An Extended Shallow-water-like Model Applied to Flows in Environmental and Civil Engineering

Kerger, François; Dewals, Benjamin; Erpicum, Sébastien; Archambeau, Pierre; Pirotton, Michel

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Kerger, François; Dewals, Benjamin; Erpicum, Sébastien et al.

2010 • In Hirsch, Gerhard; Kappel, Bernd (Eds.) Hydraulic Engineering: Structural Applications, Numerical Modeling and Environmental Impacts

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Abstract :

[en] Objective of this text is to rigorously develop a unified mathematical model to simulate a wide range of environmental flows. Particular emphasis is placed on flows relevant in civil and environmental engineering.

Research Center/Unit :

Aquapôle - ULiège

Disciplines :

Civil engineering

Author, co-author :

Kerger, François ; Université de Liège - ULiège > Département Argenco : Secteur MS2F > Hydrodynamique appl. et constructions hydrauliques (HACH)

Dewals, Benjamin ; Université de Liège - ULiège > Département Argenco : Secteur MS2F > Hydrodynamique appl. et constructions hydrauliques (HACH)

Erpicum, Sébastien ; Université de Liège - ULiège > Département Argenco : Secteur MS2F > Hydraulique génér., const. hydraul. et méc. des fluides

Archambeau, Pierre ; Université de Liège - ULiège > Département Argenco : Secteur MS2F > Hydrodynamique appl. et constructions hydrauliques (HACH)

Pirotton, Michel ; Université de Liège - ULiège > Département Argenco : Secteur MS2F > Hydrodynamique appl. et constructions hydrauliques (HACH)

Language :

English

Title :

An Extended Shallow-water-like Model Applied to Flows in Environmental and Civil Engineering

Publication date :

2010

Main work title :

Hydraulic Engineering: Structural Applications, Numerical Modeling and Environmental Impacts

Editor :

Hirsch, Gerhard

Kappel, Bernd

Publisher :

Nova Science Publishers, New-York, United States

ISBN/EAN :

978-1-60876-825-7

Collection name :

Engineering Tools, Techniques and Tables

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique

Available on ORBi :

since 29 September 2009

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Bibliography

Carrascal, E. S. Response of the shoreline due to the Longshore Sediment Transport in Cancun Mexico, Master THE-Delft.
Erpicum, S., Meile, T., Dewals, B. J., Pirotton, M. & Schleiss, A. (2009). 2D numerical flow modeling in a macro-rough channel. International Journal for Numerical Methods in Fluids,. published online.
Cunge, J. A., Holly, F. M. & Verwey, A. (1980). Practical Aspects of Computational River Hydraulics. Monographs and surveys in water resources engineering. Boston: Pitman Advanced Pub. Program.
Detrembleur, S., Dewals, B. J., Archambeau, P., Erpicum, S. & Pirotton, M. (2009). Modélisation numérique et gestion du risque inondation en milieu urbain sur base de modèles topographiques à haute résolution. Techniques -Sciences -Méthodes, Accepted.
Khuat Duy, B., Archambeau, P., Erpicum, S., Dewals, B. J. & Pirotton, M. (2009). Modélisation hydrologique à grande échelle des zones imperméables égouttées. Houille Blanche-Rev. Int., accepted.
Dewals, B. J., Detrembleur, S., Archambeau, P., Erpicum, S. & Pirotton, M. (2008). Detailed 2D hydrodynamic simulations as an onset for evaluating socio-economic impacts of floods considering climate change, in Flood Risk Management: Research and Practice, P. Samuels, et al., Editors. Taylor & Francis: London. 125-135.
Erpicum, S., Archambeau, P., Detrembleur, S., Dewals, B. & Pirotton, M. (2008). A 2D finite volume multiblock flow solver applied to flood extension forecasting, in Numerical modelling of hydrodynamics for water ressources, G. N. Pilar & P. Enrique, Editors. Taylor & Francis: London. 321-325.
Caleffi, V., Valiani, A. & Zanni, A. (2003). Finite volume method for simulating extreme flood events in natural channels. Journal of Hydraulic Research, 41(2), 167-177.
Bates, P. D. & de Roo, A. P. J. (2000). A simple raster-based model for flood inundation simulation. Journal of Hydrology, 236, 54-77.
McMillan, H. K. & Brasington, J. (2007). Reduced complexity strategies for modelling urban floodplain inundation. Geomorphology, 90, 226-243.
Kerger, F., Archambeau, P., Erpicum, S., Dewals, B. J. & Pirotton, M. (2009). Simulation numérique des écoulements mixtes hautement transitoire dans les conduites d'évacuation des eaux. Houille Blanche-Rev. Int., Octobre 2009, 5, 159-167.
Vasconcelos, J., Wright, S. & Roe, P. L. (2006). Improved Simulation of Flow Regime Transition in Sewers: The Two-Component Pressure Approach. Journal of Hydraulic Engineering, 132(6), 553-562.
Dewals, B. J., Kantoush, Erpicum, S., Pirotton, M. & Schleiss, A. (2008). Experimental and numerical analysis of flow instabilities in rectangular shallow basins. Environmental Fluid Mechanics, 8(1), 31-54.
Machiels, O., Erpicum, S., Archambeau, P., Dewals, B. J. & Pirotton, M. (2009). Analyse expérimentale du fonctionnement hydraulique des déversoirs en touches de piano. Houille Blanche-Rev. Int., 2009.
Dewals, B. J., Erpicum, S., Archambeau, P., Detrembleur, S. & Pirotton, M. (2006). Depth-Integrated Flow Modelling Taking into Account Bottom Curvature. Journal of Hydraulic Research, 44(6), 787-795.
Krüger, S. (2001). Computational Contribution to Highly Supercritical Flows. Mitteilungen der Versuchsanstalt für Wasserbau, Hydrologie un Glaziologie, H. E. Minor, (Ed). Vol. 167. Zürich: ETHZ. 171.
Erpicum, S., Dewals, B. J., Archambeau, P. & Pirotton, M. (2009). Dam-break flow computation based on an efficient flux-vector splitting. J. Comput. Appl. Math., accepted.
Dewals, B. J., Erpicum, S., Detrembleur, S., Archambeau, P. & Pirotton, M. (2009). Flow induced by the failure or breaching of dams arranged in complex. J. Hydraul. Eng.-ASCE, To be submitted.
Roger, S., Dewals, B. J., Erpicum, S., Schwanenberger, D., Schüttrumpf, H. & Köngetter, J. (2009). Experimental und numerical investigations of dike-break induced flows. Journal of Hydraulic Research, in press.
Marche, C., Gagnon, J., Quach, T. T., Kahawita, R., & Beauchemin, P. (1997). Simulation of dam failures in multidike reservoirs arranged in cascade. J. Hydraul. Eng.-ASCE, 123, 950-961.
Schwanenberg, D. & Harms, M. (2004). Discontinuous Galerkin finite-element method for transcritical two-dimensional shallow water flows. J. Hydraul. Eng.-ASCE, 130, 412-421.
Ernst, J., Dewals, B. J., Detrembleur, S., Archambeau, P., Erpicum, S. & Pirotton, M. (2008). Integration of accurate 2D inundation modelling, vector land use database and economic damage evaluation, in Flood Risk Management: Research and Practice, P. Samuels, et al., Editors. Taylor & Francis: London. 1643-1653.
McMillan, H. K. & Brasington, J. (2008). End-to-end risk assessment: A coupled model cascade with uncertainty estimation. Water Resources Research, 44, 14.
García, M. H. (2008). Sedimentation engineering: processes, measurements, modeling, and practice. Reston, Va.: American Society of Civil Engineers. 1132.
Dufresne, M., Pirotton, M., Dewals, B. J., Erpicum, S. & Archambeau, P. (2009). Experimental investigation of flow and deposit patterns in rectangular shallow reservoirs: preliminary analysis, in Proc. International Workshop on Environmental Hydraulics -Theoretical, Experimental and Computational Solutions. Taylor & Francis: Valencia, Spain.
Stovin, V. R. & Saul, A. J. (1996). Efficiency prediction for storage chambers using computational fluid dynamics. Wat. Sci. Tech., 33, 163-170.
Wu, W. (2008). Computational river dynamics. London: Taylor & Francis. 494.
Castro, M. J., Garcia-Rodriguez, A., Gonzales-Vida, J. M., Macias, J., Pares, C. &. Vazquez-Cendon, M. E. (2004). Numerical simulation of two-layer shallow water flows through channels with irregular geometry. J. Comput. Phys., 195(1), 202-235.
Kerger, F., Detrembleur, S., Archambeau, P., Erpicum, S., Dewals, B. J. & Pirotton, M. (2009). An Experimental and Numerical Analysis of Effects Induced by Moving Bodies in Free Surface Water, in Hydraulic Structures, S. Pagliara, Editor. Pisa University Press. 179-189.
Kerger, F., Detrembleur, S., Archambeau, P., Erpicum, S., Dewals, B. J. & Pirotton, M. (2009). Hydrodynamic forces acting on vertically translating bodies in free surface water, in WIT Transactions on The Built Environment, Vol 105, Fluid Structure Interaction V, W. Press, Editor. 183-193.
Erpicum, S., Archambeau, P., Dewals, B. J., Ernst, J. & Pirotton, M. (2009). Dam-break flow numerical modeling considering structural impacts on buildings, in 33rd IAHR Biennial Congress: Water Engineering for a Sustainable Environment, IAHR, Editor. Vancouver, Canada.
Benkhaldoun, F., Elmahi, I. & Seaïd, M. (2007). Well-balanced finite volume schemes for pollutant transport by shallow water equations on unstructured meshes. Journal of computational physics, 226(1), 180-203.
Dewals, B. J., Andre, S., Pirotton, M. & Schleiss. A. (2003). Quasi 2D-numerical model of aerated flow over stepped chutes. In 30th IAHR Congress. Greece.
Erpicum, S., Kerger, F., Archambeau, P., Dewals, B. J. & Pirotton. M. (2009). Experimental and numerical investigation of mixed flow in a Gallery. In Multiphase Flow. New Forest.
Kerger, F., Erpicum, S., Archambeau, P., Dewals, B. J. & Pirotton. M. (2009). Numerical Simulation of 1D Mixed Flow with Air/Water Interaction in Multiphase Flow New Forest.
Dewals, B. J., Erpicum, S., Archambeau, P., Detrembleur, S. & Pirotton, M. (2008). Hétérogénéité des échelles spatio-temporelles d'écoulements hydrosédimentaires et modélisation numérique. Houille Blanche-Rev. Int., 109-114.
Ishii, M. & Hibiki, T. (2006). Thermo-fluid dynamics of two-phase flow. First ed. Springer Science, USA. 430.
Drew, D. A. & Passman, S. L. (1999). Theory of Multicomponent Fluids. Applied Mathematical Sciences, 135.
Manninen, M., Taivassalo, V. & Kallio S. (1996). On the mixture model for multiphase flow, V.t.u. (VTT), Editor. Technical Research Center of Finland: Espoo. 67.
Drew, D. A. (1983). Mathematical Modeling of Two-Phase Flow. Annual Review of Fluid Mechanics, 15(1), 261-291.
Guo, Q. C. & Jin, Y. C. (1999). Modeling Sediment Transport Using Depth-Averaged and Moment Equations. J. Hydraul. Eng.-ASCE, 125, 1262-1269.
De Henau, V. & Raithby, G. D. (1995). A transient two-fluid model for the simulation of slug flow in pipelines--II. Validation. International Journal of Multiphase Flow, 21(3), 351-363.
Issa, R. I. & Kempf, M. H. W. (2003). Simulation of slug flow in horizontal and nearly horizontal pipes with the two-fluid model. International Journal of Multiphase Flow, 29(1), 69-95.
Toro, F. E. (1997). Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer-Verlag ed. 600.
Toro, F. E. (2000). Shock-Capturing Methods for Free-Surface Shallow Flows, ed. John Wiley and Sons Ltd. Chichester -NY -Weinheim -Brisbane -Singapore -Toronto. 310.
LeVeque, R. J. (1998). Balancing Source Terms and Flux Gradients in High-Resolution Godunov Methods: The Quasi-Steady Wave-Propagation Algorithm. Journal of computational physics, 146(1), 346-365.
Guinot, V. (2003). Godunov-type Schemes: An introduction for engineers, ed. E. Science. Amsterdam. 480.
Glaister, P. (1988). Approximate Riemann solutions of the shallow water equations. Journal of Hydraulic Research, 26(3), 293-306.
Ghamry, H. K. & Steffler, P. M. (2002). Effect of applying different distribution shapes for velocities and pressure on simulation of curved open channels. J. Hydraul. Eng. ASCE, 128, 969-982.
Castro-Orgaz, O., Giraldez, J. V. & Ayuso, J. L. (2008). Critical Flow over Circular Crested Weirs. Journal of hydraulic Engineering, 134, 1661-1664.
Castro-Orzag, O. & Dey, S. (2008). One-dimensional channel flow equations with curvature revisited. J. Hydraul. Res., 47, 157-166.
Anh, T. N. & Hosoda, T. (2007). Depth-averaged model of open-channel flows over an arbitrary 3D surface and its applications to analysis of water surface profile. J. Hydraul. Eng.-ASCE, 133, 350-360.
Causin, P. & Miglio, E. (2002). Parallel Computing for the Simulation of 3D Free Surface Flows in Environmental Applications, in Proceedings of the 9th European PVM/MPI Users' Group Meeting on Recent Advances in Parallel Virtual Machine and Message Passing Interface. Springer-Verlag.
Causin, P., Miglio, E. & Saleri, F. (2002). Algebraic factorizations for 3D non-hydrostatic free surface flows. Computing and Visualization in Science, 5(2), 85-94.
Vincenzo Casulli and Ralph T. (1992). Cheng, Semi-implicit finite difference methods for three-dimensional shallow water flow. International Journal for Numerical Methods in Fluids, 15(6), 629-648.
Paquier, A. & Kadi, K. E. (2008). A Model for Bed-Load Transport and Morphological Evolution in Rivers:Description and Pertinence, in Hyperbolic Problems: Theory, Numerics, Applications. 285-296.
Balayn, P. Contribution à la modélisation numérique de l'évolution morphologique des cours d'eau aménagés lors de crues, Université Claude-Bernard.
Ishii, M. (1977). One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes. Medium: X; Size: Pages: 62.
Yulistiyanto, B., Zech, Y. & Graf, W. H. (1998). Flow around a Cylinder: Shallow-Water Modeling with Diffusion-Dispersion. J. Hydraul. Eng.-ASCE, 124, 419-429.
Beffa, C. J. (1994). Praktische Lösung der tiefengemittelten Flachwassergleichungen. Mitteilungen der Versuchsanstalt für Wasserbau, Hydrologie un Glaziologie, ed. D. Vischer. Vol. 133. Zürich: ETHZ. 128.
Steffler, P. M. & Y.C. (1993). Jin, Depth averaged and moment equations for moderately shallow free surface flow. J. Hydraul. Res., 31, 5-17.
Khan, A. A. & Steffler, P. M. (1996). Vertically averaged and moment equations model for flow over curved beds. J. Hydraul. Eng.-ASCE, 122, 3-9.
Ghamry, H. K. & Steffler, P. M. (2002). Two dimensional vertically averaged and moment equations for rapidly varied flows. J. Hydraul. Res., 40, 579-587.
Jin, Y. C. & Steffler, P. M. (1993). Predicting flow in curved open channels by depth-averaged method. J. Hydraul. Eng.-ASCE, 119, 109-124.
Khan, A. A. & Steffler, P. M. (1996). Modelling overfalls using vertically averaged and moment equations. J. Hydraul. Eng.-ASCE, 122, 397-402.
Näf, D. R. (1997). Numerische Simulation von Stosswellen in Freispiegelströmungen. Mitteilungen der Versuchsanstalt für Wasserbau, Hydrologie un Glaziologie, ed. D. Vischer. Vol. 148. Zürich: ETHZ. 175.
Rottman, J. W. & Simpson, J. E. (1983). Gravity currents produced by instantaneous releases of a heavy fluid in a rectangular channel. Cambridge Journals Online, 95-110
Moodie, T.B., Pascal, J. P. & Swaters, G. E. (1998). Sediment Transport and Deposition from a Two-layer Fluid Model of Gravity Currents on Sloping Bottoms. Studies in Applied Mathematics, 100(3), 215-244.
Rhyming, G. L. (1985). Dynamique des fluides, ed. romandes. Lausanne.
Liggett, J. A. (1994). Fluid Mechanics. McGraw-Hill, inc.
Spurk, J. H. & Aksel, N. (2008). Fluid Mechanics. Berlin, Heidelberg: Springer. 531.
Streeter, V. L., Wylie, E. B. & Bedford, K.W. (1998). Fluid Mechanichs. Ninth ed, ed. McGraw-Hill.
Candel, S. (1990). Mécanique des fluides, ed. Dunod. Vol. 1-2. Paris. 450.
Aris, R., (Ed). (1962). Vectors, Tensors and the Basic Equations of Fluid Mechanics. Prentice-Hall: Englewood Cliffs, N.J.
Truesdell, C. & Toupin, R. (1960). The Classical Field Theories. Handbuch der Physik, ed. Springer-Verlag. Berlin-Heidelberg.
Hibiki, T. & Ishii, M. (2003). One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes. International Journal of Heat and Mass Transfer, 46(25), 4935-4948.
Verloop, W. C. (1995). The inertial coupling force. International Journal of Multiphase Flow, 21(5), 929-933.
Ungarish, M. (1995). On the modeling and investigation of polydispersed rotating suspensions. International Journal of Multiphase Flow, 21(2) 267-284.
Johansen, S. T., Anderson, N. M. & de Silva, S. R. (1990). A two-phase model for particle local equilibrium applied to air classification of powders. Powder Technology, 63(2), 121-132.
Flåtten, T. & Munkejord, S. T. (2006). The approximate Riemann solver of Roe applied to a drift-flux two-phase flow model. M2AN, 40(4), 735-764.
Masella, J. M., Tran, Q. H. Ferre, D. & Pauchon, C. (1998). Transient simulation of two-phase flows in pipes. International Journal of Multiphase Flow, 24(5), 739-755.
Romate, J. E. (1998). An approximate Riemann solver for a two-phase flow model with numerically given slip relation. Computers & Fluids, 27(4), 455-477.
Fjelde, K. K. & Karlsen, K. H. (2002). High-resolution hybrid primitive-conservative upwind schemes for the drift flux model. Computers & Fluids, 31(3), 335-367.
Wallis, G. B. (1969). One-dimensional Two-phase Flow, ed. M. H.B. Company. 410.
Corradini, M. L. (1997). Fundamentals of Multiphase Flow, ed. U.o.W. Department of Engineering Physics.
García-Cascales, J. R. Conservative Numerical Schemes for Unsteady 1D Two Phase Flow, PhD Universidad Politécnica de Valencia, Spain.
Ramos, J. I. (1995). One-dimensional, time-dependent, homogeneous, two-phase flow in volcanic conduits. International Journal for Numerical Methods in Fluids, 21(3): p. 253-278.
Sharma, Y., Scoggins, J. M. W., Shoham, O. & Brill, J. P. (1985). Simulation of transient two-phase flow in pipelines, in The 2nd International Conference on Multiphase Flow. London, UK.
Mori, Y., Huikata, K. & Ohmori, T. (1976). Propagation of a pressure wave in two-phase flow with very high void fraction. International Journal of Multiphase Flow, 2(4), 453-464.
Chahed, J., Roig, V. & Masbernat, L. (2003). Eulerian-Eulerian two-fluid model for turbulent gas-liquid bubbly flows. International Journal of Multiphase Flow,. 29(1), 23-49.
Omgba-Essama, C. Numerical Modelling of Transient Gas-Liquid Flows (Application to Stratified & Slug Flow Regimes), Phd Cranfield University.
Ullmann, A. & Brauner, N. (2006). Closure relations for two-fluid models for two-phase stratified smooth and stratified wavy flows. International Journal of Multiphase Flow, 32(1), 82-105.
Ullmann, A., Goldstein, A., Zamir, M. & Brauner, N. (2004). Closure relations for the shear stresses in two-fluid models for laminar stratified flow. International Journal of Multiphase Flow, 30(7-8), 877-900.
Issa, R. I., Bonizzi, M. & Barbeau, S. (2006). Improved closuremodels for gas entrainment and interfacial shear for slug flow modelling in horizontal pipes. International Journal of Multiphase Flow, 32(10-11), 1287-1293.
Gudmunson, R. L. A Numerical Study of The Two-Fluid Models for Dispersed Two-Phase Flow, Phd thesis, Numerical Analysis and Computer Science, Royal Institute of Technology, Stockholm.
De Henau, V. & Raithby, G. D. (1995). A transient two-fluid model for the simulation of slug flow in pipelines--I. Theory. International Journal of Multiphase Flow, 21(3),. 335-349.
Wilcox, C. D. (1994). Turbulence modeling for CFD, ed. C. Industries. La Canada, California.
Sagaut, P., Deck, S. & Terracol, M. (2006). Multiscale and multiresolution approaches in turbulence. Imperial College Pr.
Daniels, L. C., Guardino, C. & Thompson, C. P. (2002). An Implicit Two-Phase Compressible Flow Solver For Pipelines. Multiphase Science and Technology, 14(2), 96.
Yadigaroglu, G. & Lahey Jr, R. T. (1976). On the various forms of the conservation equations in two-phase flow. International Journal of Multiphase Flow, 2(5-6), 477-494.
Mathers, W., Ferch, R. L., Hancox, W. T. & McDonald. B. H. (1978). Equations For Transient Flow-Boiling In A Duct. in 2nd CSNI Specialist Meeting on Transient Two-Phase Flow. Paris, France.
Nigmatulin, R. I. (1979). Spatial averaging in the mechanics of heterogeneous and dispersed systems. International Journal of Multiphase Flow, 5(5), 353-385.
Lahey Jr, R. T. & Drew, D. A. (1988). Three Dimensional Time and Volume Averaged Conservation Equations of Two-Phase Flow, in Advance in Nuclear Science and Technology. 1-69.
Brennen, C. E. (2005). Fundamentals of Multiphase Flows. Cambridge University Press.
Kolev, N. I. (2007). Multiphase Flow Dynamics. Springer. 308.
Awad, M. M. & Muzychka, Y. S. (2008). Effective property models for homogeneous two-phase flows. Experimental Thermal and Fluid Science, 33(1), 106-113.
Awad, M. M. & Muzychka. Y.S. (2005). Bounds on Two-Phase Flow -Part 1 -Frictional Pressure Gradient in Circular Pipes. In ASME International Mechanical Engineering Congress and Exposition. Orlando, Florida.
Sethian, J. A. (2001). Evolution, implementation, and application of level set and fast marching methods for advancing fronts. Journal of computational physics, 169(2), 503-555.
Sethian, J. (1999). Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science, ed. C.U. Press.
Detrembleur, S., Archambeau, P., Erpicum, S., Dewals, B. J. & Pirotton, M. (2008). An Explicit Projection Method for Solving Incompressible Navier-Stokes Equations. to publish.
Lafaurie, B., Nardone, C., Scardovelli, R., Zaleski, S. & Zanetti, G. (1994). Modeling Merging and Fragmentation in Multiphase Flows with Surfer. Journal of computational physics, 113(1), 134-147.
Harlow, B. L. & Welch, K. (1970). The SMAC method: A numerical Technique for Calculating Incompressible Fluid Flows. Los Alamos Laboratory Report.
Erpicum, S., Dewals, B. J., Archambeau, P. & Pirotton, M. (2009). Dam-break flow computation based on an efficient flux-vector splitting. Journal of Computational and Applied Mathematics, accepted.
Dewals, B. J. Une approche unifié pour la modélisation d'écoulements à surface libre, de leur effet érosif sur une structure et de leur intéraction avec divers constituants, Phd thesis, Applied Hydrodynamics and Hydraulic Constructions, Liège University.
Whitham, G. B. (1974). Linear and Nonlinear Waves. New York: John Wiley & Sons.636.
Stewart, J. (2001). Analyse, concepts et contextes: Volume 1, Fonctions d'une variable, ed. D. Boek. 790.
Tejedor, L., Izquierdo, A., Sein, D. V. & Kagan, B. A. (1998). Tides and tidal energetics of the Strait of Gibraltar: a modelling approach. Tectonophysics, 294(3-4), 333-347.
Chen, S. C. & Peng, S. H. (2006). Two-dimensional numerical model of two-layer shallow water equations for confluence simulation. Advances in Water Resources, 29(11), 1608-1617.
Berthelsen, P. A. & Ytrehus, T. (2005). Calculations of stratified wavy two-phase flow in pipes. International Journal of Multiphase Flow, 31(5), 571-592.
Brockmeier, U., Schaffrath, A. & Unger, H. (1995). Verification of the two-phase stratified-flow model in by separate effect tests. Nuclear Engineering and Design, 154(1), 43-50.
Audusse, E. (2004). A Multilayer Saint-Venant Model. HAL -CCSd -CNRS.
Audusse, E. & Bristeau, M. O. (2007). Finite-Volume Solvers for a Multilayer Saint-Venant System. International Journal of Applied Mathematics and Computer Science, 17(3), 311-320.
Audusse, E., Bristeau, M. O. & Decoene, A. (2006). 3D Free Surface Flows Simulations Using a Multilayer Saint-Venant Model. Comparisons with Navier-Stokes Solutions, in Numerical Mathematics and Advanced Applications. 181-189.
Audusse, E., Bristeau, M. O. Perthame, B. & Sainte-Marie, J. (2009). A multilayer Saint-Venant system with mass exchanges for Shallow Water flows. Derivation and numerical validation.
Castro, M., Macías, J. & Parés, C. (2001). A q-scheme for a class of systems of coupled conservation laws with source term. Application to a two-layer 1-D shallow water system. M2AN, 35(1), 107-127.
Castro, M. J., García-Rodríguez, J. A., González-Vida, J. M., Macías, J. & Parés, C. (2007). Improved FVM for two-layer shallow-water models: Application to the Strait of Gibraltar. Advances in Engineering Software, 38(6), 386-398.
Abbott, M. B. (1982). A Modelling System for the Design and Operation of Stormwater Sewer Network. First Edition ed. Engineering applications of computational hydraulics. Pitman Advanced Publishing Program.
Rodi, W. (1984). Turbulence models and their application in hydraulics -A state of the art review. Delft: IAHR. 104.
ASCE, (1988). Task Committee on Turbulence Models in Hydraulic Computations, Turbulence modeling of surface water flow and transport: Part I. J. Hydraul. Eng. ASCE, 114, 970-991.
Fisher, H. B. (1981). Transport models for Inland and Coastal Waters. New York: Academic Press.
Moody, L. F. (1944). Friction factors for pipe flow. Transactions of the ASME, 66(8): p. 671-684.
Nikuradse, J. Laws of flow in rough pipes. 1950, National Advisory Committee for Aeronautics (NACA): Washington. 62.
Brownlie, W. R. (1981). Re-Examination of Nikuradse Roughness Data. Journal of the Hydraulics Division, 107, 115-119.
Montes, J.S. (1998). Hydraulics of Open Channel Flow. Available from: http://ecite.utas.edu.au/13441.
US, (1989). Geological Survey, Guide for selecting Manning's roughness coefficients for natural channels and flood plains. Water Supply paper, 2339.
Smart, G. (2004). An improved flow resistance formula, in Proc. 2nd Int. Conf. on Fluvial Hydraulics: River Flow 2004, G., Massimo, C. Armando, & R. Della Morte, (Editors.) Balkema: Leiden, etc. 259-263.
Arbenz, K.& Bachmann, O. (1992). Eléments d'analyse numérique et appliquée. Presses Polytechniques et Universitaires Romandes (PPUR).
Hirsch, C. (1988). Numerical Computation of Internal and External Flows -Fundamentals of Numerical Discretization. Vol. 1. Chichester: Wiley. 515.
Hirsch, C. (1990). Numerical Computation of Internal and External Flows -Computational Methods for Inviscid and Viscous Flows. Vol. 2. Chichester: Wiley. 691.
Dewals, B. J., Erpicum, S., Archambeau, P., Detrembleur, S. & Pirotton, M. (2006). Numerical tools for dam break risk assessment: validation and application to a large complex of dams, in Improvements in reservoir construction, operation and maintenance, H. Henry, Editor. Thomas Telford: London. 272-282.
Erpicum, S., Archambeau, P., Dewals, B. J., Ernst, J. & Pirotton, M. (2009). Dam-break flow numerical modeling considering structural impacts on buildings, in Proc. 33rd IAHR Congress -Water engineering for a sustainable environment. IAHR: Vancouver, British Columbia.
Chanson, H. (1991). Self-Aerated Flows on Chutes and Spillways. Journal of hydraulic Engineering, 119(2), 220-243.
Falvey, H. T. (1980). Air-Water Flow in Hydraulic Structures. Engineering Monogaph. Vol. 41, United States Department of the Interior.
Wilhelms, S. C. & Gulliver, J. S. (1994). Self-aerated Flow on Corps of Engineers Spillways, in Water Quality Research Program, U.A.C.o. Engineers, Editor. 112.
Andre, S. (2004). High Velocity Aerated Flows onStepped Chutes with Macro-Roughness Element. Communications du laboratoire de constructions hydrauliques, ed. Ecole Polytechnique Fédérale de Lausanne. Lausanne. 270.
Chanson, H. & Gonzales, C. A. (2004). Recent advances in stepped spillway design: air-water flow on stepped chutes, embankment dam stepped spillway and other considerations, in Fluvial, Environmental and Coastal Developments in Hydraulic Engineering, M. Mossa, Yasuda & Chanson, (Editor). Taylor&Francis.
Zuber, N. & Findlay, J. A. (1965). Average volumetric concentration in two-phase flow systems. Journal Name: Journal of Heat Transfer (U.S.); Journal Volume: Vol: 87; Other Information: Orig. Receipt Date: 31-DEC-66, Medium: X; Size: Pages: 453-68.
Zuber, N., Staub, F. W., Bijwaard, G.& Kroeger, P. G. (1967). Steady state and transient void fraction in two-phase flow systems., in Other Information: Work Performed under United States--Euratom Joint Research and Development Program. UNCL. Orig. Receipt Date: 31-DEC-68. Medium: X; Size: Pages: 422.
Enrique Julia, J., Hibiki, T., Ishii, M., Yun, B. J. &u Park, G. C. (2009). Drift-flux model in a sub-channel of rod bundle geometry. International Journal of Heat and Mass Transfer, 52(13-14), 3032-3041.
Goda, H., Hibiki, T., Kim, S., Ishii, M., & Uhle, J. (2003). Drift-flux model for downward two-phase flow. International Journal of Heat and Mass Transfer, 46(25): p. 4835-4844.
Hibiki, T., Goda, H., Kim, S., Ishii, M. & Uhle, J. (2004). Structure of vertical downward bubbly flow. International Journal of Heat and Mass Transfer, 47(8-9), 1847-1862.
Hibiki, T. & Ishii, M. (2003). One-dimensional drift-flux model for two-phase flow in a large diameter pipe. International Journal of Heat and Mass Transfer, 46(10), 17731790.
Coddington, P. & Macian, R. (2002). A study of the performance of void fraction correlations used in the context of drift-flux two-phase flow models. Nuclear Engineering and Design, 215(3), 199-216.
Rouhani, S. Z. & Axelsson, E. (1970). Calculation of void volume fraction in the subcooled and quality boiling regions. International Journal of Heat and Mass Transfer, 13(2), 383-393.
Hibiki, T. & Ishii, M. (2002). Distribution parameter and drift velocity of drift-flux model in bubbly flow. International Journal of Heat and Mass Transfer, 45(4), 707-721.
Woldesemayat, M. A. & Ghajar, A. J. (2007). Comparison of void fraction correlations for different flow patterns in horizontal and upward inclined pipes. International Journal of Multiphase Flow, 33(4), 347-370.
Dukler, A. E., Moye Wicks III, & Cleveland, R. G. (1964). Frictional pressure drop in two-phase flow: A. A comparison of existing correlations for pressure loss and holdup. AIChE Journal, 10(1), 38-43.
Diener, R.& Friedel, L. (1998). Reproductive accuracy of selected void fraction correlations for horizontal and vertical upflow. Forschung im Ingenieurwesen, 64(4), 87-97.
Dubois, J. (1998). Comportement hydraulique et modélisation des écoulements de surface. Communication 8, Laboratoire de constructions hydrauliques, Editor Schleiss A;. Lausanne.
Archambeau, P. Contribution à la modélisation de la genèse et de la propagation des crues et inondations, Phd thesis, Applied Hydrodynamics and Hydraulic Constructions, Liège University.
Wood, I. R. (1991). Air entrainment in free-surface flows. Balkema: Rotterdam. 142.
Chepaikin, G. A. & Donchenko, E. G. (1987). Certain Effects of Flow Aeration in Spillways. Hydrotechnical Construction, 636-640.
Chanson, H. & Gonzalez, C. A. (2005). Physical modelling and scale effects of air-water flows on stepped spillways. Journal of Zhejiang University SCIENCE, 6A(3), 243-250.
Galappatti, G. & Vreugdenhil, C. B. (1985). A depth-integrated model for suspended sediment transport. J. Hydraul. Res., 23, 359-375.
van Rijn, L. C. Mathematical modelling of morphological processes in the case of suspended sediment transport, thesis, Delft Hydraulic Laboratory Communication, Delft Technological University.
Julien, P. Y. (1995). Erosion and Sedimentation. Cambridge: Cambridge University Press. 280.
Bouchard, J. P. (2001). La gestion des sédiments par chasse: Outils d'optimisation et de prévision d'impact. Houille Blanche-Rev. Int., 62-66.