A higher-order non-hydrostatic σ model for simulating non-linear refraction-diffraction of water waves

Coastal Engineering

Volumn 56, Issue 9, 2009, Pages 919-930

  Young, Chih Chieh ^a   Wu, Chin H ^b   Liu, Wen Cheng ^c   Kuo, Jan Tai ^a  

^a NATIONAL TAIWAN UNIVERSITY   (Taiwan)

^b UNIVERSITY OF WISCONSIN MADISON   (United States)

^c NATIONAL UNITED UNIVERSITY   (Taiwan)

Author keywords

model; Dispersion; Non hydrostatic; Non linearity; Refraction diffraction

Indexed keywords

BOUSSINESQ-TYPE EQUATIONS; DINGER EQUATION; HIGHER ORDER; HORIZONTAL PRESSURE; LINEAR WAVES; MILD SLOPE EQUATIONS; NON-HYDROSTATIC; NON-LINEAR; NON-LINEAR REFRACTION; NON-LINEARITY; PRESSURE TREATMENTS; SPATIAL DISCRETIZATION; WAVE ENERGY;

DIFFRACTION; DISPERSIONS; ENERGY TRANSFER; HYDRAULICS; HYDRODYNAMICS; LAPLACE EQUATION; LINEARIZATION; PRESSURE GRADIENT; REFRACTION; WATER WAVES; WAVE ENERGY CONVERSION;

DISPERSION (WAVES);

NONLINEARITY; WATER WAVE; WAVE DIFFRACTION; WAVE MODELING; WAVE PROPAGATION;

EID: 67651111839     PISSN: 03783839     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.coastaleng.2009.05.004     Document Type: Article

References (56)

1. Beji S., and Battjes J.A. Experimental investigation of wave propagation over a bar. Coastal Engineering 19 (1993) 151-162
2. Berkhoff J.C.W. Computation of combined refraction-diffraction. Proc. 13th Int. Conf. Coastal Eng., Vancouver, BC (1972) 471-491
3. Bradford S.F. Godunov-based model for nonhydrostatic wave dynamics. Journal of Waterway, Port, Coastal, and Ocean Engineering 131 (2005) 226-238
4. Casulli V. A semi-implicit finite difference method for non-hydrostatic, free-surface flows. International Journal for Numerical Methods in Fluids 30 (1999) 425-440
5. Cea, L., Stelling, G., Zijlema, M., in press. Non-hydrostatic 3D free surface layer-structures finite volume model for short wave propagation. International Journal for Numerical Methods in Fluids. doi:10.1002/fld.1961.
6. Chen Y., and Liu P.L.-F. Modified Boussinesq equations and associated parabolic models for water wave propagation. Journal of Fluid Mechanics 288 (1995) 351-381
7. Chen X. A fully hydrodynamic model for three-dimensional, free-surface flows. International Journal for Numerical Methods in Fluids 42 9 (2003) 929-952
8. Dold J.W. An efficient surface-integral algorithm applied to unsteady gravity waves. Journal of Computational Physics 103 (1992) 90-115
9. Dommermuth D.G., and Yue D.K.P. A high-order spectral method for the study of nonlinear gravity waves. Journal of Fluid Mechanics 184 (1987) 267-288
10. Engsig-Karup A.P., Bingham H.B., and Lindberg O. An efficient flexible-order model for 3D nonlinear water waves. Journal of Computational Physics 228 (2009) 2100-2118
11. Fenton J.D. High-order cnoidal wave theory. Journal of Fluid Mechanics 94 (1979) 129-161
12. Fenton J.D. A fifth-order Stokes theory for steady waves. Journal of Waterway, Port, Coastal, and Ocean Engineering 111 (1985) 216-234
13. Fochessato C., and Dias F. A fast method for nonlinear three-dimensional free-surface waves. Proceedings of the Royal Society of London. Series A vol. 462 (2006) 2715-2735
14. Fructus D., Clamond D., Grue J., and Kristiansen Ǿ. An efficient model for three-dimensional surface wave simulations. Part I. Free space problems. J. Comput. Phys 205 (2005) 665-685
15. 4). Journal of Fluid Mechanics 405 (2000) 182-210
16. Guyenne P., and Grilli S.T. Numerical study of three-dimensional overturning waves in shallow water. Journal of Fluid Mechanics 547 (2006) 361-388
17. Haney R.L. On the pressure gradient force over steep topography in σ coordinate ocean models. Journal of Physical Oceanography 21 (1991) 610-619
18. Hsiao S.C., Lynett P., Hwung H.H., and Liu P.L.-F. Numerical simulations of nonlinear short waves using a multilayer model. Journal of Engineering Mechanics 131 3 (2005) 231-243
19. Janssen T.T., Herbers T.H.C., and Battjes J.A. Generalized evolution equations for nonlinear surface gravity waves over two-dimensional topography. Journal of Fluid Mechanics 552 (2006) 393-418
20. Kaihatu J.M., and Kirby J.T. Nonlinear transformation of waves in finite water depth. Physics of Fluid 7 8 (1995) 1-12
21. Kirby J.T. Nonlinear, dispersive long waves in water of variable depth. In: Hunt J.N. (Ed). Gravity Waves in Water of Finite Depth (1997), Computational Mechanics Publications 55-125
22. Kirby J.T., and Dalrymple R.A. A parabolic equation for the combined refraction-diffraction of Stokes waves by mildly varying topography. Journal of Fluid Mechanics 136 (1983) 453-466
23. Kocyigit M.B., Falconer R.A., and Lin B. Three-dimensional numerical modeling of free surface flows with non-hydrostatic pressure. International Journal for Numerical Methods in Fluids 40 (2002) 1145-1162
24. Laitone E.V. The second approximation to cnoidal and solitary waves. Journal of Fluid Mechanics 9 3 (1960) 430-444
25. Li B. A 3-D model based on Navier-Stokes equations for regular and irregular water wave propagation. Ocean Engineering 35 (2008) 1842-1853
26. Li B., and Fleming C.A. A three dimensional multigrid model for fully nonlinear water waves. Coastal Engineering 30 (1997) 235-258
27. Li B., and Fleming C.A. Three-dimensional model of Navier-Stokes equations for water waves. Journal of Waterway, Port, Coastal, and Ocean Engineering 127 (2001) 16-25
28. Lin P., and Li C.W. A s-coordinate three-dimensional numerical model for surface wave propagation. International Journal for Numerical Methods in Fluids 38 (2002) 1045-1068
29. Liu P.L.-F., and Losada I.J. Wave propagation modeling in coastal engineering. Journal of Hydraulic Research 40 3 (2002) 229-240
30. Liu P.L.-F., Simarro G., Vandever J., and Orfila A. Experimental and numerical investigation of viscous effects on solitary wave propagation in a wave tank. Coastal Engineering 53 2-3 (2006) 181-190
31. Liu P.L.-F., and Tsay T.-K. Refraction-diffraction model for weakly nonlinear waves. Journal of Fluid Mechanics 141 (1984) 265-274
32. Liu P.L.-F., Yoon S.B., and Kirby J.T. Nonlinear refraction-diffraction model of waves in shallow water. Journal of Fluid Mechanics 153 (1985) 185-201
33. Longuet-Higgins M.S., and Cokelet E.D. The deformation of steep surface waves on water. I A numerical method of computation. Proceedings of the Royal Society of London. Series A vol. 95 (1976) 1-26
34. Lynett P., and Liu P.L.-F. A two-layer approach to wave modeling. Proceedings of the Royal Society of London. Series A vol. 460 (2049) (2004) 2637-32669
35. 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 (1992) 183-204
36. Madsen P.A., Bingham H.B., and Liu H. A new Boussinesq method for fully nonlinear waves from shallow to deep water. Journal of Fluid Mechanics 462 (2002) 1-30
37. Mayer S., Garapon A., and Sørensen L.S. A fractional step method for unsteady free-surface flow with applications to non-linear wave dynamics. International Journal for Numerical Methods in Fluids 28 (1998) 293-315
38. Mei C.-C., and Liu P.L.-F. Surface waves and coastal dynamics. Annual Review of Fluid Mechanics 25 (1993) 215-240
39. Namin M., Lin B., and Falconer R. An implicit numerical algorithm for solving non-hydrostatic free-surface flow problems. International Journal for Numerical Methods in Fluids 35 (2001) 341-356
40. Nwogu O. Alternative form of Boussinesq equations for nearshore wave propagation. Journal of Waterway, Port, Coastal, and Ocean Engineering 119 (1993) 618-638
41. Peregrine D.H. Long waves on a beach. Journal of Fluid Mechanics 27 (1967) 815-827
42. Rygg O.B. Nonlinear refraction-diffraction of surface waves in intermediate and shallow water. Coastal Engineering 12 (1988) 191-211
43. Sørensen O.R., Hemming A.S., and Sørensen L.S. Boussinesq-type modelling using an unstructured finite element technique. Coastal Engineering 50 (2004) 181-198
44. 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
45. Sitanggang K.I., and Lynett P. Parallel computation of a highly nonlinear Boussinesq equation model through domain decomposition. International Journal for Numerical Methods in Fluids 49 (2005) 57-74
46. Tang Y., and Ouellet Y. A new kind of nonlinear mild-slope equation for combined refraction-diffraction of multifrequency waves. Coastal Engineering 31 (1997) 3-36
47. Tsai W.T., and Yue D.K.P. Computation of nonlinear free-surface flows. Annual Review of Fluid Mechanics 28 (1996) 249-278
48. Wei G., Kirby J.T., Grilli S.T., and Subramanya R. A fully nonlinear Boussinesq model for surface waves. I. Highly nonlinear unsteady waves. Journal of Fluid Mechanics 294 (1995) 71-92
49. Whalin R.W. The limit of applicability of linear wave refraction theory in convergence zone. Res. Rep. H-71-3, U.S. Army Corps of Engineers (1971), Waterways Expt. Station, Vicksburg, MS
50. Wu T.Y. A unified theory for modeling water waves. Advances in Applied Mechanics 37 (2001) 1-88
51. Young C.-C., Wu C.H., Kuo J.-T., and Liu W.-C. A higher-order σ-coordinate non-hydrostatic model for nonlinear surface waves. Ocean Engineering 34 10 (2007) 1357-1370
52. Young C.-C., and Wu C.H. An efficient and accurate non-hydrostatic model with embedded Boussinesq-type like equations for surface wave modeling. International Journal for Numerical Methods in Fluids 60 1 (2009) 27-53
53. Yuan H., and Wu C.H. A two-dimensional vertical non-hydrostatic s model with an implicit method for free-surface flows. International Journal for Numerical Methods in Fluids 44 8 (2004) 811-835
54. Yuan H., and Wu C.H. An implicit 3D fully non-hydrostatic model for free-surface flows. International Journal for Numerical Methods in Fluids 46 7 (2004) 709-733
55. Yuan H., and Wu C.H. Fully nonhydrostatic modeling of surface waves. Journal of Engineering Mechanics 132 4 (2006) 447-456
56. Zijlema M., and Stelling G.S. Efficient computation of surf zone waves using the nonlinear shallow water equations with non-hydrostatic pressure. Coastal Engineering 55 (2008) 780-790