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Modeling and analysis of pooled stepped chutes
1. | Dipartimento di Matematica e Applicazioni, Università degli studi di Milano–Bicocca, Via Roberto Cozzi, 53 - 20125 Milano, Italy, Italy |
2. | Mathematik (Kontinuierliche Optimierung), RWTH Aachen University, Templergraben 55 D-52056 Aachen, Germany |
References:
[1] |
M. K. Banda, M. Herty and A. Klar, Coupling conditions for gas networks governed by the isothermal Euler equations, Networks and Heterogeneous Media, 1 (2006), 295-314.
doi: 10.3934/nhm.2006.1.295. |
[2] |
M. K. Banda, M. Herty and A. Klar, Gas flow in pipeline networks, Networks and Heterogeneous Media, 1 (2006), 41-56.
doi: 10.3934/nhm.2006.1.41. |
[3] |
G. Bastin, B. Haut, J.-M. Coron and B. D'Andréa-Novel, Lyapunov stability analysis of networks of scalar conservation laws, Netw. Heterog. Media, 2 (2007), 751-759 (electronic).
doi: 10.3934/nhm.2007.2.751. |
[4] |
F. W. Blaisdell, Equation for the free-falling nappe, Proceedings ASCE, no. 482, 80 (1954). |
[5] |
J. N. Bradley and A. J. Peterka, The hydraulic design of sitlling basins, Journal of the Hydraulics Division, 83 (1957) 1401.1-1401.24. |
[6] |
A. Bressan, "Hyperbolic Systems of Conservation Laws. The One-Dimensional Cauchy Problem,'' Oxford Lecture Series in Mathematics and its Applications, 20, Oxford University Press, Oxford, 2000. |
[7] |
M. Chamani and N. Rajaratnam, Jet flow on stepped spillways, Journal of the Hydraulic Engineering, 125 (1994), 254-259.
doi: 10.1061/(ASCE)0733-9429(1994)120:2(254). |
[8] |
H. Chanson, Comparison of energy dissipation between nappe and skimming flow regimes on stepped chutes, Journal of the Hydraulic Research, 32 (1994), 213-218.
doi: 10.1080/00221689409498724. |
[9] |
H. Chanson, "Hydraulic Design of Stepped Cascades, Channels, Weirs and Spillways,'' Pergamon Press, Oxford, England, 1994. |
[10] |
H. Chanson, "The Hydraulics of Stepped Chutes and Spillways,'' Taylor & Francis, 2002. |
[11] |
R. M. Colombo and M. Garavello, On the Cauchy problem for the $p$-system at a junction, SIAM J. on Math. Anal., 39 (2008), 1456-1471.
doi: 10.1137/060665841. |
[12] |
R. M. Colombo and G. Guerra, On general balance laws with boundary, J. Differential Equations, 248 (2010), 1017-1043.
doi: 10.1016/j.jde.2009.12.002. |
[13] |
R. M. Colombo, G. Guerra, M. Herty and V. Schleper, Optimal control in networks of pipes and canals, SIAM J. Control Optim., 48 (2009), 2032-2050.
doi: 10.1137/080716372. |
[14] |
R. M. Colombo and F. Marcellini, Smooth and discontinuous junctions in the $p$-system, J. Math. Anal. Appl., 361 (2010), 440-456.
doi: 10.1016/j.jmaa.2009.07.022. |
[15] |
R. M. Colombo and C. Mauri, Euler system for compressible fluids at a junction, Journal of Hyperbolic Differential Equations, 5 (2008), 547-568.
doi: 10.1142/S0219891608001593. |
[16] |
J. de Halleux, C. Prieur, J.-M. Coron, B. d'Andréa Novel and G. Bastin, Boundary feedback control in networks of open channels, Automatica J. IFAC, 39 (2003), 1365-1376.
doi: 10.1016/S0005-1098(03)00109-2. |
[17] |
V. Dos Santos, G. Bastin, J.-M. Coron and B. d'Andréa Novel, Boundary control with integral action for hyperbolic systems of conservation laws: Stability and experiments, Automatica J. IFAC, 44 (2008), 1310-1318.
doi: 10.1016/j.automatica.2007.09.022. |
[18] |
R. Dressler, Mathematical solution to the problem of roll-waves in inclined open channels, Communication in Pure and Applied Mathematics, 2 (1949), 149-194.
doi: 10.1002/cpa.3160020203. |
[19] |
M. El-Kmamash, M. Loewen and N. Rajarantnam, An experimental investigation of jet flow on a stepped chute, Journal of Hydraulic Research, 43 (2005), 31-43. |
[20] |
G. Guerra, F. Marcellini and V. Schleper, Balance laws with integrable unbounded sources, SIAM J. Math. Anal., 41 (2009), 1164-1189.
doi: 10.1137/080735436. |
[21] |
M. Gugat, Nodal control of conservation laws on networks, in "Control and Boundary Analysis" (eds. John Cagnol, et al.), Lecture Notes in Pure and Applied Mathematics, 240, Chapman & Hall/CRC, Boca Raton, FL, (2005), 201-215. |
[22] |
G. Leugering and E. J. P. G. Schmidt, On the modelling and stabilization of flows in networks of open canals, SIAM J. Control Optim., 41 (2002), 164-180 (electronic). |
[23] |
X. Litrico, V. Fromion, J.-P. Baume, C. Arranja and M. Rijo, Experimental validation of a methodology to control irrigation canals based on saint-venant equations, Control Engineering Practice, 13 (2005), 1425-1437.
doi: 10.1016/j.conengprac.2004.12.010. |
[24] |
A. Marigo, Entropic solutions for irrigation networks, SIAM J. Appl. Math., 70 (2009/10), 1711-1735.
doi: 10.1137/09074783X. |
[25] |
I. Ohtsu, Y. Yashuda and M. Takahashi, Flow characteristics of skimming flows in stepped channels, Journal of Hydraulic Engineering, 130 (2004), 860-869.
doi: 10.1061/(ASCE)0733-9429(2004)130:9(860). |
[26] |
W. Rand, Flow geometry at straight drop spillways, Proceedings ASCE, no. 791, 81 (1955). |
[27] |
H. Rouse, Discharge characteristics of the free overfall, Civil Engineering, 6 (1936), 257-260. |
[28] |
R. M. Sorenson, Stepped spillway hydraulic model investigation, Journal of Hydraulic Engineering, 111 (1985), 1461-1472.
doi: 10.1061/(ASCE)0733-9429(1985)111:12(1461). |
[29] | |
[30] |
J. Thorwarth, "Hydraulisches Verhalten von Treppengerinnen mit eingetieften Stufen - selbstinduzierte Abflussinstationariäten und Energiedissipation,'' Ph.D Thesis, RWTH Aachen University, Department of Civil Engineering. 2008. |
show all references
References:
[1] |
M. K. Banda, M. Herty and A. Klar, Coupling conditions for gas networks governed by the isothermal Euler equations, Networks and Heterogeneous Media, 1 (2006), 295-314.
doi: 10.3934/nhm.2006.1.295. |
[2] |
M. K. Banda, M. Herty and A. Klar, Gas flow in pipeline networks, Networks and Heterogeneous Media, 1 (2006), 41-56.
doi: 10.3934/nhm.2006.1.41. |
[3] |
G. Bastin, B. Haut, J.-M. Coron and B. D'Andréa-Novel, Lyapunov stability analysis of networks of scalar conservation laws, Netw. Heterog. Media, 2 (2007), 751-759 (electronic).
doi: 10.3934/nhm.2007.2.751. |
[4] |
F. W. Blaisdell, Equation for the free-falling nappe, Proceedings ASCE, no. 482, 80 (1954). |
[5] |
J. N. Bradley and A. J. Peterka, The hydraulic design of sitlling basins, Journal of the Hydraulics Division, 83 (1957) 1401.1-1401.24. |
[6] |
A. Bressan, "Hyperbolic Systems of Conservation Laws. The One-Dimensional Cauchy Problem,'' Oxford Lecture Series in Mathematics and its Applications, 20, Oxford University Press, Oxford, 2000. |
[7] |
M. Chamani and N. Rajaratnam, Jet flow on stepped spillways, Journal of the Hydraulic Engineering, 125 (1994), 254-259.
doi: 10.1061/(ASCE)0733-9429(1994)120:2(254). |
[8] |
H. Chanson, Comparison of energy dissipation between nappe and skimming flow regimes on stepped chutes, Journal of the Hydraulic Research, 32 (1994), 213-218.
doi: 10.1080/00221689409498724. |
[9] |
H. Chanson, "Hydraulic Design of Stepped Cascades, Channels, Weirs and Spillways,'' Pergamon Press, Oxford, England, 1994. |
[10] |
H. Chanson, "The Hydraulics of Stepped Chutes and Spillways,'' Taylor & Francis, 2002. |
[11] |
R. M. Colombo and M. Garavello, On the Cauchy problem for the $p$-system at a junction, SIAM J. on Math. Anal., 39 (2008), 1456-1471.
doi: 10.1137/060665841. |
[12] |
R. M. Colombo and G. Guerra, On general balance laws with boundary, J. Differential Equations, 248 (2010), 1017-1043.
doi: 10.1016/j.jde.2009.12.002. |
[13] |
R. M. Colombo, G. Guerra, M. Herty and V. Schleper, Optimal control in networks of pipes and canals, SIAM J. Control Optim., 48 (2009), 2032-2050.
doi: 10.1137/080716372. |
[14] |
R. M. Colombo and F. Marcellini, Smooth and discontinuous junctions in the $p$-system, J. Math. Anal. Appl., 361 (2010), 440-456.
doi: 10.1016/j.jmaa.2009.07.022. |
[15] |
R. M. Colombo and C. Mauri, Euler system for compressible fluids at a junction, Journal of Hyperbolic Differential Equations, 5 (2008), 547-568.
doi: 10.1142/S0219891608001593. |
[16] |
J. de Halleux, C. Prieur, J.-M. Coron, B. d'Andréa Novel and G. Bastin, Boundary feedback control in networks of open channels, Automatica J. IFAC, 39 (2003), 1365-1376.
doi: 10.1016/S0005-1098(03)00109-2. |
[17] |
V. Dos Santos, G. Bastin, J.-M. Coron and B. d'Andréa Novel, Boundary control with integral action for hyperbolic systems of conservation laws: Stability and experiments, Automatica J. IFAC, 44 (2008), 1310-1318.
doi: 10.1016/j.automatica.2007.09.022. |
[18] |
R. Dressler, Mathematical solution to the problem of roll-waves in inclined open channels, Communication in Pure and Applied Mathematics, 2 (1949), 149-194.
doi: 10.1002/cpa.3160020203. |
[19] |
M. El-Kmamash, M. Loewen and N. Rajarantnam, An experimental investigation of jet flow on a stepped chute, Journal of Hydraulic Research, 43 (2005), 31-43. |
[20] |
G. Guerra, F. Marcellini and V. Schleper, Balance laws with integrable unbounded sources, SIAM J. Math. Anal., 41 (2009), 1164-1189.
doi: 10.1137/080735436. |
[21] |
M. Gugat, Nodal control of conservation laws on networks, in "Control and Boundary Analysis" (eds. John Cagnol, et al.), Lecture Notes in Pure and Applied Mathematics, 240, Chapman & Hall/CRC, Boca Raton, FL, (2005), 201-215. |
[22] |
G. Leugering and E. J. P. G. Schmidt, On the modelling and stabilization of flows in networks of open canals, SIAM J. Control Optim., 41 (2002), 164-180 (electronic). |
[23] |
X. Litrico, V. Fromion, J.-P. Baume, C. Arranja and M. Rijo, Experimental validation of a methodology to control irrigation canals based on saint-venant equations, Control Engineering Practice, 13 (2005), 1425-1437.
doi: 10.1016/j.conengprac.2004.12.010. |
[24] |
A. Marigo, Entropic solutions for irrigation networks, SIAM J. Appl. Math., 70 (2009/10), 1711-1735.
doi: 10.1137/09074783X. |
[25] |
I. Ohtsu, Y. Yashuda and M. Takahashi, Flow characteristics of skimming flows in stepped channels, Journal of Hydraulic Engineering, 130 (2004), 860-869.
doi: 10.1061/(ASCE)0733-9429(2004)130:9(860). |
[26] |
W. Rand, Flow geometry at straight drop spillways, Proceedings ASCE, no. 791, 81 (1955). |
[27] |
H. Rouse, Discharge characteristics of the free overfall, Civil Engineering, 6 (1936), 257-260. |
[28] |
R. M. Sorenson, Stepped spillway hydraulic model investigation, Journal of Hydraulic Engineering, 111 (1985), 1461-1472.
doi: 10.1061/(ASCE)0733-9429(1985)111:12(1461). |
[29] | |
[30] |
J. Thorwarth, "Hydraulisches Verhalten von Treppengerinnen mit eingetieften Stufen - selbstinduzierte Abflussinstationariäten und Energiedissipation,'' Ph.D Thesis, RWTH Aachen University, Department of Civil Engineering. 2008. |
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