Shock-capturing Boussinesq-type model for nearshore wave processes

Coastal Engineering

Volumn 57, Issue 4, 2010, Pages 407-423

  Roeber, Volker ^a   Cheung, Kwok Fai ^a   Kobayashi, Marcelo H ^b  

^a UNIVERSITY OF HAWAII   (United States)

^b University of Hawaii at Manoa   (United States)

Author keywords

Boussinesq type equations; Breaking waves; Fringing reefs; Godunov type schemes; Momentum conservation; Nonlinear shallow water equations

Indexed keywords

BOUSSINESQ-TYPE EQUATIONS; BREAKING WAVES; GODUNOV-TYPE SCHEMES; MOMENTUM CONSERVATIONS; SHALLOW WATER EQUATIONS;

COASTAL ENGINEERING; ENERGY DISSIPATION; MOMENTUM; NONLINEAR EQUATIONS; OCEANOGRAPHY; REEFS;

WATER WAVES;

BOUSSINESQ EQUATION; BREAKING WAVE; COASTAL ZONE; FRINGING REEF; NEARSHORE DYNAMICS; NUMERICAL MODEL; OCEAN WAVE; SHALLOW-WATER EQUATION; TROPICAL ENVIRONMENT; WAVE BREAKING; WAVE PROPAGATION;

EID: 76949100376     PISSN: 03783839     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.coastaleng.2009.11.007     Document Type: Article

References (47)

1. Begnudelli L., Sanders B.F., and Bradford S.F. Adaptive Godunov-based model for flood simulation. Journal of Hydraulic Engineering 134 6 (2008) 714-725
2. Beji S., and Battjes J.A. Experimental investigation of wave propagation over a bar. Coastal Engineering 19 1-2 (1993) 151-162
3. Bredmose H., Schäffer H.A., and Madsen P.A. Boussinesq evolution equations: numerical efficiency, breaking and amplitude dispersion. Journal of Coastal Engineering 51 11-12 (2004) 1117-1142
4. Brocchini M., and Dodd N. Nonlinear shallow water equation modeling for coastal engineering. Journal of Waterway, Port, Coastal, and Ocean Engineering 134 2 (2008) 104-120
5. Cheung K.F., Phadke A.C., Wei Y., Rojas R., Douyere Y.J.-M., Martino C.D., Houston S.H., Liu P.L.-F., Lynett P.J., Dodd N., Liao S., and Nakazaki E. Modeling of storm-induced coastal flooding for emergency management. Ocean Engineering 30 11 (2003) 1353-1386
6. Dodd N. Numerical model of wave run-up, overtopping, and regeneration. Journal of Waterway, Port, Coastal and Ocean Engineering 124 2 (1998) 73-81
7. Eskilsson C., and Sherwin S.J. Discontinuous Galerkin spectral/hp element modelling of dispersive shallow water systems. Journal of Scientific Computing 22-23 2 (2005) 269-288
8. Eskilsson C., and Sherwin S.J. Spectral/hp discontinuous Galerkin methods for modelling 2D Boussinesq equations. Journal of Computational Physics 212 2 (2006) 566-589
9. Ferziger J.H., and Perić M. Computational Methods for Fluid Dynamics. 3rd edition (2002), Springer-Verlag, Berlin, Heidelberg, New York
10. Fuhrman D.R., and Madsen P.A. Tsunami generation, propagation, and run-up with a higher order Boussinesq model. Coastal Engineering 56 7 (2009) 747-758
11. 4. Journal of Fluid Mechanics 405 (2000) 181-210
12. Hall J.V., and Watts J.W. Laboratory investigation of the vertical rise of solitary waves on impermeable slopes. Technical Memo No. 33, Beach Erosion Board, US Army Corps of Engineers (1953)
13. Heitner K.L., and Housner G.W. Numerical model for tsunami runup. Journal of Waterway, Port, Coastal, and Ocean Engineering 96 (1970) 701-719
14. Kennedy A.B., Chen Q., Kirby J.T., and Dalrymple R.A. Boussinesq modeling of wave transformation, breaking, and runup. Part I: 1D. Journal of Waterway, Port, Coastal, and Ocean Engineering 126 1 (2000) 39-47
15. Kim K.H., and Kim C. Accurate, efficient and monotonic numerical methods for multi-dimensional compressible flows Part II: Multi-dimensional limiting process. Journal of Computational Physics 208 1 (2005) 570-615
16. LeVeque R.J. Finite Volume Methods for Hyperbolic Problems (2002), Cambridge University Press, Cambridge
17. Li Y., and Raichlen F. Non-breaking and breaking solitary wave run-up. Journal of Fluid Mechanics 456 (2002) 295-318
18. Liu P.L.-F. Model equations for wave propagation from deep to shallow water. In: Liu P.L.-F. (Ed). Advances in Coastal Engineering vol. 1 (1994) 125-157
19. Luth H.R., Klopman G., and Kitou N. Project 13G: Kinematics of waves breaking partially on an offshore bar; LDV measurements for waves with and without a net onshore current. Technical Report H1573 (1994), Delft Hydraulics, The Netherlands
20. Lynett P.J. Nearshore wave modeling with higher-order Boussinesq-type equations. Journal of Waterway, Port, Coastal, and Ocean Engineering. 132 5 (2006) 348-357
21. Lynett P.J., Wu T.R., and Liu P.L.F. Modeling wave runup with depth-integrated equations. Coastal Engineering 46 2 (2002) 89-107
22. Madsen P.A., and Schäffer H.A. Higher order Boussinesq-type equations for surface gravity waves-derivation and analysis. Philosophical Transactions of the Royal Society of London. A 356 (1998) 3123-3186
23. Madsen P.A., and Sørensen O.R. A new form of the Boussinesq equations with improved linear dispersion characteristics. Part 2. A slowly-varying bathymetry. Coastal Engineering 18 3-4 (1992) 183-204
24. Madsen P.A., Murray R., and Sørensen O.R. A new form of Boussinesq equations with improved linear dispersion characteristics. Coastal Engineering 15 4 (1991) 371-388
25. Madsen P.A., Sørensen O.R., and Schäffer H.A. Surf zone dynamics simulated by a Boussinesq type model. Part I. Model description and cross-shore motion of regular waves. Coastal Engineering 32 4 (1997) 255-287
26. Madsen P.A., Bingham H.B., and Schäffer H.A. Boussinesq-type formulations for fully nonlinear and extremely dispersive water waves: derivation and analysis. Proceedings of the Royal Society of London. A 459 (2003) 1075-1104
27. Munger S., and Cheung K.F. Resonance in Hawaii waters from the 2006 Kuril Islands Tsunami. Geophysical Research Letters 35 7 (2008) L07605 10.1029/2007GL032843
28. Nwogu O. An alternative form of the Boussinesq equations for nearshore wave propagation. Journal of Waterway, Port, Coastal, and Ocean Engineering 119 6 (1993) 618-638
29. Pan C.H., Lin B.Y., and Mao X.Z. Case study: numerical modeling of the tidal bore on the Qiantang River, China. Journal of Hydraulic Engineering 133 2 (2007) 130-138
30. Peregrine D.H. Long waves on a beach. Journal of Fluid Mechanics 27 (1967) 815-827
31. Schäffer H.A., Madsen P.A., and Deigaard R. A Boussinesq model for waves breaking in shallow water. Coastal Engineering 20 3-4 (1993) 185-202
32. Sørensen O.R., Schäffer H.A., and Sørensen L.S. Boussinesq-type modeling using an unstructured finite element technique. Coastal Engineering 50 4 (2004) 181-198
33. Stelling G., and Zijlema M. An accurate and efficient finite-difference algorithm for non-hydrostatic free-surface flow with application to wave propagation. International Journal for Numerical Methods in Fluids 43 1 (2003) 1-23
34. Svendsen I.A. Wave heights and setup in a surf zone. Coastal Engineering 8 4 (1984) 303-329
35. Synolakis C.E. The runup of solitary waves. Journal of Fluid Mechanics 185 (1987) 523-545
36. Ting F.C.K., and Kirby J.T. Observation of undertow and turbulence in a laboratory surf zone. Coastal Engineering 24 3-4 (1994) 51-80
37. Titov V.V., and Synolakis C.E. Modeling of breaking and nonbreaking long-wave evolution and runup using VTCS-2. Journal of Waterway, Port, Coastal, and Ocean Engineering 121 6 (1995) 308-316
38. Toro E.F. Shock-Capturing Methods for Free-Surface Shallow Flows (2001), Wiley, New York
39. Veeramony J., and Svendsen I.A. The flow in the surf-zone waves. Coastal Engineering 39 2-4 (2000) 93-122
40. Von Neumann J., and Richtmyer R.D. A Method for the numerical calculation of hydrodynamic shocks. Journal of Applied Physics 21 (1950) 232-237
41. Wei G., and Kirby J.T. A time-dependent numerical code for extended Boussinesq equations. Journal of Waterway, Port, Coastal, and Ocean Engineering. 120 (1995) 251-261
42. Wei G., Kirby J.T., Grilli S.T., and Subramanya R. A fully nonlinear Boussinesq model for surface waves: Part I. Highly nonlinear unsteady waves. Journal of Fluid Mechanics 294 (1995) 71-92
43. Wei Y., Mao X.Z., and Cheung K.F. Well-balanced finite-volume model for long-wave runup. Journal of Waterway, Port, Coastal, and Ocean Engineering. 132 2 (2006) 114-124
44. Wu Y., and Cheung K.F. Explicit solution to the exact Riemann problem and application in nonlinear shallow-water equations. International Journal for Numerical Methods in Fluids 57 11 (2008) 1649-1668
45. Yamazaki, Y., Kowalik, Z., Cheung, K.F., 2009. Depth-integrated, non-hydrostatic model for wave breaking and run-up. International Journal for Numerical Methods in Fluid 61 (5), 473-497. doi:10.1022/fld.1952.
46. Zelt J.A. The runup of nonbreaking and breaking solitary waves. Coastal Engineering. 15 3 (1991) 205-246
47. Zhou J.G., Causon D.M., Mingham C.G., and Ingram D.M. The surface gradient method for the treatment of source terms in the shallow water equations. Journal of Computational Physics 168 1 (2001) 1-25