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Volumn 17, Issue 3, 2015, Pages 721-760

Discontinuous-galerkin discretization of a new class of green-naghdi equations

Author keywords

Discontinuous Galerkin; Green Naghdi equations; Nonlinear and dispersive water waves; Shallow water equations; Wave breaking

Indexed keywords


EID: 84961288277     PISSN: 18152406     EISSN: 19917120     Source Type: Journal    
DOI: 10.4208/cicp.150414.101014a     Document Type: Article
Times cited : (42)

References (85)
  • 1
    • 0037016628 scopus 로고    scopus 로고
    • A posteriori error estimation for discontinuous Galerkin solutions of hyperbolic problems
    • S. Adjerid, K. Devine, J. Flaherty, and L. Krivodonova. A posteriori error estimation for discontinuous Galerkin solutions of hyperbolic problems. Comput. Meth. Appl. Mech. Engrg, 191(11):1097-1112, 2002.
    • (2002) Comput. Meth. Appl. Mech. Engrg , vol.191 , Issue.11 , pp. 1097-1112
    • Adjerid, S.1    Devine, K.2    Flaherty, J.3    Krivodonova, L.4
  • 2
    • 42549163819 scopus 로고    scopus 로고
    • A Nash-Moser theorem for singular evolution equations application to the Serre and Green-Naghdi equations
    • B. Alvarez-Samaniego and D. Lannes. A Nash-Moser theorem for singular evolution equations. application to the Serre and Green-Naghdi equations. Indiana Univ. Math. J., 57:97-131, 2008.
    • (2008) Indiana Univ. Math. J. , vol.57 , pp. 97-131
    • Alvarez-Samaniego, B.1    Lannes, D.2
  • 3
    • 34247217171 scopus 로고    scopus 로고
    • Space-time discontinuous Galerkin finite element method for shallow water flows
    • V.R. Ambati and O. Bokhove. Space-time discontinuous Galerkin finite element method for shallow water flows. J. Comput. App.Math., 204:452-462, 2007.
    • (2007) J. Comput. App.Math , vol.204 , pp. 452-462
    • Ambati, V.R.1    Bokhove, O.2
  • 4
    • 0036410391 scopus 로고    scopus 로고
    • Unified analysis of discontinuous Galerkin methods for elliptic problems
    • D.N. Arnold, F. Brezzi, B. Cockburn, and L.D. Marini. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal., 39(5):1749-1779, 2002.
    • (2002) SIAM J. Numer. Anal , vol.39 , Issue.5 , pp. 1749-1779
    • Arnold, D.N.1    Brezzi, F.2    Cockburn, B.3    Marini, L.D.4
  • 5
    • 0001416032 scopus 로고    scopus 로고
    • A high-order accurate discontinuous finite elementmethod for the numerical solution of the compressible Navier-Stokes equations
    • F. Bassi and S. Rebay. A high-order accurate discontinuous finite elementmethod for the numerical solution of the compressible Navier-Stokes equations. J. Comput. Phys., 131:267-279, 1997.
    • (1997) J. Comput. Phys , vol.131 , pp. 267-279
    • Bassi, F.1    Rebay, S.2
  • 6
    • 0027333936 scopus 로고
    • Experimental investigation of wave propagation over a bar
    • S. Beji and J.A. Battjes. Experimental investigation of wave propagation over a bar. Coast. Engrg., 19:151-162, 1993.
    • (1993) Coast. Engrg , vol.19 , pp. 151-162
    • Beji, S.1    Battjes, J.A.2
  • 7
    • 49749110380 scopus 로고    scopus 로고
    • A positive preserving high order VFRoe scheme for shallow water equations: A class of relaxation schemes SIAMJ
    • C. Berthon and F. Marche. A positive preserving high order VFRoe scheme for shallow water equations: a class of relaxation schemes. SIAMJ. Sci. Comput., 30:2587-2612, 2008.
    • (2008) Sci. Comput , vol.30 , pp. 2587-2612
    • Berthon, C.1    Marche, F.2
  • 8
    • 34147181096 scopus 로고    scopus 로고
    • Modelling of periodic wave transformation in the inner surf zone
    • P. Bonneton. Modelling of periodic wave transformation in the inner surf zone. Ocean Engineering, 34(10):1459-1471, 2007.
    • (2007) Ocean Engineering , vol.34 , Issue.10 , pp. 1459-1471
    • Bonneton, P.1
  • 9
    • 78650568860 scopus 로고    scopus 로고
    • A splitting approach for the fully nonlinear and weakly dispersive Green - Naghdi model
    • P. Bonneton, F. Chazel, D. Lannes, F. Marche, and M. Tissier. A splitting approach for the fully nonlinear and weakly dispersive Green - Naghdi model. J. Comput. Phys., 230:1479- 1498, 2011.
    • (2011) J. Comput. Phys , vol.230 , pp. 1479-1498
    • Bonneton, P.1    Chazel, F.2    Lannes, D.3    Marche, F.4    Tissier, M.5
  • 10
    • 0001314736 scopus 로고    scopus 로고
    • A problem-independent limiter for high-order runge-kutta discontinuous Galerkin methods
    • A. Burbeau, P. Sagaut, and Ch.-H. Bruneau. A problem-independent limiter for high-order runge-kutta discontinuous Galerkin methods. J. Comput. Phys., 169:111-150, 2001.
    • (2001) J. Comput. Phys , vol.169 , pp. 111-150
    • Burbeau, A.1    Sagaut, P.2    Bruneau Ch.-, H.3
  • 11
    • 79959525052 scopus 로고    scopus 로고
    • Numerical simulation of strongly nonlinear and dispersive waves using a Green - Naghdi model
    • F. Chazel, D. Lannes, and F. Marche. Numerical simulation of strongly nonlinear and dispersive waves using a Green - Naghdi model. J. Sci. Comput., pages 105-116, 2011.
    • (2011) J. Sci. Comput , pp. 105-116
    • Chazel, F.1    Lannes, D.2    Marche, F.3
  • 13
    • 33746360902 scopus 로고    scopus 로고
    • A Fourth-order Compact Finite Volume Scheme for Fully Nonlinear and Weakly Dispersive Boussinesq-type Equations. I: Model Development and Analysis
    • R. Cienfuegos, E. Barthélemy, and P. Bonneton. A fourth-order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq-type equations. I: Model development and analysis. Int. J. Num. Meth. Fluids, 51(11):1217-1253, 2006.
    • (2006) Int. J. Num. Meth. Fluids , vol.51 , Issue.11 , pp. 1217-1253
    • Cienfuegos, R.1    Barthélemy, E.2    Bonneton, P.3
  • 14
    • 76349112042 scopus 로고    scopus 로고
    • A wave-breakingmodel for Boussinesq-type equations including mass-induced effects
    • R. Cienfuegos, E. Barthelemy, and P. Bonneton. A wave-breakingmodel for Boussinesq-type equations including mass-induced effects. J. Water. Port Coast. and Oc. Engrg., 136:10-26, 2010.
    • (2010) J. Water. Port Coast. and Oc. Engrg , vol.136 , pp. 10-26
    • Cienfuegos, R.1    Barthelemy, E.2    Bonneton, P.3
  • 15
    • 76349112042 scopus 로고    scopus 로고
    • Wave-breaking model for Boussinesq type equations including roller effects in the mass conservation equation
    • R. Cienfuegos, E. Barthélemy, and P. Bonneton. Wave-breaking model for Boussinesq type equations including roller effects in the mass conservation equation. J. Water. Port. Coast. and Oc. Engrg., 136:10-26, 2010.
    • (2010) J. Water. Port. Coast. and Oc. Engrg , vol.136 , pp. 10-26
    • Cienfuegos, R.1    Barthélemy, E.2    Bonneton, P.3
  • 16
    • 0000076512 scopus 로고    scopus 로고
    • Runge-Kutta discontinuous Galerkin methods for convectiondominated problems
    • B. Cockburn and C.-W. Shu. Runge-Kutta discontinuous Galerkin methods for convectiondominated problems. J. Sci. Comput., 16(3):173-260, 2001.
    • (2001) J. Sci. Comput , vol.16 , Issue.3 , pp. 173-260
    • Cockburn, B.1    Shu, C.-W.2
  • 17
    • 0344393366 scopus 로고    scopus 로고
    • The Local Discontinuous Galerkin method for time-dependent convection-diffusion systems
    • B. Cockburn and S.-W. Shu. The Local Discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM J. Numer. Anal., 141:2440-2463, 1998.
    • (1998) SIAM J. Numer. Anal , vol.141 , pp. 2440-2463
    • Cockburn, B.1    Shu, S.-W.2
  • 19
    • 0031541111 scopus 로고    scopus 로고
    • An unsymmetric-pattern multifrontal method for sparse LU factorization
    • T.A. Davis and I.S. Duff. An unsymmetric-pattern multifrontal method for sparse LU factorization. SIAMJ. on Matrix Anal. and Applications, 18:140-158, 1997.
    • (1997) SIAMJ on Matrix Anal. and Applications , vol.18 , pp. 140-158
    • Davis, T.A.1    Duff, I.S.2
  • 20
    • 0003810103 scopus 로고
    • Comparison of computations with Boussinesq-like models and laboratory measurements
    • M.W. Dingemans. Comparison of computations with Boussinesq-like models and laboratory measurements. Delft Hydr., Report H-1684.12, 32, 1994.
    • (1994) Delft Hydr. Report H-1684.12 , vol.32
    • Dingemans, M.W.1
  • 21
    • 84903388615 scopus 로고    scopus 로고
    • Recent advances on the discontinuous Galerkinmethod for shallow water equations with topography source terms
    • A. Duran and F. Marche. Recent advances on the discontinuous Galerkinmethod for shallow water equations with topography source terms. Comput. & Fluids, 101:88-104, 2014.
    • (2014) Comput. & Fluids , vol.101 , pp. 88-104
    • Duran, A.1    Marche, F.2
  • 22
    • 84870985121 scopus 로고    scopus 로고
    • On thewell-balanced numerical discretization of shallow water equations on unstructured meshes
    • A. Duran, F. Marche, and Q. Liang. On thewell-balanced numerical discretization of shallow water equations on unstructured meshes. J. Comput. Phys., 235:565-586, 2013.
    • (2013) J. Comput. Phys , vol.235 , pp. 565-586
    • Duran, A.1    Marche, F.2    Liang, Q.3
  • 23
    • 79951767730 scopus 로고    scopus 로고
    • Finite volume schemes for dispersive wave propagation and runup
    • D. Dutykh, T. Katsaounis, and D. Mitsotakis. Finite volume schemes for dispersive wave propagation and runup. J. Comput. Phys., 230:3035 - 3061, 2011.
    • (2011) J. Comput. Phys , vol.230 , pp. 3035-3061
    • Dutykh, D.1    Katsaounis, T.2    Mitsotakis, D.3
  • 25
    • 38149019934 scopus 로고    scopus 로고
    • DG-FEM solution for nonlinear wave-structure interaction using Boussinesq-type equations
    • A.P. Engsig-Karup, J.S. Hesthaven, H.B. Bingham, and T. Warburton. DG-FEM solution for nonlinear wave-structure interaction using Boussinesq-type equations. Coast. Engrg., 55:197-208, 2008.
    • (2008) Coast. Engrg , vol.55 , pp. 197-208
    • Engsig-Karup, A.P.1    Hesthaven, J.S.2    Bingham, H.B.3    Warburton, T.4
  • 26
    • 28144441044 scopus 로고    scopus 로고
    • Hybrid finite-volume finite-difference scheme for the solution of Boussinesq equations
    • K. Erduran, S. Ilic, and V. Kutija. Hybrid finite-volume finite-difference scheme for the solution of Boussinesq equations. Int. J. Num. Meth. Fluids, 49:1213-1232, 2005.
    • (2005) Int. J. Num. Meth. Fluids , vol.49 , pp. 1213-1232
    • Erduran, K.1    Ilic, S.2    Kutija, V.3
  • 27
    • 33846536702 scopus 로고    scopus 로고
    • Further application of hybrid solution to another form of Boussinesq equations and comparisons
    • K.S. Erduran. Further application of hybrid solution to another form of Boussinesq equations and comparisons. Int. J. Num. Meth. Fluids, 53:827-849, 2007.
    • (2007) Int. J. Num. Meth. Fluids , vol.53 , pp. 827-849
    • Erduran, K.S.1
  • 28
    • 33847673327 scopus 로고    scopus 로고
    • Discontinuous Galerkin methods for Friedrichs' systems I. General theory
    • A. Ern and J.-L. Guermond. Discontinuous Galerkin methods for Friedrichs' systems. i. general theory. SIAMJ. Numer. Anal., 44(2):753-778, 2006.
    • (2006) SIAMJ. Numer. Anal , vol.44 , Issue.2 , pp. 753-778
    • Ern, A.1    Guermond, J.-L.2
  • 29
    • 34547406929 scopus 로고    scopus 로고
    • Discontinuous Galerkin methods for Friedrichs' systems II. Second-order elliptic pdes
    • A. Ern and J.-L. Guermond. Discontinuous Galerkin methods for Friedrichs' systems. ii. second-order elliptic pdes. SIAMJ. Numer. Anal., 44(6):2363-2388, 2006.
    • (2006) SIAMJ. Numer. Anal , vol.44 , Issue.6 , pp. 2363-2388
    • Ern, A.1    Guermond, J.-L.2
  • 30
    • 50249144099 scopus 로고    scopus 로고
    • A well- balanced Runge-Kutta discontinuous Galerkin method for the shallow-water equationswith flooding and drying
    • A. Ern, S. Piperno, and K. Djadel. A well- balanced Runge-Kutta discontinuous Galerkin method for the shallow-water equationswith flooding and drying. Int. J. Num.Meth. Fluids, 58:1-25, 2008.
    • (2008) Int. J. Num.Meth. Fluids , vol.58 , pp. 1-25
    • Ern, A.1    Piperno, S.2    Djadel, K.3
  • 31
    • 0038043549 scopus 로고    scopus 로고
    • An hp/spectral element model for efficient long-time integration of Boussinesq-type equations
    • C. Eskilsson and S. J. Sherwin. An hp/spectral element model for efficient long-time integration of Boussinesq-type equations. Coast. Engrg., 45:295-320, 2003.
    • (2003) Coast. Engrg , vol.45 , pp. 295-320
    • Eskilsson, C.1    Sherwin, S.J.2
  • 32
    • 14844358935 scopus 로고    scopus 로고
    • Discontinuous Galerkin spectral/hp element modelling of dispersive shallow water systems
    • C. Eskilsson and S.J. Sherwin. Discontinuous Galerkin spectral/hp element modelling of dispersive shallow water systems. J. Sci. Comput., 22 - 23:269-288, 2005.
    • (2005) J. Sci. Comput , vol.22-23 , pp. 269-288
    • Eskilsson, C.1    Sherwin, S.J.2
  • 33
    • 29144479606 scopus 로고    scopus 로고
    • Spectral/hp discontinuous Galerkin method for modelling 2D Boussinesq equations
    • C. Eskilsson and S.J. Sherwin. Spectral/hp discontinuous Galerkin method for modelling 2D Boussinesq equations. J. Comput. Phys., 212:566-589, 2006.
    • (2006) J. Comput. Phys , vol.212 , pp. 566-589
    • Eskilsson, C.1    Sherwin, S.J.2
  • 34
    • 33749323582 scopus 로고    scopus 로고
    • An unstructured spectral/hp element model for enhanced Boussinesq-type equations
    • C. Eskilsson, S.J. Sherwin, and L. Bergdahl. An unstructured spectral/hp element model for enhanced Boussinesq-type equations. Coast. Engrg., 53(947-963), 2006.
    • (2006) Coast. Engrg , vol.53 , Issue.947-963
    • Eskilsson, C.1    Sherwin, S.J.2    Bergdahl, L.3
  • 35
    • 0035273564 scopus 로고    scopus 로고
    • Strong stability preserving high order time discretization methods
    • S. Gottlieb, C.-W. Shu, and Tadmor E. Strong stability preserving high order time discretization methods. SIAMReview, 43:89-112, 2001.
    • (2001) SIAMReview , vol.43 , pp. 89-112
    • Gottlieb, S.1    Shu, C.-W.2    Tadmor, E.3
  • 36
    • 0016876595 scopus 로고
    • A derivation of equations for wave propagation in water of variable depth
    • A.E. Green and P.M. Naghdi. A derivation of equations for wave propagation in water of variable depth. J. Fluid Mech., 78:237-246, 1976.
    • (1976) J. Fluid Mech , vol.78 , pp. 237-246
    • Green, A.E.1    Naghdi, P.M.2
  • 38
    • 70449685747 scopus 로고    scopus 로고
    • Tsunami-like solitary waves impinging and overtopping an impermeable seawall: Experiment and rans modeling
    • S-C. Hsiao and T-C. Lin. Tsunami-like solitary waves impinging and overtopping an impermeable seawall: Experiment and rans modeling. Coast. Engrg., 57:1-18, 2010.
    • (2010) Coast. Engrg , vol.57 , pp. 1-18
    • Hsiao, S.-C.1    Lin, T.-C.2
  • 39
    • 84862656431 scopus 로고    scopus 로고
    • An unstructured finite volume numerical scheme for extended 2DBoussinesq-type equations
    • M. Kazolea, A.I. Delis, I.K. Nikolos, and C.E. Synolakis. An unstructured finite volume numerical scheme for extended 2DBoussinesq-type equations. Coast. Engrg., 69:42-66, 2012.
    • (2012) Coast. Engrg , vol.69 , pp. 42-66
    • Kazolea, M.1    Delis, A.I.2    Nikolos, I.K.3    Synolakis, C.E.4
  • 40
    • 84901260953 scopus 로고    scopus 로고
    • Numerical treatment of wave breaking on unstructured finite volume approximations for extended Boussinesq-type equations
    • M. Kazolea, A.I. Delis, and C.E. Synolakis. Numerical treatment of wave breaking on unstructured finite volume approximations for extended Boussinesq-type equations. J. Comput. Phys., 271:281-305, 2014.
    • (2014) J. Comput. Phys , vol.271 , pp. 281-305
    • Kazolea, M.1    Delis, A.I.2    Synolakis, C.E.3
  • 44
    • 59649093678 scopus 로고    scopus 로고
    • Derivation of asymptotic two-dimensional time-dependent equations for surface water wave propagation
    • D. Lannes and P. Bonneton. Derivation of asymptotic two-dimensional time-dependent equations for surface water wave propagation. Physics of fluids, 21:016601, 2009.
    • (2009) Physics of Fluids , vol.21 , pp. 016601
    • Lannes, D.1    Bonneton, P.2
  • 46
    • 73649106498 scopus 로고    scopus 로고
    • A numerical scheme for the Green-Naghdimodel
    • O. LeMétayer, S. Gavrilyuk, and S. Hank. A numerical scheme for the Green-Naghdimodel. J. Comput. Phys., (229):2034-2045, 2010.
    • (2010) J. Comput. Phys. , Issue.229 , pp. 2034-2045
    • Lemétayer, O.1    Gavrilyuk, S.2    Hank, S.3
  • 47
    • 84886260329 scopus 로고    scopus 로고
    • High order well-balanced CDG-FE methods for shallow water waves by a Green-Naghdi model
    • M Li, P. Guyenne, F. Li, and F. Xu. High order well-balanced CDG-FE methods for shallow water waves by a Green-Naghdi model. J. Comput. Phys., 257:169-192, 2014.
    • (2014) J. Comput. Phys , vol.257 , pp. 169-192
    • Li, M.1    Guyenne, P.2    Li, F.3    Xu, F.4
  • 48
    • 0033167143 scopus 로고    scopus 로고
    • Numericalmodeling of Boussinesq equations by finite element method
    • Y.S. Li, S.X. Liu, Y.X. Yu, and G.Z. Lai. Numericalmodeling of Boussinesq equations by finite element method. Coast. Engrg., 37:97-122, 1999.
    • (1999) Coast. Engrg , vol.37 , pp. 97-122
    • Li, Y.S.1    Liu, S.X.2    Yu, Y.X.3    Lai, G.Z.4
  • 49
    • 55949108414 scopus 로고    scopus 로고
    • Adaptive quadtree simulation of shallow flows with wetdry fronts over complex topography
    • Q. Liang and A. G. L. Borthwick. Adaptive quadtree simulation of shallow flows with wetdry fronts over complex topography. Comput. & Fluids, 38(2):221-234, 2009.
    • (2009) Comput. & Fluids , vol.38 , Issue.2 , pp. 221-234
    • Liang, Q.1    Borthwick, A.G.L.2
  • 50
    • 67349101335 scopus 로고    scopus 로고
    • Numerical resolution of well-balanced shallow water equations with complex source terms
    • Q. Liang and F. Marche. Numerical resolution of well-balanced shallow water equations with complex source terms. Adv.Water Res., 32:873-884, 2009.
    • (2009) Adv.Water Res , vol.32 , pp. 873-884
    • Liang, Q.1    Marche, F.2
  • 51
    • 0037055049 scopus 로고    scopus 로고
    • A new Boussinesq method for fully nonlinear waves from shallow to deep water
    • P.A. Madsen, H.B. Bingham, and H. Liu. A new Boussinesq method for fully nonlinear waves from shallow to deep water. J. Fluid Mech., 462:1-30, 2002.
    • (2002) J. Fluid Mech , vol.462 , pp. 1-30
    • Madsen, P.A.1    Bingham, H.B.2    Liu, H.3
  • 52
    • 0141848956 scopus 로고    scopus 로고
    • Boussinesq-type formulations for fully nonlinear and extremely dispersive water waves: Derivation and analysis
    • P.A. Madsen, H.B. Bingham, and H.A. Schaffer. Boussinesq-type formulations for fully nonlinear and extremely dispersive water waves: derivation and analysis. Proc. R. Soc. A, 459:1075-1104, 2003.
    • (2003) Proc. R. Soc. A , vol.459 , pp. 1075-1104
    • Madsen, P.A.1    Bingham, H.B.2    Schaffer, H.A.3
  • 53
    • 0026191546 scopus 로고
    • A new form of the Boussinesq equations with improved linear dispersion characteristics
    • P.A. Madsen, R. Murray, and O.R. Sorensen. A new form of the Boussinesq equations with improved linear dispersion characteristics. Coast. Engrg., 15(4):371-388, 1991.
    • (1991) Coast. Engrg , vol.15 , Issue.4 , pp. 371-388
    • Madsen, P.A.1    Murray, R.2    Sorensen, O.R.3
  • 54
    • 0027007549 scopus 로고
    • A newformof the Boussinesq equations with improved linear dispersion characteristics. Part 2: A slowing varying bathymetry
    • P.A. Madsen and O.R. Sørensen. A newformof the Boussinesq equations with improved linear dispersion characteristics. Part 2: A slowing varying bathymetry. Coast. Engrg., 18:183-204, 1992.
    • (1992) Coast. Engrg , vol.18 , pp. 183-204
    • Madsen, P.A.1    Sørensen, O.R.2
  • 55
    • 84906951164 scopus 로고    scopus 로고
    • On the Galerkin/finite-element method for the Serre equations
    • D. Mitsotakis, B. Ilan, and D. Dutykh. On the Galerkin/finite-element method for the Serre equations. J. Sci. Comput., 2014.
    • (2014) J. Sci. Comput
    • Mitsotakis, D.1    Ilan, B.2    Dutykh, D.3
  • 56
    • 0027789687 scopus 로고
    • Alternative form of Boussinesq equations for nearshore wave propagation
    • O. Nwogu. Alternative form of Boussinesq equations for nearshore wave propagation. J. Water. Port Coast. and Oc. Engrg., 119:618-638, 1993.
    • (1993) J. Water. Port Coast. and Oc. Engrg , vol.119 , pp. 618-638
    • Nwogu, O.1
  • 57
    • 81455154002 scopus 로고    scopus 로고
    • From the paddle to the beach - A Boussinesq shallow water numerical wave tank based on Madsen and Sørensen's equations
    • J. Orszaghova, A.G.L. Borthwick, and P.H. Taylor. From the paddle to the beach - A Boussinesq shallow water numerical wave tank based on Madsen and Sørensen's equations. J. Comput. Phys., 231:328-344, 2012.
    • (2012) J. Comput. Phys , vol.231 , pp. 328-344
    • Orszaghova, J.1    Borthwick, A.G.L.2    Taylor, P.H.3
  • 58
    • 77955516813 scopus 로고    scopus 로고
    • A pseudo-spectral algorithm and test cases for the numerical solution of the two-dimensional rotatingGreen-Naghdi shallowwater equations
    • J.D. Pearce and J.G. Esler. A pseudo-spectral algorithm and test cases for the numerical solution of the two-dimensional rotatingGreen-Naghdi shallowwater equations. J. Comput. Phys., 229:7594-7608, 2010.
    • (2010) J. Comput. Phys , vol.229 , pp. 7594-7608
    • Pearce, J.D.1    Esler, J.G.2
  • 59
    • 84958426983 scopus 로고
    • Long waves on a beach
    • D. Peregrine. Long waves on a beach. J. Fluid Mech., 27:815-827, 1967.
    • (1967) J. Fluid Mech , vol.27 , pp. 815-827
    • Peregrine, D.1
  • 60
    • 84958426983 scopus 로고
    • Long waves on a beach
    • D.H. Peregrine. Long waves on a beach. J. Fluid Mech., 27:815-827, 1967.
    • (1967) J. Fluid Mech , vol.27 , pp. 815-827
    • Peregrine, D.H.1
  • 61
    • 33646565327 scopus 로고    scopus 로고
    • A comparison of troubled-cell indicators for Runge-Kutta discontinuous Galerkin methods using weighted essentially nonoscillatory limiters
    • J. Qiu and C.-W. Shu. A comparison of troubled-cell indicators for Runge-Kutta discontinuous Galerkin methods using weighted essentially nonoscillatory limiters. SIAM J. Sci. Comput., 27:995-1013, 2005.
    • (2005) SIAM J. Sci. Comput , vol.27 , pp. 995-1013
    • Qiu, J.1    Shu, C.-W.2
  • 62
    • 84901267262 scopus 로고    scopus 로고
    • Upwind residual discretization of enhanced Boussinesq equations for wave propagation over complex bathymetries
    • in press
    • M. Ricchiuto and A.G. Filippini. Upwind residual discretization of enhanced Boussinesq equations for wave propagation over complex bathymetries. J. Comput. Phys., in press, 2014.
    • (2014) J. Comput. Phys
    • Ricchiuto, M.1    Filippini, A.G.2
  • 63
    • 84864075104 scopus 로고    scopus 로고
    • Boussinesq-type model for energetic breaking waves in fringing reef environments
    • V. Roeber and K.F. Cheung. Boussinesq-type model for energetic breaking waves in fringing reef environments. Coast. Engrg., 70(0):1 - 20, 2012.
    • (2012) Coast. Engrg , vol.70 , Issue.0 , pp. 1-20
    • Roeber, V.1    Cheung, K.F.2
  • 64
    • 0035864599 scopus 로고    scopus 로고
    • Adaptive Q-tree Godunov-type scheme for shallow water equations
    • B. Rogers, M. Fujihara, and A. Borthwick. Adaptive Q-tree Godunov-type scheme for shallow water equations. Int. J. Num. Meth. Fluids, 35:247-280, 2001.
    • (2001) Int. J. Num. Meth. Fluids , vol.35 , pp. 247-280
    • Rogers, B.1    Fujihara, M.2    Borthwick, A.3
  • 65
    • 0027788993 scopus 로고
    • A Boussinesq model for waves breaking in shallow water
    • H. Schaeffer. A Boussinesq model for waves breaking in shallow water. Coast. Engrg., 20:185-202, 1993.
    • (1993) Coast. Engrg , vol.20 , pp. 185-202
    • Schaeffer, H.1
  • 66
    • 84988988996 scopus 로고
    • Contribution á l'étude des écoulements permanents et variables dans les canaux
    • F. Serre. Contribution á l'étude des écoulements permanents et variables dans les canaux. Houille Blanche, 6:830-872, 1953.
    • (1953) Houille Blanche , vol.6 , pp. 830-872
    • Serre, F.1
  • 67
    • 84855748954 scopus 로고    scopus 로고
    • A high-order adaptive timestepping tvd solver for Boussinesq modeling of breaking waves and coastal inundation
    • F. Shi, J.T. Kirby, J.C. Harris, J.D. Geiman, and S.T. Grilli. A high-order adaptive timestepping tvd solver for Boussinesq modeling of breaking waves and coastal inundation. Ocean Modelling, 43-44:36-51, 2012.
    • (2012) Ocean Modelling , vol.43-44 , pp. 36-51
    • Shi, F.1    Kirby, J.T.2    Harris, J.C.3    Geiman, J.D.4    Grilli, S.T.5
  • 68
    • 52649145898 scopus 로고    scopus 로고
    • A second-order semi-implicit hybrid scheme for onedimensional Boussinesq-type waves in rectangular channels
    • S. Soares-Frazão and V. Guinot. A second-order semi-implicit hybrid scheme for onedimensional Boussinesq-type waves in rectangular channels. Int. J. Num. Meth. Fluids, 58:237-261, 2008.
    • (2008) Int. J. Num. Meth. Fluids , vol.58 , pp. 237-261
    • Soares-Frazão, S.1    Guinot, V.2
  • 69
    • 0037711792 scopus 로고    scopus 로고
    • Surf zone dynamics simulated by a Boussinesq type model. III. Wave-induced horizontal nearshore circulation
    • O. Sørensen, H. Schäffer, and P. Madsen. Surf zone dynamics simulated by a Boussinesq type model. III. Wave-induced horizontal nearshore circulation. Coast. Engrg., 33:155-176, 1998.
    • (1998) Coast. Engrg , vol.33 , pp. 155-176
    • Sørensen, O.1    Schäffer, H.2    Madsen, P.3
  • 70
    • 1342268708 scopus 로고    scopus 로고
    • Boussinesq-type modelling using an unstructured finite element technique
    • O.R. Sørensen, H.A. Schaffer, and L.S. Sørensen. Boussinesq-type modelling using an unstructured finite element technique. Coast. Engrg., 50:181-198, 2004.
    • (2004) Coast. Engrg , vol.50 , pp. 181-198
    • Sørensen, O.R.1    Schaffer, H.A.2    Sørensen, L.S.3
  • 71
    • 0023563975 scopus 로고
    • The runup of solitary waves
    • C.E. Synolakis. The runup of solitary waves. J. Fluid Mech., 185:523-545, 1981.
    • (1981) J. Fluid Mech , vol.185 , pp. 523-545
    • Synolakis, C.E.1
  • 72
    • 84860791117 scopus 로고    scopus 로고
    • A new approach to handle wave breaking in fully non-linear Boussinesq models
    • M. Tissier, P. Bonneton, F. Marche, F. Chazel, and D. Lannes. A new approach to handle wave breaking in fully non-linear Boussinesq models. Coast. Engrg., 67:54-66, 2012.
    • (2012) Coast. Engrg , vol.67 , pp. 54-66
    • Tissier, M.1    Bonneton, P.2    Marche, F.3    Chazel, F.4    Lannes, D.5
  • 73
    • 62649110750 scopus 로고    scopus 로고
    • Hybrid finite volume- finite difference scheme for 2dh improved Boussinesq equations
    • M. Tonelli and M. Petti. Hybrid finite volume- finite difference scheme for 2dh improved Boussinesq equations. Coast. Engrg., 56(5-6):609-620, 2009.
    • (2009) Coast. Engrg , vol.56 , Issue.5-6 , pp. 609-620
    • Tonelli, M.1    Petti, M.2
  • 74
    • 77951128147 scopus 로고    scopus 로고
    • Finite volume scheme for the solution of 2d extended Boussinesq equations in the surf zone
    • M. Tonelli and M. Petti. Finite volume scheme for the solution of 2d extended Boussinesq equations in the surf zone. Ocean Engineering, 37:567-582, 2010.
    • (2010) Ocean Engineering , vol.37 , pp. 567-582
    • Tonelli, M.1    Petti, M.2
  • 75
    • 84855829867 scopus 로고    scopus 로고
    • Shock-capturing Boussinesq model for irregular wave propagation
    • M. Tonelli and M. Petti. Shock-capturing Boussinesq model for irregular wave propagation. Coastal Engineering, 61:8-19, 2012.
    • (2012) Coastal Engineering , vol.61 , pp. 8-19
    • Tonelli, M.1    Petti, M.2
  • 76
    • 0003122153 scopus 로고
    • Restoration of the contact surface in the HLL Riemann solver
    • E.F. Toro, M. Spruce, and W. Speare. Restoration of the contact surface in the HLL Riemann solver. Shock waves, 4:25-34, 1994.
    • (1994) Shock Waves , vol.4 , pp. 25-34
    • Toro, E.F.1    Spruce, M.2    Speare, W.3
  • 77
    • 0037055484 scopus 로고    scopus 로고
    • A finite element method for the two-dimensional extended Boussinesq equations
    • M. Walkley and M. Berzins. A finite element method for the two-dimensional extended Boussinesq equations. Int. J. Num. Meth. Fluids, 39(10):865-885, 2002.
    • (2002) Int. J. Num. Meth. Fluids , vol.39 , Issue.10 , pp. 865-885
    • Walkley, M.1    Berzins, M.2
  • 78
    • 79959423655 scopus 로고    scopus 로고
    • A 2D shallow flow model for practical dam-break simulations
    • Y. Wang, Q. Liang, G. Kesserwani, and J.W. Hall. A 2D shallow flow model for practical dam-break simulations. J. Hydraulic Res., 49(3):307-316, 2011.
    • (2011) J. Hydraulic Res , vol.49 , Issue.3 , pp. 307-316
    • Wang, Y.1    Liang, Q.2    Kesserwani, G.3    Hall, J.W.4
  • 79
    • 0029478516 scopus 로고
    • Time-dependent numerical code for extended Boussinesq equations
    • G. Wei and J. Kirby. Time-dependent numerical code for extended Boussinesq equations. J. Water. Port Coast. and Oc. Engrg., 121:251-261, 1995.
    • (1995) J. Water. Port Coast. and Oc. Engrg , vol.121 , pp. 251-261
    • Wei, G.1    Kirby, J.2
  • 80
    • 0029343414 scopus 로고
    • A fully nonlinear Boussinesqmodel for surface waves. Part 1. Highly nonlinear unsteady waves
    • G. Wei, J. Kirby, S. Grilli, and R. Subramanya. A fully nonlinear Boussinesqmodel for surface waves. Part 1. Highly nonlinear unsteady waves. J. Fluid Mech., 294:71-92, 1995.
    • (1995) J. Fluid Mech , vol.294 , pp. 71-92
    • Wei, G.1    Kirby, J.2    Grilli, S.3    Subramanya, R.4
  • 81
    • 33749149018 scopus 로고    scopus 로고
    • 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
    • Y. Xing and C.-W. 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., 1:100-134, 2006.
    • (2006) Commun. Comput. Phys , vol.1 , pp. 100-134
    • Xing, Y.1    Shu, C.-W.2
  • 82
    • 84883488494 scopus 로고    scopus 로고
    • Positivity-preserving well-balanced discontinuous Galerkin methods for the shallow water equations on unstructured triangular meshes
    • Y. Xing and X. Zhang. Positivity-preserving well-balanced discontinuous Galerkin methods for the shallow water equations on unstructured triangular meshes. J. Sci. Comput., 57:19- 41, 2013.
    • (2013) J. Sci. Comput , vol.57 , pp. 19-41
    • Xing, Y.1    Zhang, X.2
  • 83
    • 78649632959 scopus 로고    scopus 로고
    • Positivity-preserving high order well-balanced discontinuous Galerkin methods for the shallow water equations
    • Y. Xing, X. Zhang, and C.-W. Shu. Positivity-preserving high order well-balanced discontinuous Galerkin methods for the shallow water equations. Advances in Water Resources, 33(12):1476 - 1493, 2010.
    • (2010) Advances in Water Resources , vol.33 , Issue.12 , pp. 1476-1493
    • Xing, Y.1    Zhang, X.2    Shu, C.-W.3
  • 84
    • 76449116016 scopus 로고    scopus 로고
    • Local Discontinuous Galerkin methods for high-order time-dependent partial differential equations
    • Y. Xu and C.-W. Shu. Local Discontinuous Galerkin methods for high-order time-dependent partial differential equations. Commun. Comput. Phys., 7(1):1-46, 2010.
    • (2010) Commun. Comput. Phys , vol.7 , Issue.1 , pp. 1-46
    • Xu, Y.1    Shu, C.-W.2
  • 85
    • 77949317923 scopus 로고    scopus 로고
    • On maximum-principle-satisfying high order schemes for scalar conservation laws
    • X. Zhang and C.-W. Shu. On maximum-principle-satisfying high order schemes for scalar conservation laws. J. Comput. Phys., 229(9):3091 - 3120, 2010.
    • (2010) J. Comput. Phys , vol.229 , Issue.9 , pp. 3091-3120
    • Zhang, X.1    Shu, C.-W.2


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