Y. Achdou, O. Pironneau, and F. Valentin, Effective Boundary Conditions for Laminar Flows over Periodic Rough Boundaries, Journal of Computational Physics, vol.147, issue.1, pp.187-218, 1998.
DOI : 10.1006/jcph.1998.6088

E. Audusse, F. Bouchut, M. Bristeau, R. Klein, and B. Perthame, A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows, SIAM Journal on Scientific Computing, vol.25, issue.6, pp.2050-2065, 2004.
DOI : 10.1137/S1064827503431090

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.401.8273

E. Audusse, M. Bristeau, B. Perthame, and J. Sainte-marie, A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation, ESAIM: Mathematical Modelling and Numerical Analysis, vol.45, issue.1, pp.169-200, 2011.
DOI : 10.1051/m2an/2010036

URL : https://hal.archives-ouvertes.fr/hal-00355730

E. Berger, M. Deverge, A. Hirschberg, P. Lagrée, and C. Vilain, Characterization of the pressure drop in a 2d symmetrical pipe: some asymptotical, numerical and experimental comparisons, ZAMM, vol.85, issue.2, pp.141-146, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00363818

V. Bonnaillie-noël, M. Dambrine, F. Hérau, and G. Vial, On Generalized Ventcel's Type Boundary Conditions for Laplace Operator in a Bounded Domain, SIAM Journal on Mathematical Analysis, vol.42, issue.2, pp.931-945, 2010.
DOI : 10.1137/090756521

F. Bouchut, J. L. Sommer, and V. Zeitlin, Frontal geostrophic adjustment and nonlinear wave phenomena in one-dimensional rotating shallow water. Part 2. High-resolution numerical simulations, Journal of Fluid Mechanics, vol.514, pp.35-63, 2004.
DOI : 10.1017/S0022112004009991

F. Bouchut, Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources, Frontiers in Mathematics, 2004.

M. Boutounet, J. Monnier, and J. Vila, Multi-Regime Shallow Free-Surface Flow Models for Quasi-Newtonian Fluids. working paper or preprint, 2013.
DOI : 10.1016/j.euromechflu.2015.10.005

URL : https://hal.archives-ouvertes.fr/hal-00877471

D. Bresch and P. Noble, Mathematical Justification of a Shallow Water Model, Methods and Applications of Analysis, vol.14, issue.2, pp.87-118, 2007.
DOI : 10.4310/MAA.2007.v14.n2.a1

URL : https://hal.archives-ouvertes.fr/hal-00385922

D. Bucur, E. Feireisl, and . Ne?asová, Influence of wall roughness on the slip behaviour of viscous fluids, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.138, issue.05, pp.957-973, 2008.
DOI : 10.1017/S0308210507000376

J. Burguete and P. García-navarro, Implicit schemes with large time step for non-linear equations: application to river flow hydraulics, International Journal for Numerical Methods in Fluids, vol.46, issue.6, pp.607-636, 2004.
DOI : 10.1002/fld.772

URL : https://digital.csic.es/bitstream/10261/86716/1/BurgueteJ_IntJNumMeth_2004.pdf

V. Caleffi, A. Valiani, and A. Zanni, Finite volume method for simulating extreme flood events in natural channels, Journal of Hydraulic Research, vol.338, issue.2, pp.167-177, 2003.
DOI : 10.1016/S0045-7930(97)00071-6

M. Cathala, Problématiques d'analyse numérique et de modélisation pourécoulementspourécoulements de fluides environnementaux. Theses, 2013.

P. Chassaing, Mécanique des fluides.Cépadù es edition, 2010.

V. T. Chow, Open-channel hydraulics, 1959.

J. Cousteix and J. Mauss, Asymptotic analysis and boundary layers. Scientific Computation, 2007.

A. Dalibard, D. Gérard, and . Varet, Effective boundary condition at a rough surface starting from a slip condition, Journal of Differential Equations, vol.251, issue.12, pp.3450-3487, 2011.
DOI : 10.1016/j.jde.2011.07.017

URL : https://hal.archives-ouvertes.fr/hal-00498555

A. Dalibard and N. Masmoudi, Phénomène de séparation pour l'´ equation de prandtl stationnaire, Séminaire Laurent Schwartz ? EDP et applications, pp.1-18
DOI : 10.5802/slsedp.80

O. Delestre, C. Lucas, P. Ksinant, F. Darboux, C. Laguerre et al., SWASHES: a compilation of shallow water analytic solutions for hydraulic and environmental studies, International Journal for Numerical Methods in Fluids, vol.74, issue.3, pp.72269-300, 2013.
DOI : 10.1002/fld.3865

URL : https://hal.archives-ouvertes.fr/hal-00628246

O. Delestre, Rain water overland flow on agricultural fields simulation. Theses, Université d'Orléans, 2010.
URL : https://hal.archives-ouvertes.fr/tel-00531377

O. Delestre, S. Cordier, F. Darboux, and F. James, A limitation of the hydrostatic reconstruction technique for Shallow Water equations, Comptes Rendus Mathematique, vol.350, issue.13-14, pp.13-14677, 2012.
DOI : 10.1016/j.crma.2012.08.004

URL : https://hal.archives-ouvertes.fr/hal-00710654

O. Delestre, S. Cordier, F. James, and F. Darboux, Simulation of rain-water overland-flow In Hyperbolic problems: theory, numerics and applications, Proc. Sympos. Appl. Math, vol.67, pp.537-546, 2009.

D. O. Edmund, K. J. Maki, and R. F. Beck, An improved viscous / inviscid velocity decomposition method, International Workshop on Water Waves and Floating Bodies (IWWWFB), 2011.

M. Esteves, X. Faucher, S. Galle, and M. Vauclin, Overland flow and infiltration modelling for small plots during unsteady rain: numerical results versus observed values, Journal of Hydrology, vol.228, issue.3-4, pp.3-4265, 2000.
DOI : 10.1016/S0022-1694(00)00155-4

L. David and . George, Finite volume methods and adaptive refinement for tsunami propagation and inundation, Thesis (Ph.D.)?, 2006.

D. Gerard-varet and N. Masmoudi, Well-posedness for the Prandtl system without analyticity or monotonicity. ArXiv e-prints, 2013.

D. Gérard, -. Varet, and N. Masmoudi, Relevance of the Slip Condition for Fluid Flows Near an Irregular Boundary, Communications in Mathematical Physics, vol.19, issue.2, pp.99-137, 2010.
DOI : 10.1007/s00220-009-0976-0

J. Gerbeau and B. Perthame, Derivation of viscous Saint-Venant system for laminar shallow water; numerical validation, Discrete Contin. Dyn. Syst. Ser. B, vol.1, issue.1, pp.89-102, 2001.
URL : https://hal.archives-ouvertes.fr/inria-00072549

E. Godlewski and P. Raviart, Numerical approximation of hyperbolic systems of conservation laws, Applied Mathematical Sciences, vol.118, 1996.
DOI : 10.1007/978-1-4612-0713-9

N. Goutal and F. Maurel, Proceedings of the 2 nd workshop on dam-break wave simulation, 1997.

R. S. Govindaraju, Modeling Overland Flow Contamination by Chemicals Mixed in Shallow Soil Horizons Under Variable Source Area Hydrology, Water Resources Research, vol.109, issue.3, pp.753-758, 1996.
DOI : 10.1016/0022-1694(89)90021-8

P. Guilcher, Contribution au développement d'une méthode SPH pour la simulation numérique des interactions houle-structure. Theses, 2008.

J. Andrew, D. Hogg, and . Pritchard, The effects of hydraulic resistance on dam-break and other shallow inertial flows, J. Fluid Mech, vol.501, pp.179-212, 2004.

F. James, P. Lagrée, and M. Legrand, A viscous layer model for a shallow water free surface flow. working paper or preprint, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01341563

S. Kalliadasis, C. Ruyer-quil, B. Scheid, and M. G. Velarde, Falling liquid films, Applied Mathematical Sciences, vol.176
DOI : 10.1007/978-1-84882-367-9

D. Kim, Y. Cho, and Y. Yi, Propagation and run-up of nearshore tsunamis with HLLC approximate Riemann solver, Ocean Engineering, vol.34, issue.8-9, pp.8-91164, 2007.
DOI : 10.1016/j.oceaneng.2006.07.001

P. Lagrée and S. Lorthois, The RNS/Prandtl equations and their link with other asymptotic descriptions: Application to the wall shear stress scaling in a constricted pipe, International Journal of Engineering Science, vol.43, issue.3-4, pp.3-4352, 2005.
DOI : 10.1016/j.ijengsci.2004.09.009

P. Lagrée, Interactive boundary layer (IBL) In Asymptotic methods in fluid mechanics: survey and recent advances, of CISM Courses and Lectures, pp.247-286, 2010.

P. Lagrée, A. Van-hirtum, and X. Pelorson, Asymmetrical effects in a 2D stenosis, European Journal of Mechanics - B/Fluids, vol.26, issue.1, pp.83-92, 2007.
DOI : 10.1016/j.euromechflu.2006.05.003

M. Le, S. Cordier, C. Lucas, and O. Cerdan, A faster numerical scheme for a coupled system modeling soil erosion and sediment transport, Water Resources Research, vol.3, issue.8, pp.987-1005, 2015.
DOI : 10.1029/WR003i003p00753

P. Luchini, F. Ois, and . Charru, Consistent section-averaged equations of quasi-one-dimensional laminar flow, Journal of Fluid Mechanics, vol.3, issue.008, pp.337-341
DOI : 10.1146/annurev.fluid.36.050802.121918

S. Popinet, Quadtree-adaptative tsunami modelling, Ocean Engineering, vol.61, issue.9, pp.1261-1285, 2011.
DOI : 10.1007/s10236-011-0438-z

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.374.7506

G. L. Richard and S. L. Gavrilyuk, A new model of roll waves: comparison with Brock???s experiments, Journal of Fluid Mechanics, vol.10, pp.374-405, 2012.
DOI : 10.1098/rspa.1984.0079

J. Rivlin and R. Wallach, An Analytical Solution for the Lateral Transport of Dissolved Chemicals in Overland Flow, Water Resources Research, vol.32, issue.3, pp.1031-1040, 1995.
DOI : 10.13031/2013.31089

C. Ruyer-quil and P. Manneville, Modeling film flows down inclined planes, The European Physical Journal B, vol.6, issue.2, pp.277-292, 1998.
DOI : 10.1007/s100510050550

C. Ruyer-quil and P. Manneville, Improved modeling of flows down inclined planes, The European Physical Journal B, vol.15, issue.2, pp.357-369, 2000.
DOI : 10.1007/s100510051137

URL : https://hal.archives-ouvertes.fr/hal-01025361

H. Schlichting, Boundary layer theory McGraw-Hill Series in Mechanical Engineering, 1968.

F. T. Smith, FLOW THROUGH CONSTRICTED OR DILATED PIPES AND CHANNELS: PART 1, The Quarterly Journal of Mechanics and Applied Mathematics, vol.29, issue.3, pp.343-376, 1976.
DOI : 10.1093/qjmam/29.3.343

C. H. Stephens and A. S. Arena, Application of the transpiration method for aeroservoelastic prediction using CFD, 39th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, 1998.
DOI : 10.2514/6.1998-2071

K. Stewartson, ON THE IMPULSIVE MOTION OF A FLAT PLATE IN A VISCOUS FLUID, The Quarterly Journal of Mechanics and Applied Mathematics, vol.4, issue.2, pp.182-198, 1951.
DOI : 10.1093/qjmam/4.2.182

J. J. Stoker, Water waves: The mathematical theory with applications, Pure and Applied Mathematics, 1957.
DOI : 10.1002/9781118033159

P. G. Tucker, Unsteady computational fluid dynamics in aeronautics, volume 104 of Fluid Mechanics and its Applications

A. Valiani, V. Caleffi, and A. Zanni, Case Study: Malpasset Dam-Break Simulation using a Two-Dimensional Finite Volume Method, Journal of Hydraulic Engineering, vol.128, issue.5, pp.460-472, 2002.
DOI : 10.1061/(ASCE)0733-9429(2002)128:5(460)

M. Van-dyke, Perturbation Method in Fluid Mechanics, Journal of Applied Mechanics, vol.43, issue.1, 1975.
DOI : 10.1115/1.3423785

G. B. Whitham, Linear and nonlinear waves, Pure and Applied Mathematics
DOI : 10.1002/9781118032954

J. R. Womersley, An elastic tube theory of pulse transmission and oscillatory flow in mammalian arteries, 1957.