V. Aizinger and C. Dawson, A discontinuous Galerkin method for two-dimensional flow and transport in shallow water, Advances in Water Resources, vol.25, issue.1, pp.67-84, 2002.
DOI : 10.1016/S0309-1708(01)00019-7

V. R. Ambati and O. Bokhove, Space???time discontinuous Galerkin finite element method for shallow water flows, Journal of Computational and Applied Mathematics, vol.204, issue.2, pp.452-462, 2007.
DOI : 10.1016/j.cam.2006.01.047

E. Audusse, F. Bouchut, M. O. 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

E. Audusse and M. O. Bristeau, A well-balanced positivity preserving ???second-order??? scheme for shallow water flows on unstructured meshes, Journal of Computational Physics, vol.206, issue.1, pp.311-333, 2005.
DOI : 10.1016/j.jcp.2004.12.016
URL : https://hal.archives-ouvertes.fr/inria-00070738

A. Bermudez and M. Vazquez, Upwind methods for hyperbolic conservation laws with source terms, Computers & Fluids, vol.23, issue.8, pp.1049-1071, 1994.
DOI : 10.1016/0045-7930(94)90004-3

P. Bernard, J. Remacle, R. Comblen, V. Legat, and K. Hillewaert, High-order discontinuous Galerkin schemes on general 2D manifolds applied to the shallow water equations, Journal of Computational Physics, vol.228, issue.17, pp.6514-6535, 2009.
DOI : 10.1016/j.jcp.2009.05.046

C. Berthon, Robustness of MUSCL schemes for 2D unstructured meshes, Journal of Computational Physics, vol.218, issue.2, pp.495-509, 2006.
DOI : 10.1016/j.jcp.2006.02.028

C. Berthon and F. Foucher, Efficient well-balanced hydrostatic upwind schemes for shallow-water equations, Journal of Computational Physics, vol.231, issue.15, pp.4993-5015, 2012.
DOI : 10.1016/j.jcp.2012.02.031

C. Berthon and F. Marche, A Positive Preserving High Order VFRoe Scheme for Shallow Water Equations: A Class of Relaxation Schemes, SIAM Journal on Scientific Computing, vol.30, issue.5, pp.2587-2612, 2008.
DOI : 10.1137/070686147
URL : https://hal.archives-ouvertes.fr/hal-00370486

R. Biswas, K. D. Devine, and J. E. Flaherty, Parallel, adaptive finite element methods for conservation laws, Applied Numerical Mathematics, vol.14, issue.1-3, pp.255-283, 1994.
DOI : 10.1016/0168-9274(94)90029-9

O. Bokhove, Flooding and Drying in Discontinuous Galerkin Finite-Element Discretizations of Shallow-Water Equations. Part 1: One Dimension, Journal of Scientific Computing, vol.171, issue.1-3, pp.22-2347, 2005.
DOI : 10.1007/s10915-004-4136-6

A. Bollermann, S. Noelle, and M. Lukacova-medvidova, Abstract, Communications in Computational Physics, vol.183, issue.02, pp.371-404, 2011.
DOI : 10.4208/cicp.220210.020710a

S. Bryson, Y. Epshteyn, A. Kurganov, and G. Petrova, Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system, ESAIM: Mathematical Modelling and Numerical Analysis, vol.45, issue.3, pp.423-446, 2011.
DOI : 10.1051/m2an/2010060

S. Bunya, E. J. Kubatko, J. J. Westerink, and C. Dawson, A wetting and drying treatment for the Runge???Kutta discontinuous Galerkin solution to the shallow water equations, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.17-20, pp.1548-1562, 2009.
DOI : 10.1016/j.cma.2009.01.008

A. Burbeau, P. Sagaut, and C. Bruneau, A Problem-Independent Limiter for High-Order Runge???Kutta Discontinuous Galerkin Methods, Journal of Computational Physics, vol.169, issue.1, pp.111-150, 2001.
DOI : 10.1006/jcph.2001.6718

V. Caleffi, A. Valiani, and A. Bernini, Fourth-order balanced source term treatment in central WENO schemes for shallow water equations, Journal of Computational Physics, vol.218, issue.1, pp.228-245, 2006.
DOI : 10.1016/j.jcp.2006.02.001

G. Carrier and H. Greenspan, Water waves of finite amplitude on a sloping beach, Journal of Fluid Mechanics, vol.1, issue.01, pp.97-109, 1958.
DOI : 10.1017/S0022112058000331

M. Castro, J. Gallardo, J. López-garcía, and C. Parés, Well-Balanced High Order Extensions of Godunov's Method for Semilinear Balance Laws, SIAM Journal on Numerical Analysis, vol.46, issue.2, pp.1012-1039, 2008.
DOI : 10.1137/060674879

M. Castro, A. Milanes, and C. Pares, WELL-BALANCED NUMERICAL SCHEMES BASED ON A GENERALIZED HYDROSTATIC RECONSTRUCTION TECHNIQUE, Mathematical Models and Methods in Applied Sciences, vol.17, issue.12, pp.2055-2113, 2007.
DOI : 10.1142/S021820250700256X

M. J. Castro, J. A. Lò, I. Apez-garcì, I. Aa, C. Parè et al., High order exactly well-balanced numerical methods for shallow water systems, Journal of Computational Physics, vol.246, pp.242-264, 2013.
DOI : 10.1016/j.jcp.2013.03.033

G. Chavent and J. Jaffré, Mathematical Models and Finite Elements for Reservoir Simulation, Studies in Mathematics and its applications, 1986.

B. Cockburn and C. Shu, The Runge???Kutta Discontinuous Galerkin Method for Conservation Laws V, Journal of Computational Physics, vol.141, issue.2, pp.199-224, 1998.
DOI : 10.1006/jcph.1998.5892

B. Cockburn and C. Shu, Runge-Kutta discontinuous Galerkin methods for convection-dominated problems, Journal of Scientific Computing, vol.16, issue.3, pp.173-261, 2001.
DOI : 10.1023/A:1012873910884

D. T. Cox, Experimental and numerical modelling of surf zone hydrodynamics, 1995.

C. Dawson and V. Aizinger, A Discontinuous Galerkin Method for Three-Dimensional Shallow Water Equations, Journal of Scientific Computing, vol.20, issue.5, pp.22-23245, 2005.
DOI : 10.1007/s10915-004-4139-3

A. J. De-saint-venant, Théorie du mouvement non-permanent des eaux, avec application aux crues des rivì eres etàetà l'introduction des marées dans leur lit, C.R. Acad. Sci. Paris, Section Mécanique, vol.73, pp.147-154, 1871.

O. Delestre and F. Marche, A Numerical Scheme for a Viscous Shallow Water Model with Friction, Journal of Scientific Computing, vol.26, issue.11, pp.41-51, 2011.
DOI : 10.1007/s10915-010-9393-y
URL : https://hal.archives-ouvertes.fr/hal-00799076

M. Dubiner, Spectral methods on triangles and other domains, Journal of Scientific Computing, vol.1, issue.1, pp.345-390, 1991.
DOI : 10.1007/BF01060030

A. Duran, F. Marche, and Q. Liang, On the well-balanced numerical discretization of shallow water equations on unstructured meshes, Journal of Computational Physics, vol.235, pp.565-586, 2013.
DOI : 10.1016/j.jcp.2012.10.033

D. Dutykh, R. Poncet, and F. Dias, The VOLNA code for the numerical modeling of tsunami waves: Generation, propagation and inundation, European Journal of Mechanics - B/Fluids, vol.30, issue.6, pp.598-615, 2011.
DOI : 10.1016/j.euromechflu.2011.05.005

A. Ern, S. Piperno, and K. Djadel, A well-balanced Runge-Kutta discontinuous Galerkin method for the shallow-water equations with flooding and drying, International Journal for Numerical Methods in Fluids, vol.107, issue.2, pp.1-25, 2008.
DOI : 10.1002/fld.1674
URL : https://hal.archives-ouvertes.fr/hal-00153788

C. Eskilsson and S. J. Sherwin, A triangular spectral/hp discontinuous Galerkin method for modelling 2D shallow water equations, International Journal for Numerical Methods in Fluids, vol.45, issue.6, pp.605-623, 2004.
DOI : 10.1002/fld.709

J. M. Gallardo, C. Parés, and M. Castro, On a well-balanced high-order finite volume scheme for shallow water equations with topography and dry areas, Journal of Computational Physics, vol.227, issue.1, pp.574-601, 2007.
DOI : 10.1016/j.jcp.2007.08.007

T. Gallouët, J. M. Hérard, and N. Seguin, Some approximate Godunov schemes to compute shallow-water equations with topography, Computers & Fluids, vol.32, issue.4, pp.479-513, 2003.
DOI : 10.1016/S0045-7930(02)00011-7

J. Gerbeau and B. Perthame, Derivation of viscous saint-venant system for laminar shallow water; numerical validation, Disc. Contin. Dyn. Syst. Ser. B, vol.1, issue.1, pp.89-102, 2001.
URL : https://hal.archives-ouvertes.fr/hal-00691701

F. X. Giraldo, J. S. Hesthaven, and T. Warburton, Nodal High-Order Discontinuous Galerkin Methods for the Spherical Shallow Water Equations, Journal of Computational Physics, vol.181, issue.2, pp.499-525, 2002.
DOI : 10.1006/jcph.2002.7139

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

L. Gosse, A well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms, Computers & Mathematics with Applications, vol.39, issue.9-10, pp.135-159, 2000.
DOI : 10.1016/S0898-1221(00)00093-6

S. Gottlieb, C. Shu, and E. Tadmor, Strong Stability-Preserving High-Order Time Discretization Methods, SIAM Review, vol.43, issue.1, pp.89-112, 2001.
DOI : 10.1137/S003614450036757X

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

J. M. Greenberg and A. Y. Leroux, A Well-Balanced Scheme for the Numerical Processing of Source Terms in Hyperbolic Equations, SIAM Journal on Numerical Analysis, vol.33, issue.1, pp.1-16, 1996.
DOI : 10.1137/0733001

Y. Guo, R. Liu, Y. Duan, and Y. Li, A characteristic-based finite volume scheme for shallow water equations, Journal of Hydrodynamics, Ser. B, vol.21, issue.4, pp.531-540, 2009.
DOI : 10.1016/S1001-6058(08)60181-X

A. Harten, P. D. Lax, and B. Van-leer, On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws, SIAM Review, vol.25, issue.1, pp.35-61, 1983.
DOI : 10.1137/1025002

H. Hoteit, P. Ackerer, R. Mosé, J. Erhel, and B. Philippe, New two-dimensional slope limiters for discontinuous Galerkin methods on arbitrary meshes, International Journal for Numerical Methods in Engineering, vol.39, issue.14, pp.612566-2593, 2004.
DOI : 10.1002/nme.1172
URL : https://hal.archives-ouvertes.fr/inria-00072097

M. E. Hubbard and N. Dodd, A 2D numerical model of wave run-up and overtopping, Coastal Engineering, vol.47, issue.1, pp.1-26, 2002.
DOI : 10.1016/S0378-3839(02)00094-7

G. Jiang and C. Shu, Efficient Implementation of Weighted ENO Schemes, Journal of Computational Physics, vol.126, issue.1, pp.202-228, 1996.
DOI : 10.1006/jcph.1996.0130

S. Jin, A steady-state capturing method for hyperbolic systems with geometrical source terms, ESAIM: Mathematical Modelling and Numerical Analysis, vol.35, issue.4, pp.631-645, 2001.
DOI : 10.1051/m2an:2001130

S. Jin and Z. Xin, The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications on Pure and Applied Mathematics, vol.54, issue.3, pp.235-276, 1995.
DOI : 10.1002/cpa.3160480303

T. Katsaounis, B. Perthame, and C. Simeoni, Upwinding sources at interfaces in conservation laws, Applied Mathematics Letters, vol.17, issue.3, pp.309-316, 2004.
DOI : 10.1016/S0893-9659(04)90068-7
URL : https://hal.archives-ouvertes.fr/hal-00922830

G. Kesserwani, Q. Liang, J. Vazquez, and R. Mosé, Well-balancing issues related to the RKDG2 scheme for the shallow water equations, International Journal for Numerical Methods in Fluids, vol.56, issue.7, pp.428-448, 2010.
DOI : 10.1002/fld.1879
URL : https://hal.archives-ouvertes.fr/hal-00515639

G. Kesserwani and Q. Liang, A discontinuous Galerkin algorithm for the two-dimensional shallow water equations, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.49-52, pp.3356-3368, 2010.
DOI : 10.1016/j.cma.2010.07.007

G. Kesserwani and Q. Liang, Locally Limited and Fully Conserved RKDG2 Shallow Water Solutions with Wetting and Drying, Journal of Scientific Computing, vol.51, issue.EMAC2009, pp.120-144, 2012.
DOI : 10.1007/s10915-011-9476-4

L. Krivodonova, Limiters for high-order discontinuous Galerkin methods, Journal of Computational Physics, vol.226, issue.1, pp.879-896, 2007.
DOI : 10.1016/j.jcp.2007.05.011

L. Krivodonova, J. Xin, J. Remacle, N. Chevaugeon, and J. E. Flaherty, Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws, Applied Numerical Mathematics, vol.48, issue.3-4, pp.323-338, 2004.
DOI : 10.1016/j.apnum.2003.11.002
URL : https://hal.archives-ouvertes.fr/hal-01007288

E. J. Kubatko, J. J. Westerink, and C. Dawson, hp Discontinuous Galerkin methods for advection dominated problems in shallow water flow, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.1-3, pp.437-451, 2006.
DOI : 10.1016/j.cma.2006.05.002

E. J. Kubatko, S. Bunya, C. Dawson, and J. J. Westerink, Dynamic p-adaptive Runge???Kutta discontinuous Galerkin methods for the shallow water equations, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.21-26, pp.1766-1774, 2009.
DOI : 10.1016/j.cma.2009.01.007

A. Kurganov and D. Levy, Central-Upwind Schemes for the Saint-Venant System, ESAIM: Mathematical Modelling and Numerical Analysis, vol.36, issue.3, pp.397-425, 2002.
DOI : 10.1051/m2an:2002019

A. Kurganov and G. Petrova, A Second-Order Well-Balanced Positivity Preserving Central-Upwind Scheme for the Saint-Venant System, Communications in Mathematical Sciences, vol.5, issue.1, pp.133-160, 2007.
DOI : 10.4310/CMS.2007.v5.n1.a6

R. J. Leveque, Balancing Source Terms and Flux Gradients in High-Resolution Godunov Methods: The Quasi-Steady Wave-Propagation Algorithm, Journal of Computational Physics, vol.146, issue.1, pp.346-365, 1998.
DOI : 10.1006/jcph.1998.6058

M. Lauter, F. X. Giraldo, and D. , A discontinuous Galerkin method for the shallow water equations in spherical triangular coordinates, Journal of Computational Physics, vol.227, issue.24, pp.10226-10242, 2008.
DOI : 10.1016/j.jcp.2008.08.019

H. Li and R. Liu, The discontinuous Galerkin finite element method for the 2D shallow water equations, Mathematics and Computers in Simulation, vol.56, issue.3, pp.223-233, 2001.
DOI : 10.1016/S0378-4754(01)00277-4

Q. Liang and A. G. Borthwick, Adaptive quadtree simulation of shallow flows with wet???dry fronts over complex topography, Computers & Fluids, vol.38, issue.2, pp.221-234, 2009.
DOI : 10.1016/j.compfluid.2008.02.008

Q. Liang and F. Marche, Numerical resolution of well-balanced shallow water equations with complex source terms, Advances in Water Resources, vol.32, issue.6, pp.873-884, 2009.
DOI : 10.1016/j.advwatres.2009.02.010
URL : https://hal.archives-ouvertes.fr/hal-00799080

P. L. Liu, Y. Cho, M. J. Briggs, U. Kanoglu, and C. E. Synolakis, Runup of solitary waves on a circular Island, Journal of Fluid Mechanics, vol.31, pp.259-285, 1995.
DOI : 10.1016/0378-3839(92)90059-4

M. Lukacova, S. Noelle, and M. Kraft, Well-balanced finite volume evolution Galerkin methods for the shallow water equations, Journal of Computational Physics, vol.221, issue.1, pp.122-147, 2007.
DOI : 10.1016/j.jcp.2006.06.015

H. Luo, J. D. Baum, and R. Lohner, A Hermite WENO-based limiter for discontinuous Galerkin method on unstructured grids, Journal of Computational Physics, vol.225, issue.1, pp.686-713, 2007.
DOI : 10.1016/j.jcp.2006.12.017

F. Marche, Derivation of a new two-dimensional viscous shallow water model with varying topography, bottom friction and capillary effects, European Journal of Mechanics - B/Fluids, vol.26, issue.1, pp.49-63, 2007.
DOI : 10.1016/j.euromechflu.2006.04.007

F. Marche, Theoretical and numerical study of shallow water models. Applications to nearshore hydrodynamics, 2005.

F. Marche, Derivation of a new two-dimensional viscous shallow water model with varying topography, bottom friction and capillary effects, European Journal of Mechanics - B/Fluids, vol.26, issue.1, pp.49-63, 2007.
DOI : 10.1016/j.euromechflu.2006.04.007

F. Marche, P. Bonneton, P. Fabrie, and N. Seguin, Evaluation of well-balanced bore-capturing schemes for 2D wetting and drying processes, International Journal for Numerical Methods in Fluids, vol.107, issue.5, pp.867-894, 2007.
DOI : 10.1002/fld.1311
URL : https://hal.archives-ouvertes.fr/hal-00295018

R. D. Nair, S. J. Thomas, and R. D. Loft, A Discontinuous Galerkin Global Shallow Water Model, Monthly Weather Review, vol.133, issue.4, pp.876-888, 2004.
DOI : 10.1175/MWR2903.1

I. K. Nikolos and A. I. Delis, An unstructured node-centered finite volume scheme for shallow water flows with wet/dry fronts over complex topography, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.47-48, pp.3723-3750, 2009.
DOI : 10.1016/j.cma.2009.08.006

S. Noelle, N. Pankratz, G. Puppo, and J. R. Natvig, Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows, Journal of Computational Physics, vol.213, issue.2, pp.474-499, 2006.
DOI : 10.1016/j.jcp.2005.08.019

S. Noelle, Y. Xing, and C. Shu, High-order well-balanced finite volume WENO schemes for shallow water equation with moving water, Journal of Computational Physics, vol.226, issue.1, pp.29-58, 2007.
DOI : 10.1016/j.jcp.2007.03.031

H. T. Ozkan-haller and J. T. Kirby, A Fourier-Chebyshev collocation method for the shallow water equations including shoreline runup, Applied Ocean Research, vol.19, issue.1, pp.21-34, 1997.
DOI : 10.1016/S0141-1187(97)00011-4

B. Perthame, Kinetic Formulations of Conservation Laws, 2002.
URL : https://hal.archives-ouvertes.fr/hal-01146188

B. Perthame and Y. Qiu, A Variant of Van Leer's Method for Multidimensional Systems of Conservation Laws, Journal of Computational Physics, vol.112, issue.2, pp.370-381, 1994.
DOI : 10.1006/jcph.1994.1107

B. Perthame and C. W. Shu, On positivity preserving finite volume schemes for Euler equations, Numerische Mathematik, vol.73, issue.1, pp.119-130, 1996.
DOI : 10.1007/s002110050187

J. Qiu and C. Shu, Hermite WENO schemes and their application as limiters for Runge???Kutta discontinuous Galerkin method: one-dimensional case, Journal of Computational Physics, vol.193, issue.1, pp.115-135, 2003.
DOI : 10.1016/j.jcp.2003.07.026

J. Qiu and C. Shu, Runge--Kutta Discontinuous Galerkin Method Using WENO Limiters, SIAM Journal on Scientific Computing, vol.26, issue.3, pp.907-929, 2005.
DOI : 10.1137/S1064827503425298

J. Qiu and C. Shu, A Comparison of Troubled-Cell Indicators for Runge--Kutta Discontinuous Galerkin Methods Using Weighted Essentially Nonoscillatory Limiters, SIAM Journal on Scientific Computing, vol.27, issue.3, pp.995-1013, 2005.
DOI : 10.1137/04061372X

S. Rhebergen, O. Bokhove, and J. J. , Discontinuous Galerkin finite element methods for hyperbolic nonconservative partial differential equations, Journal of Computational Physics, vol.227, issue.3, pp.1887-1922, 2008.
DOI : 10.1016/j.jcp.2007.10.007

J. Remacle, S. Soares-frazão, X. Li, and M. S. Shephard, An adaptive discretization of shallow-water equations based on discontinuous Galerkin methods, International Journal for Numerical Methods in Fluids, vol.30, issue.8, pp.52903-923, 2006.
DOI : 10.1002/fld.1204

M. Ricchiuto and A. Bollermann, Stabilized residual distribution for shallow water simulations, Journal of Computational Physics, vol.228, issue.4, pp.1071-1115, 2009.
DOI : 10.1016/j.jcp.2008.10.020
URL : https://hal.archives-ouvertes.fr/inria-00538892

N. Rnjariic, Balanced finite volume WENO and central WENO schemes for the shallow water and the openchannel flow equations, J. Comput. Phys, vol.200, issue.2, pp.512-548, 2004.

B. Rogers, M. Fujihara, and A. Borthwick, Adaptive Q-tree Godunov-type scheme for shallow water equations, International Journal for Numerical Methods in Fluids, vol.14, issue.3, pp.247-280, 2001.
DOI : 10.1002/1097-0363(20010215)35:3<247::AID-FLD89>3.0.CO;2-E

B. D. Rogers, A. Borthwick, and P. Taylor, Mathematical balancing of flux gradient and source terms prior to using Roe???s approximate Riemann solver, Journal of Computational Physics, vol.192, issue.2, pp.422-451, 2003.
DOI : 10.1016/j.jcp.2003.07.020

G. Russo, Central schemes for conservation laws with application to shallow water equations. in Trends and applications of mathematics to mechanics, pp.225-246, 2005.

D. Schwanenberg and J. Kongeter, A discontinuous Galerkin method for the shallow water equations with source terms. Discontinuous Galerkin Methods, Lecture Notes in Computational Science and Engineering, vol.11, pp.289-309, 2000.

D. Schwanenberg and M. Harms, Discontinuous Galerkin Finite-Element Method for Transcritical Two-Dimensional Shallow Water Flows, Journal of Hydraulic Engineering, vol.130, issue.5, pp.412-421, 2004.
DOI : 10.1061/(ASCE)0733-9429(2004)130:5(412)

J. J. Stoker, Water Waves, Interscience, 1957.

P. A. Tassi, O. Bokhove, and C. A. Vionnet, Space discontinuous Galerkin method for shallow water flows???kinetic and HLLC flux, and potential vorticity generation, Advances in Water Resources, vol.30, issue.4, pp.998-1015, 2007.
DOI : 10.1016/j.advwatres.2006.09.003

E. F. Toro, M. Spruce, and W. Speare, Restoration of the contact surface in the HLL-Riemann solver, Shock Waves, vol.54, issue.1, pp.25-34, 1994.
DOI : 10.1007/BF01414629

C. J. Trahan and C. Dawson, Local time-stepping in Runge???Kutta discontinuous Galerkin finite element methods applied to the shallow-water equations, Computer Methods in Applied Mechanics and Engineering, vol.217, issue.220, pp.139-152, 2012.
DOI : 10.1016/j.cma.2012.01.002

S. Tu and S. Aliabadi, A slope limiting procedure in discontinuous galerkin finite element method for gasdynamic applications, Int. J. Numer. Anal. Model, vol.2, issue.2, pp.163-178, 2005.

J. J. Van-der-vegt, H. Van-der, and . Ven, Space???Time Discontinuous Galerkin Finite Element Method with Dynamic Grid Motion for Inviscid Compressible Flows, Journal of Computational Physics, vol.182, issue.2, pp.546-585, 2002.
DOI : 10.1006/jcph.2002.7185

B. Van-leer, Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method, Journal of Computational Physics, vol.32, issue.1, pp.227-248, 1997.
DOI : 10.1016/0021-9991(79)90145-1

J. Wang and R. Liu, A comparative study of finite volume methods on unstructured meshes for simulation of 2D shallow water wave problems, Mathematics and Computers in Simulation, vol.53, issue.3, pp.171-184, 2000.
DOI : 10.1016/S0378-4754(00)00173-7

Y. Wang, Q. Liang, G. Kesserwani, and J. W. Hall, A 2D shallow flow model for practical dam-break simulations, Journal of Hydraulic Research, vol.47, issue.3, pp.307-316, 2011.
DOI : 10.1006/jcph.2000.6670

W. R. Wolf and J. L. Azevedo, High-order ENO and WENO schemes for unstructured grids, International Journal for Numerical Methods in Fluids, vol.54, issue.10, pp.55917-943, 2007.
DOI : 10.1002/fld.1469

Y. Xing and C. Shu, High order finite difference WENO schemes with the exact conservation property for the shallow water equations, Journal of Computational Physics, vol.208, issue.1, pp.206-227, 2005.
DOI : 10.1016/j.jcp.2005.02.006

Y. Xing and C. Shu, High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms, Journal of Computational Physics, vol.214, issue.2, pp.567-598, 2006.
DOI : 10.1016/j.jcp.2005.10.005

Y. Xing and C. Shu, A new approach of high order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms, Commun. Comput. Phys, vol.1, pp.100-134, 2006.

Y. Xing, X. Zhang, and C. Shu, Positivity-preserving high order well-balanced discontinuous Galerkin methods for the shallow water equations, Advances in Water Resources, vol.33, issue.12, pp.1476-1493, 2010.
DOI : 10.1016/j.advwatres.2010.08.005

Y. Xing, C. Shu, and S. Noelle, On the Advantage of Well-Balanced Schemes for??Moving-Water Equilibria of the Shallow Water Equations, Journal of Scientific Computing, vol.214, issue.1-3, pp.339-349, 2011.
DOI : 10.1007/s10915-010-9377-y

Y. Xing and X. Zhang, Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for the Shallow Water Equations on Unstructured Triangular Meshes, Journal of Scientific Computing, vol.50, issue.1, pp.19-41, 2013.
DOI : 10.1007/s10915-013-9695-y

Y. Xing, Exactly well-balanced discontinuous Galerkin methods for the shallow water equations with moving water equilibrium, Journal of Computational Physics, vol.257, pp.536-553, 2014.
DOI : 10.1016/j.jcp.2013.10.010

]. J. Zelt, Tsunamis: the response of harbors with sloping boundaries to long wave exitation

. Tech and . Rep, KH-R-47 1986; California Institute of Technology., Laboratory of Hydraulics and Water Resources, Division of Engineering and Applied Science, California Institute of Technology, p.47, 1986.

X. Zhang and C. Shu, On maximum-principle-satisfying high order schemes for scalar conservation laws, Journal of Computational Physics, vol.229, issue.9, pp.8918-8934, 2010.
DOI : 10.1016/j.jcp.2009.12.030

X. Zhang and C. Shu, On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes, Journal of Computational Physics, vol.229, issue.23, pp.3091-3120, 2010.
DOI : 10.1016/j.jcp.2010.08.016

X. Zhang, Y. Xia, and C. Shu, Maximum-Principle-Satisfying and Positivity-Preserving High Order Discontinuous Galerkin Schemes for??Conservation Laws on Triangular Meshes, Journal of Scientific Computing, vol.229, issue.1, pp.29-62, 2012.
DOI : 10.1007/s10915-011-9472-8

X. Zhong and C. Shu, A simple weighted essentially nonoscillatory limiter for Runge???Kutta discontinuous Galerkin methods, Journal of Computational Physics, vol.232, issue.1, pp.397-415, 2013.
DOI : 10.1016/j.jcp.2012.08.028

J. G. Zhou, D. M. Causon, and C. G. Mingham, The Surface Gradient Method for the Treatment of Source Terms in the Shallow-Water Equations, Journal of Computational Physics, vol.168, issue.1, pp.1-25, 2001.
DOI : 10.1006/jcph.2000.6670

J. Zhu, J. Qiu, C. Shu, and M. Dumbser, Runge???Kutta discontinuous Galerkin method using WENO limiters II: Unstructured meshes, Journal of Computational Physics, vol.227, issue.9, pp.4330-4353, 2008.
DOI : 10.1016/j.jcp.2007.12.024

J. Zhu, J. Zhong, J. Qiu, and C. Shu, Runge???Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes, Journal of Computational Physics, vol.248, pp.200-220, 2013.
DOI : 10.1016/j.jcp.2013.04.012