M. L. Yates and M. Benoit, Accuracy and efficiency of two numerical methods of solving the potential flow problem for highly nonlinear and dispersive water waves, International Journal for Numerical Methods in Fluids, vol.32, issue.1, pp.616-640, 2015.
DOI : 10.1016/S0378-3839(97)81747-4

URL : https://hal.archives-ouvertes.fr/hal-01143724

C. Raoult, M. Benoit, and M. Yates, Validation of a fully nonlinear and dispersive wave model with laboratory non-breaking experiments, Coastal Engineering, vol.114, pp.194-207, 2016.
DOI : 10.1016/j.coastaleng.2016.04.003

URL : https://hal.archives-ouvertes.fr/hal-01334598

P. L. Liu, P. Lin, K. Chang, and T. Sakakiyama, Numerical Modeling of Wave Interaction with Porous Structures, Journal of Waterway, Port, Coastal, and Ocean Engineering, vol.125, issue.6, pp.322-330, 1999.
DOI : 10.1061/(ASCE)0733-950X(1999)125:6(322)

S. Shao, Incompressible SPH simulation of wave breaking and overtopping with turbulence modelling, International Journal for Numerical Methods in Fluids, vol.9, issue.5, pp.597-621, 2006.
DOI : 10.1002/fld.1068

J. L. Lara, N. Garcia, and I. J. Losada, RANS modelling applied to random wave interaction with submerged permeable structures, Coastal Engineering, vol.53, issue.5-6, pp.395-417, 2006.
DOI : 10.1016/j.coastaleng.2005.11.003

R. A. Dalrymple and B. D. Rogers, Numerical modeling of water waves with the SPH method, Coastal Engineering, vol.53, issue.2-3, pp.141-147, 2006.
DOI : 10.1016/j.coastaleng.2005.10.004

P. Higuera, J. L. Lara, and I. J. Losada, Realistic wave generation and active wave absorption for Navier-Stokes application to openFOAM R ? , Coastal Eng, pp.71-102, 2013.

J. Berkhoff, Computation of Combined Refraction ??? Diffraction, Coastal Engineering 1972, pp.471-490, 1972.
DOI : 10.1061/9780872620490.027

J. Boussinesq, Théorie des ondes et des remous qui se propagent le long d'un canal rectangulaire horizontal, en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond, J. Math. Pures Appl, issue.2, pp.17-55, 1872.

F. Serre, Contribution à l'étude des écoulements permanents et variables dans les canaux, Houille Blanche, vol.6, issue.3, pp.374-388, 1953.

A. E. Green and P. Naghdi, A derivation of equations for wave propagation in water of variable depth, Journal of Fluid Mechanics, vol.338, issue.02, pp.237-246, 1976.
DOI : 10.1017/S0022112076002425

D. H. Peregrine, Long waves on a beach, Journal of Fluid Mechanics, vol.13, issue.04, pp.815-827, 1967.
DOI : 10.1029/JZ071i002p00393

O. G. Nwogu, Alternative Form of Boussinesq Equations for Nearshore Wave Propagation, Journal of Waterway, Port, Coastal, and Ocean Engineering, vol.119, issue.6, pp.618-638, 1993.
DOI : 10.1061/(ASCE)0733-950X(1993)119:6(618)

P. A. Madsen and H. A. Schäffer, Higher-order Boussinesq-type equations for surface gravity waves: derivation and analysis, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.356, issue.1749, pp.3123-3181, 1998.
DOI : 10.1098/rsta.1998.0309

J. T. Kirby, Boussinesq models and applications to nearshore wave propagation, surfzone processes and wave-induced currents, Advances in Coastal Modeling, pp.1-31, 2003.

G. Wei, J. T. Kirby, S. T. Grilli, and R. Subramanya, A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves, Journal of Fluid Mechanics, vol.107, issue.-1, pp.71-92, 1995.
DOI : 10.1063/1.865459

Y. Agnon, P. A. Madsen, and H. A. Schäffer, A new approach to high-order Boussinesq models, Journal of Fluid Mechanics, vol.399, pp.319-333, 1999.
DOI : 10.1017/S0022112099006394

A. B. Kennedy, J. T. Kirby, Q. Chen, and R. A. Dalrymple, Boussinesq-type equations with improved nonlinear performance, Wave Motion, vol.33, issue.3, pp.225-243, 2001.
DOI : 10.1016/S0165-2125(00)00071-8

P. A. Madsen, H. B. Bingham, and H. Liu, A new Boussinesq method for fully nonlinear waves from shallow to deep water, Journal of Fluid Mechanics, vol.462, pp.1-30, 2002.
DOI : 10.1017/S0022112002008467

P. A. Madsen, H. B. Bingham, and H. A. Schäffer, Boussinesq-type formulations for fully nonlinear and extremely dispersive water waves: derivation and analysis, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.459, issue.2033, pp.459-1075, 2003.
DOI : 10.1098/rspa.2002.1067

P. A. Madsen, D. Fuhrman, and B. Wang, A Boussinesq-type method for fully nonlinear waves interacting with a rapidly varying bathymetry, Coastal Engineering, vol.53, issue.5-6, pp.487-504, 2006.
DOI : 10.1016/j.coastaleng.2005.11.002

P. Lynett and P. L. Liu, A two-layer approach to wave modelling, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.460, issue.2049, pp.460-2637, 2004.
DOI : 10.1098/rspa.2004.1305

F. Chazel, M. Benoit, A. Ern, and S. Piperno, A double-layer Boussinesq-type model for highly nonlinear and dispersive waves, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci, pp.465-2319, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00371036

Z. Liu and K. , Two-layer Boussinesq models for coastal water waves, Wave Motion, vol.57, pp.88-111, 2015.
DOI : 10.1016/j.wavemoti.2015.03.006

Z. Liu and K. , A new two-layer Boussinesq model for coastal waves from deep to shallow water: Derivation and analysis, Wave Motion, vol.67, pp.1-14, 2016.
DOI : 10.1016/j.wavemoti.2016.07.002

M. Zijlema and G. S. Stelling, Efficient computation of surf zone waves using the nonlinear shallow water equations with non-hydrostatic pressure, Coastal Engineering, vol.55, issue.10, pp.780-790, 2008.
DOI : 10.1016/j.coastaleng.2008.02.020

G. Ma, F. Shi, and J. T. Kirby, Shock-capturing non-hydrostatic model for fully dispersive surface wave processes, Ocean Model, pp.43-44, 2012.

S. T. Grilli, J. Skourup, and I. A. Svendsen, An efficient boundary element method for nonlinear water waves, Engineering Analysis with Boundary Elements, vol.6, issue.2, pp.97-107, 1989.
DOI : 10.1016/0955-7997(89)90005-2

P. Wang, Y. Yao, and M. Tulin, An efficient numerical tank for non-linear water waves, based on the multi-subdomain approach with BEM, International Journal for Numerical Methods in Fluids, vol.83, issue.12, pp.1315-1336, 1995.
DOI : 10.1002/fld.1650201203

N. Drimer and Y. Agnon, An improved low-order boundary element method for breaking surface waves, Wave Motion, vol.43, issue.3, pp.241-258, 2006.
DOI : 10.1016/j.wavemoti.2005.09.006

C. Fochesato, S. T. Grilli, and F. Dias, Numerical modeling of extreme rogue waves generated by directional energy focusing, Wave Motion, vol.44, issue.5, pp.395-416, 2007.
DOI : 10.1016/j.wavemoti.2007.01.003

V. E. Zakharov, Stability of periodic waves of finite amplitude on the surface of a deep fluid, Journal of Applied Mechanics and Technical Physics, vol.10, issue.no. 4, pp.190-194, 1968.
DOI : 10.1007/BF00913182

J. Wilkening and V. Vasan, Comparison of Five Methods of Computing the Dirichlet???Neumann Operator for the Water Wave Problem, Nonlinear Wave Equations: Analytic and Computational Techniques, Contemporary Mathematics, 2015.
DOI : 10.1090/conm/635/12713

Y. Tian and S. Sato, A Numerical Model on the Interaction Between Nearshore Nonlinear Waves and Strong Currents, Coastal Engineering Journal, vol.2, issue.5, pp.369-395, 2008.
DOI : 10.1061/(ASCE)0733-950X(1995)121:5(251)

Y. Chen and P. L. Liu, Modified Boussinesq equations and associated parabolic models for water wave propagation, Journal of Fluid Mechanics, vol.115, issue.-1, pp.351-381, 1995.
DOI : 10.1016/0021-9991(84)90092-5

M. F. Gobbi, J. T. Kirby, and G. Wei, A fully nonlinear Boussinesq model for surface waves, J. Fluid Mech, pp.405-181, 2000.

A. B. Kennedy, J. Kirby, and M. Gobbi, Simplified higher-order Boussinesq equations, Coastal Engineering, vol.44, issue.3, pp.205-229, 2002.
DOI : 10.1016/S0378-3839(01)00032-1

C. Lee, Y. Cho, and S. Yoon, A note on linear dispersion and shoaling properties in extended Boussinesq equations, Ocean Eng, pp.1849-1867, 2003.

P. Lynett and P. L. Liu, Linear analysis of the multi-layer model, Coastal Engineering, vol.51, issue.5-6, pp.439-454, 2004.
DOI : 10.1016/j.coastaleng.2004.05.004

G. Simarro, A. Orfila, and A. Galan, Linear shoaling in Boussinesq-type wave propagation models, Coastal Engineering, vol.80, pp.100-106, 2013.
DOI : 10.1016/j.coastaleng.2013.05.009

M. Roseau, Asymptotic Wave Theory, North-Holland, p.349, 1976.

J. P. Boyd, Chebyshev and Fourier Spectral Methods: Second Edition, Revised, p.688, 2001.
DOI : 10.1007/978-3-642-83876-7

C. Raoult, Nonlinear and Dispersive Numerical Modeling of Nearshore Waves, 2016.
URL : https://hal.archives-ouvertes.fr/tel-01547187

P. A. Madsen and Y. Agnon, Accuracy and convergence of velocity formulations for water waves in the framework of Boussinesq theory, Journal of Fluid Mechanics, vol.477, pp.285-319, 2003.
DOI : 10.1017/S0022112002003257

H. B. Bingham and Y. Agnon, A Fourier???Boussinesq method for nonlinear water waves, European Journal of Mechanics - B/Fluids, vol.24, issue.2, pp.255-274, 2005.
DOI : 10.1016/j.euromechflu.2004.06.006

H. B. Bingham, P. A. Madsen, and D. R. Fuhrman, Velocity potential formulations of highly accurate Boussinesq-type models, Coastal Engineering, vol.56, issue.4, pp.467-478, 2009.
DOI : 10.1016/j.coastaleng.2008.10.012

G. A. Athanassoulis and K. A. Belibassakis, A consistent coupled-mode theory for the propagation of small-amplitude water waves over variable bathymetry regions, Journal of Fluid Mechanics, vol.389, pp.275-301, 1999.
DOI : 10.1017/S0022112099004978

R. Porter and D. Porter, Approximations to the scattering of water waves by steep topography, Journal of Fluid Mechanics, vol.562, pp.279-302, 2006.
DOI : 10.1017/S0022112006001005

C. Tsai, T. Hsu, and Y. Lin, On Step Approximation for Roseau's Analytical Solution of Water Waves, Mathematical Problems in Engineering, vol.15, issue.1, p.2011, 2011.
DOI : 10.1017/S002211209400368X