chen, H. (1994). “Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation.” Phys. Rev. E, 49(4), 2941–2948.
Stansby, P. K., and Zhou, J. G. (1998). “Shallow-water flow solver with non-hydrostatic pressure: 2D vertical plane problems.” Int. J. Numer. Methods Fluids, 28, 541–563.
Succi, S. (2001). The lattice Boltzmann equation for fluid dynamics and beyond, Oxford University Press, New York.
Sukop, M. C., and Thorne, D. T. (2005). Lattice Boltzmann modeling: An introduction for geoscientists and engineers, Springer, New York.
Thürey, N., and Rüde, U. (2009). “Stable free surface flows with the lattice Boltzmann method on adaptively coarsened grids.” Comput. Visualization Sci., 12(5), 247–263.
Wolf-Gladrow, D. A. (2000). Cellular automata modeling of physical systems, Lecture notes in mathematics, Springer, New York.
Xing, X. Q., Lee Butler, D., and Yang, C. (2007). “Lattice Boltzmann-based single-phase method for free surface tracking of droplet motions.” Int. J. Numer. Methods Fluids, 53, 333–351.
Zhou, J. G. (2004). Lattice Boltzmann methods for shallow water flows, Springer, New York.
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Published In
Journal of Irrigation and Drainage Engineering
Volume 136 • Issue 12 • December 2010
Pages: 809 - 822
Copyright
© 2010 ASCE.
History
Received: Aug 6, 2009
Accepted: Apr 19, 2010
Published online: May 7, 2010
Published in print: Dec 2010
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