Depth-integrated free-surface flow with a two-layer non-hydrostatic formulation

International Journal for Numerical Methods in Fluids

Volumn 69, Issue 2, 2012, Pages 411-429

  Bai, Yefei ^a   Cheung, Kwok Fai ^a  

^a UNIVERSITY OF HAWAII   (United States)

Author keywords

Depth integrated models; Dispersive waves; Non hydrostatic; Two layer models; Wave runup

Indexed keywords

A-PLANE; DISPERSIVE WAVES; FINITE-DIFFERENCE SCHEME; FREE-SURFACE FLOW; GOVERNING EQUATIONS; KELLER BOX SCHEME; LABORATORY EXPERIMENTS; LINEAR DISPERSION RELATIONS; MOMENTUM CONSERVATIONS; NON-HYDROSTATIC; NON-HYDROSTATIC PRESSURE; SEMI-IMPLICIT SCHEME; TWO LAYER MODEL; TWO LAYERS; VERTICAL DIRECTION; WATER DEPTH; WAVE RUNUP; WAVE TRANSFORMATIONS; WAVEBREAKING;

DISPERSION (WAVES); HYDRODYNAMICS; INTEGRATED CONTROL; POISSON EQUATION;

HYDRAULICS;

EID: 84859743889     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.2566     Document Type: Article

References (25)

1. Peregrine DH. Long waves on a beach. Journal of Fluid Mechanics 1967; 27:815-827.
2. Madsen PA, Sorensen OR. A new form of the Boussinesq equations with improved linear dispersion characteristics. Part A: slowly-varying bathymetry. Coastal Engineering 1992; 18:183-204.
3. Nwogu O. Alternative form of Boussinesq equations for nearshore wave propagation. Journal of Waterway, Port, Coastal and Ocean Engineering 1993; 119:618-638.
4. Wei G, Kirby JT. Time-dependent numerical code for extended Boussinesq equations. Journal of Waterway, Port, Coastal and Ocean Engineering 1995; 121(5):251-261.
5. Madsen PA, Bingham HB, Schäffer HA. Boussinesq-type formulations for fully nonlinear and extremely dispersive water waves: derivation and analysis. Proceedings of the Royal Society of London 2003; A459:1075-1104.
6. Roeber V, Cheung KF, Kobayashi MH. Shock-capturing Boussinesq-type model for nearshore wave processes. Coastal Engineering 2010; 57:407-423.
7. Zelt JA. The run-up of non breaking and breaking solitary waves. Coastal Engineering 1991; 15:205-246.
8. Schaffer HA, Madsen PA, Deigaard RA. A Boussinesq model for waves breaking in shallow water. Coastal Engineering 1993; 20:185-202.
9. Madsen PA, Sorensen OR. Surf zone dynamics simulated by a Boussinesq type model. Part I. Model description and cross-shore motion of regular waves. Coastal Engineering 1997; 32:255-287.
10. Lynett PJ, Wu TR, Liu P. Modeling wave runup with depth-integrated equations. Coastal Engineering 2002; 46:89-107.
11. Kennedy AB, Chen Q, Kirby JT, Dalrymple RA. Boussinesq modeling of wave transformation, breaking, and runup. 1: 1D. Journal of Waterway, Port, Coastal and Ocean Engineering 2000; 126:39-47.
12. Casulli VA, Stelling GS. Numerical simulation of 3D quasi-hydrostatic, free-surface flows. Journal of Hydraulic Engineering (ASCE) 1998; 124:678-686.
13. Stansby PK, Zhou JG. Shallow-water flow solver with non-hydrostatic pressure: 2D vertical plane problems. International Journal for Numerical Methods in Fluids 1998; 28:541-563.
14. Casulli VA. A semi-implicit finite difference method for non-hydrostatic, free-surface flows. International Journal for Numerical Methods in Fluids 1999; 30:425-440.
15. Zhou JG, Stansby PK. An arbitary Lagrangian-Eulerian σ (ALES) model with non-hydrostatic pressure for shallow water flows. Computer Methods in Applied Mechanics and Engineering 1999; 178:199-214.
16. Stelling GS, 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 2003; 43:1-23.
17. Zijlema M, Stelling GS. Further experiences with computing non-hydrostatic free-surface flows involving water waves. International Journal for Numerical Methods in Fluids 2005; 48:169-197.
18. Stelling GS, Duinmeijer SPA. A staggered conservative scheme for every Froude number in rapidly varied shallow water flows. International Journal for Numerical Methods in Fluids 2003; 43:1329-1354.
19. Zijlema M, Stelling GS. Efficient computation of surf zone waves using the nonlinear shallow water equations with non-hydrostatic pressure. International Journal for Numerical Methods in Fluids 2008; 55:780-790.
20. Yamazaki Y, Kowalik Z, Cheung KF. Depth-integrated, non-hydrostatic model for wave breaking and runup. International Journal for Numerical Methods in Fluids 2009; 61:473-497.
21. Yamazaki Y, Cheung KF, Kowalik Z. Depth-integrated, non-hydrostatic model with grid nesting for tsunami generation, propagation, and run-up. International Journal for Numerical Methods in Fluids 2010; DOI: 10.1002/fld.2485.
22. Beji S, Battjes JA. Experimental investigation of wave propagation over a bar. Coastal Engineering 1993; 19(1-2):151-162.
23. Luth HR, Klopman G, Kitou N. Project 13 G. Kinematics of waves breaking partially on an offshore bar; LDV measurements for waves with and without a net onshore current. Technical Report H1573, Delft Hydraulics, 1994.
24. Synolakis CE. The runup of solitary wave. Journal of Fluid Mechanics 1987; 185:523-545.
25. Roeber V. Boussinesq-type model for nearshore wave processes in fringing reef environment. Ph.D. Dissertation, University of Hawaii, Honolulu, 2010.