Numerical modeling of Boussinesq equations by finite element method

Coastal Engineering

Volumn 37, Issue 2, 1999, Pages 97-122

  Li, Y S ^a   Liu, S X ^a   Yu, Y X ^b   Lai, G Z ^b  

^a HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

^b DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Absorbing boundaries; Boussinesq equations; Finite element

Indexed keywords

FINITE ELEMENT METHOD; INTEGRATION; INTERPOLATION; WAVE EQUATIONS;

ABSORBING BOUNDARIES; ADAMS-BASHFORTH-MOULTON PREDICTOR-CORRECTOR METHOD; BOUSSINESQ EQUATIONS;

COASTAL ENGINEERING;

FINITE ELEMENT METHOD; MATHEMATICAL MODELING; SHALLOW-WATER EQUATION; WAVE TRANSFORMATION;

BOUSSINESQ EQUATION; FINITE ELEMENT METHOD; NUMERICAL MODEL; SHALLOW-WATER EQUATION; WAVE PROPAGATION;

EID: 0033167143     PISSN: 03783839     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-3839(99)00014-9     Document Type: Article

References (25)

1. Abbott M.B., McCowan A.D., Warren I.R. Accuracy of short wave numerical model. J. Hydr. Eng. 110(10):1984;1287-1301.
2. Antunes do Carmo J.S., Seabra Santos F.J. On breaking waves and wave-current interaction in shallow water: a 2DH finite element model. Int. J. Numer. Methods Fluids. 22:1996;429-444.
3. Antunes do Carmo J.S., Seabra Santos F.J., Barthélemy E. Surface waves propagation in shallow water: a finite element model. Int. J. Numer. Methods Fluids. 16:1993;447-459.
4. Beji S., Nadaoka K. A formal derivation and numerical modeling of the improved Boussinesq equations for varying depth. Ocean Eng. 23(8):1996;691-704.
5. Dingemans, M., 1997. Water wave propagation over uneven bottoms. Advanced Series on Ocean Engineering, Vol. 13, Parts 1 and 2. World Scientific, Singapore.
6. Hamm L., Madsen P.A., Peregrine D.H. Wave transformation in the nearshore zone: a review. Coastal Eng. 21:1993;5-39.
7. Howard D., Connolley W.M., Rollett J.S. Unsymmetric conjugate gradient methods and sparse direct methods in finite element flow simulation. Int. J. Numer. Methods Fluids. 10:1990;925-945.
8. Hughes, T.J.R., 1987. The Finite Element Method. Prentice-Hall, Englewood Cliffs, NJ.
9. Isaacson M. de St.Q. Wave runup around large circular cylinder. J. Wtrwy., Port, Coast. Oc. Division, ASCE. 104(1):1978;69-79.
10. Kashiyama K., Ito H. Three-step explicit finite element computation of shallow water flows on a massively parallel computer. Int. J. Numer. Methods Fluids. 21:1995;885-900.
11. Kirby, J.T., 1990. Modeling Shoaling Directional Spectra in Shallow Water. Proc. 22nd Int. Conf. Coast. Eng. ASCE, New York, NY, pp. 109-121.
12. Larsen J., Dancy H. Open boundaries in short wave simulation - a new approach. Coastal Eng. 7(3):1983;285-297.
13. Li Y.S., Zhan J.M. A 3-dimensional finite element method for stratified coastal seas. J. Hydr. Eng. ASCE. 124(7):1998;699-703.
14. Liu P.L.-F., Yoon S.B., Kirby J.T. Nonlinear refraction-diffraction of waves in shallow water. J. Fluid Mech. 153:1985;185-201.
15. Madsen P.A., Sørensen O.R. A new form of the Boussinesq equations with improved linear dispersion characteristics: Part 2. A slowly-varying bathymetry. Coastal Eng. 18:1992;183-204.
16. Madsen P.A., Sørensen O.R. Bound waves and triad interactions in shallow water. Ocean Eng. 20(4):1993;359-388.
17. Madsen P.A., Murray R., Sørensen O.R. A new form of the Boussinesq equations with improved linear dispersion characteristics. Coastal Eng. 15(4):1991;371-388.
18. Mase, H., Kirby, J.T., 1992. Hybrid Frequency-domain KdV Equation for Random Wave Transformation. Proc. 23rd Int. Conf. Coast. Eng., ASCE, Venice, pp. 474-487.
19. Nwogu O. An alternative form of the Boussinesq equations for nearshore wave propagation. J. Wtrwy, Port, Coast. Oc. Eng. ASCE. 119(6):1993;618-638.
20. Peregrine D.H. Long waves on a beach. J. Fluid Mech. 27:1967;815-827.
21. Schäffer H.A., Madsen P.A. Discussion of 'a formal derivation and numerical modelling of the improved Boussinesq equations for varying depth'. Ocean Eng. 25(6):1998;497-500.
22. Wei G., Kirby T. Time-dependent numerical code for extended Boussinesq equations. J. Wtrwy, Port, Coast. Oc. Eng. ASCE. 121(5):1995;251-261.
23. Whalin, R.W., 1971. The limit of applicability of linear wave refraction theory in a convergence zone. Res. Rep. H-71-3, U.S. Army Corps of Engrs., Waterways Expt. Station, Vicksburg, MS.
24. Witting J.M. A unified model for the evolution of nonlinear water waves. J. Comput. Phys. 56:1984;203-236.
25. Yu, Y.X., Liu, S.X., Li, Y.S., Wai, W.H., 1998. Refraction and diffraction of random waves through breakwater. Submitted to Ocean Engineering.