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Journal of Hydraulic Research Volume 16, 1978 - Issue 3
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Original Articles

ON THE NUMERICAL MODELLING OF SHORT WAVES IN SHALLOW WATER

M. B. Abbott International Institute for Hydraulic and Environmental Engineering, Delft, Netherlands; Computational Hydraulic Centre, Danish Hydraulic Institute, Horsholm, Denmark
,
H. M. Petersen Computational Hydraulic Centre, Danish Hydraulic Institute, Horsholm, Denmark
&
O. Skovgaard Computational Hydraulic Centre, Danish Hydraulic Institute, Horsholm, Denmark
Pages 173-204 | Received 27 Dec 1977, Published online: 25 Jan 2010

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Anastasios S. Metallinos, Maria-Eirini A. Emmanouilidou & Constantine D. Memos. (2014) Wave-induced pore pressures in submerged rubble-mound breakwaters simulated by a compound Boussinesq model. Journal of Hydraulic Research 52:1, pages 24-35.
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Mara Tonelli & Marco Petti. (2011) Simulation of wave breaking over complex bathymetries by a Boussinesq model. Journal of Hydraulic Research 49:4, pages 473-486.
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Yonas B. Dibike, Anthony W. Minns & Michael B. Abbott. (1999) Applications of artificial neural networks to the generation of wave equations from hydraulic data. Journal of Hydraulic Research 37:1, pages 81-97.
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M. KAWAHARA & J. Y. CHENG. (1994) FINITE ELEMENT METHOD FOR BOUSSINESQ WAVE ANALYSIS. International Journal of Computational Fluid Dynamics 2:1, pages 1-17.
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Yebegaeshet T. Zerihun. (2021) Non-Hydrostatic Transitional Open-Channel Flows from a Supercritical to a Subcritical State. Slovak Journal of Civil Engineering 29:2, pages 39-48.
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I Wayan Nurjaya, H Surbakti, M T Hartanto, J L Gaol & A Sulardi. (2018) Water mass dynamics in Balikpapan Bay, Eastern Kalimantan Indonesia. IOP Conference Series: Earth and Environmental Science 176, pages 012019.
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A. H. Fattah, Suntoyo, H. A. Damerianne & Wahyudi. (2018) Hydrodynamic and Sediment Transport Modelling of Suralaya Coastal Area, Cilegon, Indonesia. IOP Conference Series: Earth and Environmental Science 135, pages 012024.
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Kun Guo & Yee-chung Jin. 2018. Advances in Hydroinformatics. Advances in Hydroinformatics 157 167 .
J.P. Sierra, A. Genius, P. Lionello, M. Mestres, C. Mösso & L. Marzo. (2017) Modelling the impact of climate change on harbour operability: The Barcelona port case study. Ocean Engineering 141, pages 64-78.
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James T. Kirby. (2016) Boussinesq Models and Their Application to Coastal Processes across a Wide Range of Scales. Journal of Waterway, Port, Coastal, and Ocean Engineering 142:6.
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Victor M. Lyatkher & Alexander M. Proudovsky. 2016. Hydraulic Modeling. Hydraulic Modeling 559 577 .
S. Beji. (2016) Improved Korteweg & de Vries type equation with consistent shoaling characteristics. Coastal Engineering 109, pages 128-133.
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J. P. Sierra, M. Casas-Prat, M. Virgili, C. Mösso & A. Sánchez-Arcilla. (2015) Impacts on wave-driven harbour agitation due to climate change in Catalan ports. Natural Hazards and Earth System Sciences 15:8, pages 1695-1709.
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Jitendra K. Panigrahi, C.P. Padhy & A.S.N. Murty. (2015) Inner harbour wave agitation using boussinesq wave model. International Journal of Naval Architecture and Ocean Engineering 7:1, pages 70-86.
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Mina B. Abd-el-Malek, Nagwa A. Badran, Hossam S. Hassan & Heba H. Abbas. (2015) New solutions for solving Boussinesq equation via potential symmetries method. Applied Mathematics and Computation 251, pages 225-232.
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Maurizio Brocchini. (2013) A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469:2160, pages 20130496.
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Mohammad Hadi Jabbari, Parviz Ghadimi, Mesbah Sayehbani & Arsham Reisinezhad. (2013) A Unique Finite Element Modeling of the Periodic Wave Transformation over Sloping and Barred Beaches by Beji and Nadaoka's Extended Boussinesq Equations. The Scientific World Journal 2013, pages 1-11.
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Widyaningtias Widyaningtias, Hitoshi Tanaka & Susumu Kanayama. (2012) DEPTH OF CLOSURE DETERMINATION IN THE VICINITY OF COASTAL STRUCTURE. Coastal Engineering Proceedings:33, pages 87.
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Su-Xiang Zhang & Xi Li. (2012) Numerical simulation of standing waves in front of permeable structures. Numerical simulation of standing waves in front of permeable structures.
Mara Tonelli & Marco Petti. (2010) Finite volume scheme for the solution of 2D extended Boussinesq equations in the surf zone. Ocean Engineering 37:7, pages 567-582.
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Niranjan Pramanik, Rabindra Kumar Panda & Dhrubajyoti Sen. (2009) One Dimensional Hydrodynamic Modeling of River Flow Using DEM Extracted River Cross-sections. Water Resources Management 24:5, pages 835-852.
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Yongjin Li, Yicheng Jin, Yong Yin & Fangbing Xiao. (2009) Simulation of nearshore wave based on physical module in real-time. Simulation of nearshore wave based on physical module in real-time.
Mara Tonelli & Marco Petti. (2009) Hybrid finite volume – finite difference scheme for 2DH improved Boussinesq equations. Coastal Engineering 56:5-6, pages 609-620.
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Paulo Avilez‐Valente & Fernando J. Seabra‐Santos. (2008) A high‐order Petrov–Galerkin finite element method for the classical Boussinesq wave model. International Journal for Numerical Methods in Fluids 59:9, pages 969-1010.
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Song-Ping Zhu, Huan-Wen Liu & Timothy R. Marchant. (2009) A perturbation DRBEM model for weakly nonlinear wave run-ups around islands. Engineering Analysis with Boundary Elements 33:1, pages 63-76.
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Yongjin Li, Yicheng Jin, Yong Yin & Helong Shen. (2008) Simulation of shallow-water waves in coastal region for marine simulator. Simulation of shallow-water waves in coastal region for marine simulator.
Ramon Codina, José M. González‐Ondina, Gabriel Díaz‐Hernández & Javier Principe. (2008) Finite element approximation of the modified Boussinesq equations using a stabilized formulation. International Journal for Numerical Methods in Fluids 57:9, pages 1249-1268.
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Ramon Codina. (2008) Finite element approximation of the hyperbolic wave equation in mixed form. Computer Methods in Applied Mechanics and Engineering 197:13-16, pages 1305-1322.
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A. ZweifelD. ZuccalàD. Gatti. (2007) Comparison between Computed and Experimentally Generated Impulse Waves. Journal of Hydraulic Engineering 133:2, pages 208-216.
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A. G. Bratsos, I. Th. Famelis & A. M. Prospathopoulos. (2006) A parametric finite‐difference method for shallow sea waves. International Journal for Numerical Methods in Fluids 53:1, pages 129-147.
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X. Cai, G.K. Pedersen & H.P. Langtangen. (2005) A parallel multi-subdomain strategy for solving Boussinesq water wave equations. Advances in Water Resources 28:3, pages 215-233.
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Qin Chen, James T. Kirby, Robert A. Dalrymple, Fengyan Shi & Edward B. Thornton. (2003) Boussinesq modeling of longshore currents. Journal of Geophysical Research: Oceans 108:C11.
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Mark Walkley & Martin Berzins. (2002) A finite element method for the two‐dimensional extended Boussinesq equations. International Journal for Numerical Methods in Fluids 39:10, pages 865-885.
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Fengyan Shi, Robert A. Dalrymple, James T. Kirby, Qin Chen & Andrew Kennedy. (2001) A fully nonlinear Boussinesq model in generalized curvilinear coordinates. Coastal Engineering 42:4, pages 337-358.
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C. Skotner & C.J. Apelt. (1999) Application of a Boussinesq model for the computation of breaking waves. Ocean Engineering 26:10, pages 905-925.
Crossref
M. Walkley & M. Berzins. (1999) A finite element method for the one-dimensional extended Boussinesq equations. International Journal for Numerical Methods in Fluids 29:2, pages 143-157.
Crossref
Masahiko Isobe. 1999. Developments in Offshore Engineering. Developments in Offshore Engineering 101 162 .
Nikolaos D. KatopodesBrett F. SandersJohn P. Boyd. (1998) Short-Wave Behavior of Long-Wave Equations. Journal of Waterway, Port, Coastal, and Ocean Engineering 124:5, pages 238-247.
Crossref
T.E. Baldock, P. Holmes, S. Bunker & P. Van Weert. (1998) Cross-shore hydrodynamics within an unsaturated surf zone. Coastal Engineering 34:3-4, pages 173-196.
Crossref
C. Skotner & C.J. Apelt. (1998) Internal wave generation in an improved two-dimensional Boussinesq model. Ocean Engineering 26:4, pages 287-323.
Crossref
James M. KaihatuJames T. Kirby. (1998) Two-Dimensional Parabolic Modeling of Extended Boussinesq Equations. Journal of Waterway, Port, Coastal, and Ocean Engineering 124:2, pages 57-67.
Crossref
Qin Chen, Per A. Madsen, Hemming A. Schäffer & David R. Basco. (1998) Wave-current interaction based on an enhanced Boussinesq approach. Coastal Engineering 33:1, pages 11-39.
Crossref
Brett F. SandersNikolaos D. KatopodesJohn P. Boyd. (1998) Spectral Modeling of Nonlinear Dispersive Waves. Journal of Hydraulic Engineering 124:1, pages 2-12.
Crossref
Yue Tang & Yvon Ouellet. (1997) A new kind of nonlinear mild-slope equation for combined refraction-diffraction of multifrequency waves. Coastal Engineering 31:1-4, pages 3-36.
Crossref
. 1996. Hydrology Handbook. Hydrology Handbook 627 720 .
Hans Petter Langtangen & Geir Pedersen. 1996. Waves and Nonlinear Processes in Hydrodynamics. Waves and Nonlinear Processes in Hydrodynamics 117 126 .
Ole R. Sørensen, Hemming A. Schäffer, Per A. Madsen & Rolf Deigaard. (1995) Wave Breaking and Induced Nearshore Circulations. Wave Breaking and Induced Nearshore Circulations.
Takumi Ohyama, Wataru Kioka & Akihide Tada. (1995) Applicability of numerical models to nonlinear dispersive waves. Coastal Engineering 24:3-4, pages 297-313.
Crossref
Takumi Ohyama & Kazuo Nadaoka. (1994) Transformation of a nonlinear wave train passing over a submerged shelf without breaking. Coastal Engineering 24:1-2, pages 1-22.
Crossref
Masahiko Isobe. (1994) COMPARATIVE STUDY OF EQUATIONS FOR ANALYZING COASTAL WAVE TRANSFORMATION波浪変形解析のための波動方程式の比較研究. Doboku Gakkai Ronbunshu 1994:491, pages 1-14.
Crossref
S. Beji & J.A. Battjes. (1994) Numerical simulation of nonlinear wave propagation over a bar. Coastal Engineering 23:1-2, pages 1-16.
Crossref
Kashiyama Kazuo & Sakuraba Masaaki. (1994) Adaptive boundary-type finite element method for wave diffraction-refraction in harbors. Computer Methods in Applied Mechanics and Engineering 112:1-4, pages 185-197.
Crossref
Luc Hamm, Per A. Madsen & D.Howell Peregrine. (1993) Wave transformation in the nearshore zone: A review. Coastal Engineering 21:1-3, pages 5-39.
Crossref
Hajime MASE & James T. KIRBY. (1993) HYBRID MODEL FOR NONLINEAR TRANSFORMATION OF RANDOM WAVES不規則波のハイブリッド型断面2次元非線形変形理論. Doboku Gakkai Ronbunshu 1993:479, pages 91-100.
Crossref
Hemming A. Schäffer, Per A. Madsen & Rolf Deigaard. (1993) A Boussinesq model for waves breaking in shallow water. Coastal Engineering 20:3-4, pages 185-202.
Crossref
Steve Elgar, R. T. Guza & M. H. Freilich. (1993) Dispersion, Nonlinearity, and Viscosity in Shallow‐Water Waves. Journal of Waterway, Port, Coastal, and Ocean Engineering 119:4, pages 351-366.
Crossref
Kazuo NADAOKA & Yasuyuki NAKAGAWA. (1993) DERIVATION OF FULLY-DISPERSIVE WAVE EQUATIONS FOR IRREGULAR WAVE SIMULATION AND THEIR FUNDAMENTAL CHARACTERISTICS不規則波動シミュレーションのための強分散性波動方程式の導出とその基本特性の検討. Doboku Gakkai Ronbunshu 1993:467, pages 83-92.
Crossref
Per A. Madsen & Ole R. Sørensen. (1992) A new form of the Boussinesq equations with improved linear dispersion characteristics. Part 2. A slowly-varying bathymetry. Coastal Engineering 18:3-4, pages 183-204.
Crossref
R.M. Gorman. (1992) Wave diffraction in step-walled harbours. Coastal Engineering 18:1-2, pages 39-61.
Crossref
Steve Elgar, R. T. Guza, M. H. Freilich & M. J. Briggs. (1992) Laboratory Simulations of Directionally Spread Shoaling Waves. Journal of Waterway, Port, Coastal, and Ocean Engineering 118:1, pages 87-103.
Crossref
. 1992. Shallow Water Hydrodynamics - Mathematical Theory and Numerical Solution for a Two-dimensional System of Shallow Water Equations. Shallow Water Hydrodynamics - Mathematical Theory and Numerical Solution for a Two-dimensional System of Shallow Water Equations 1 59 .
Geir Pedersen. (2005) Finite difference representations of non‐linear waves. International Journal for Numerical Methods in Fluids 13:6, pages 671-690.
Crossref
Per A. Madsen, Russel Murray & Ole R. Sørensen. (1991) A new form of the Boussinesq equations with improved linear dispersion characteristics. Coastal Engineering 15:4, pages 371-388.
Crossref
Steve Elgar, M. H. Freilich & R. T. Guza. (2012) Model‐data comparisons of moments of nonbreaking shoaling surface gravity waves. Journal of Geophysical Research: Oceans 95:C9, pages 16055-16063.
Crossref
F. Mattioli. (1990) Propagation of periodic waves in the Lido channel of the Venice lagoon. Advances in Water Resources 13:1, pages 41-49.
Crossref
J.V. Smallman & A.J. Cooper. (1989) A mathematical model for set down in harbours. Coastal Engineering 13:3, pages 247-261.
Crossref
Nobuhisa Kobayashi, Gunamuni S. DeSilva & Keith D. Watson. (2012) Wave transformation and swash oscillation on gentle and steep slopes. Journal of Geophysical Research: Oceans 94:C1, pages 951-966.
Crossref
. 1989. Hydrodynamics of Coastal Zones. Hydrodynamics of Coastal Zones 117 155 .
Ole Birger Rygg. (1988) Nonlinear refraction-diffraction of surface waves in intermediate and shallow water. Coastal Engineering 12:3, pages 191-211.
Crossref
W. H. Hager, O. Edder & J. Rappaz. (1988) Streamline curvature effects in side-channel spillway flow. Acta Mechanica 72:1-2, pages 95-110.
Crossref
J. V. Smallman & P. J. Beresford. 1988. Design of Breakwaters. Design of Breakwaters 1 11 .
. 1988. Coastal Environments. Coastal Environments 561 609 .
Kazuo Kashiyama & Mutsuto Kawahara. (2005) A boundary‐type finite element model for water surface wave problems. International Journal for Numerical Methods in Fluids 8:1, pages 65-79.
Crossref
J.K. Kostense, K.L. Meijer, M.W. Dingemans, A.E. Mynett & P. van den Bosch. (1987) Wave Energy Dissipation in Arbitrarily Shaped Harbours of Variable Depth. Wave Energy Dissipation in Arbitrarily Shaped Harbours of Variable Depth.
Nikolaos D. Katopodes & Chien‐Tai Wu. (1987) Computation of Finite‐Amplitude Dispersive Waves. Journal of Waterway, Port, Coastal, and Ocean Engineering 113:4, pages 327-346.
Crossref
K. Anastasiou, P. Dong & D. J. Walker. 1987. Numerical Techniques for Engineering Analysis and Design. Numerical Techniques for Engineering Analysis and Design 207 215 .
J. Peraire, O. C. Zienkiewicz & K. Morgan. (2005) Shallow water problems: A general explicit formulation. International Journal for Numerical Methods in Engineering 22:3, pages 547-574.
Crossref
Kazuo KASHIYAMA & Mutsuto KAWAHARA. (1985) BOUNDARY TYPE FINITE ELEMENT METHOD FOR SURFACE WAVE PROBLEMS表面波問題のための境界型有限要素法. Doboku Gakkai Ronbunshu 1985:363, pages 205-214.
Crossref
John R. Headland & Hsao-Ling Chu. (1985) A Numerical Model for Refraction of Linear and Cnoidal Waves. A Numerical Model for Refraction of Linear and Cnoidal Waves.
W H Hager & K Hager. (2016) Streamline Curvature Effects in Distribution Channels. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 199:3, pages 165-172.
Crossref
B. Cathers & B. A. O'Connor. (2005) The group velocity of some numerical schemes. International Journal for Numerical Methods in Fluids 5:3, pages 201-224.
Crossref
Howard N. Southgate. (1985) A Harbor Ray Model of Wave Refraction‐Diffraction. Journal of Waterway, Port, Coastal, and Ocean Engineering 111:1, pages 29-44.
Crossref
James M Witting. (1984) A unified model for the evolution nonlinear water waves. Journal of Computational Physics 56:2, pages 203-236.
Crossref
Michael B. Abbott, Andrew D. McCowan & Ian R. Warren. (1984) Accuracy of Short‐Wave Numerical Models. Journal of Hydraulic Engineering 110:10, pages 1287-1301.
Crossref
James T. Kirby & Robert A. Dalrymple. (1984) Verification of a parabolic equation for propagation of weakly-nonlinear waves. Coastal Engineering 8:3, pages 219-232.
Crossref
Howard N. Southgate. (2005) Techniques of ray averaging. International Journal for Numerical Methods in Fluids 4:8, pages 725-747.
Crossref
P.A. Madsen & I.R. Warren. (1984) Performance of a numerical short-wave model. Coastal Engineering 8:1, pages 73-93.
Crossref
N. D. Katopodes & C.-T. Wu. 1984. Finite Elements in Water Resources. Finite Elements in Water Resources 437 446 .
N. D. Katopodes. 1984. Computational Methods and Experimental Measurements. Computational Methods and Experimental Measurements 151 162 .
David R. Basco. (1983) Surfzone currents. Coastal Engineering 7:4, pages 331-355.
Crossref
Jesper Larsen & Henry Dancy. (1983) Open boundaries in short wave simulations — A new approach. Coastal Engineering 7:3, pages 285-297.
Crossref
Peter Bettess & Jacqueline A. Bettess. (1982) A generalization of the radiation stress tensor. Applied Mathematical Modelling 6:3, pages 146-150.
Crossref
. 1982. HYDRAULIC MODELLING IN MARITIME ENGINEERING. HYDRAULIC MODELLING IN MARITIME ENGINEERING 135 139 .
E. C. Bowers. 1982. HYDRAULIC MODELLING IN MARITIME ENGINEERING. HYDRAULIC MODELLING IN MARITIME ENGINEERING 121 127 .
James R. Houston. (1981) Combined refraction and diffraction of short waves using the finite element method. Applied Ocean Research 3:4, pages 163-170.
Crossref
M.B. Abbott, A. McCowan & I.R. Warren. 1981. Transport Models/Inland & Coastal Waters. Transport Models/Inland & Coastal Waters 222 283 .
M.B. Abbott, R. Clarke & A. Preissmann. 1981. Logistics and Benefits of Using Mathematical Models of Hydrologic and Water Resource Systems. Logistics and Benefits of Using Mathematical Models of Hydrologic and Water Resource Systems 191 212 .
Ove Skovgaard & Ivar G. Jonsson. (1980) Transient Finite-Difference Tsunami Calculations. Transient Finite-Difference Tsunami Calculations.
A. Hauguel. (1980) A Numerical Model of Storm Waves in Shallow Water. A Numerical Model of Storm Waves in Shallow Water.
John D. Wang. 1980. Mathematical Modelling of Estuarine Physics: Proceedings of an International Symposium Held at the German Hydrographic Institute Hamburg, August 24-26, 1978. Mathematical Modelling of Estuarine Physics: Proceedings of an International Symposium Held at the German Hydrographic Institute Hamburg, August 24-26, 1978 157 171 .
John D. Wang. 1980. Mathematical Modelling of Estuarine Physics. Mathematical Modelling of Estuarine Physics 157 171 .

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