Abstract
In this chapter, we present the classical model used to describe open channel hydraulics: the Saint-Venant equations. For completeness, the equations are rigorously derived in Appendix A. We first study some of their mathematical properties, such as the characteristic form. We briefly describe some numerical methods of resolution, and then consider the linearized equations that are valid for small variations around equilibrium regimes. These equations form the basis of all the methods developed in this book.
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References
Abbott M (1966) An introduction to the method of characteristics. Elsevier, New York
Abbott MB (1979) Computational hydraulics. Elements of the theory of free surface flows. Pitman Publishing, London, 324 p
Bardos C, Le Roux A, Nedelec J (1979) First order quasilinear equations with boundary conditions. Commun in Part Diff Eqs 4(9):1017–1034
Boussinesq VJ (1877) Essai sur la théorie des eaux courantes, vol 23. Mémoires présentés par divers savants à l’Académie des Sciences, Paris
Chow V (1988) Open-channel hydraulics. McGraw-Hill, New York, 680 p
Cunge J, Holly F, Verwey A (1980) Practical aspects of computational river hydraulics. Pitman Advanced Publishing Program
Evans L (1998) Partial differential equations, Graduate studies in mathematics, vol 19. American Mathematical Society, Providence, RI
Favre H (1935) Etude théorique et expérimentale des ondes de translation dans les canaux découverts. Dunod, Paris
de Halleux J, Prieur C, Coron JM, d’Andréa Novel B, Bastin G (2003) Boundary feedback control in networks of open-channels. Automatica 39:1365–1376
Krstic M, Smyshlyaev A (2008) Boundary control of PDEs: A course on backstepping designs. SIAM
Litrico X, Fromion V (2004) Frequency modeling of open channel flow. J Hydraul Eng 130(8):806–815
Miller W, Cunge J (1975) Simplified equations of unsteady flow, in Mahmood K, Yevjevich V (eds.), Unsteady fl ow in open channels. Water Resources Publications, Fort Collins, CO, pp 183–257
Mohapatra PK, Chaudhry MH (2004) Numerical solution of Boussinesq equations to simulate dam-break flows. J Hydraul Eng 130(2):156–159
Preissmann A (1961) Propagation des intumescences dans les canaux et rivières. In: 1er Congrès de l’Association Française de Calcul, Grenoble, France, pp 433–442
Barré de Saint-Venant A (1871) Théorie du mouvement non-permanent des eaux avec application aux crues des rivières et à l’introduction des marées dans leur lit. Comptes rendus Acad Sci Paris 73:148–154, 237–240
Samuels P, Skeels C (1990) Stability limits for Preissmann’s scheme. J Hydraul Eng 116(8):997–1012
Schuurmans J (1997) Control of water levels in open-channels. PhD thesis, ISBN 90-9010995-1, Delft University of Technology
Soares-Frazao S, Zech Y (2002) Undular bores and secondary waves - experiments and hybrid finite-volume modelling. J Hydr Res 40(1):33–43
Strub I, Bayen A (2006) Weak formulation of the boundary condition for scalar conservation laws: an application to highway traffic modelling. Int J Robust Nonlin Contr 16(16):733–748
Sturm T (2001) Open-channel hydraulics. McGraw-Hill, New York
Treske A (1994) Undular bores (Favre waves) in open channels – experimental studies. J Hydr Res 32(3):355–370
Venutelli M (2002) Stability and accuracy of weighted four-point implicit finite difference schemes for open channel flow. J Hydraul Eng 128(3):281–288
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(2009). Modeling of Open Channel Flow. In: Modeling and Control of Hydrosystems. Springer, London. https://doi.org/10.1007/978-1-84882-624-3_2
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DOI: https://doi.org/10.1007/978-1-84882-624-3_2
Publisher Name: Springer, London
Print ISBN: 978-1-84882-623-6
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