An implicit two-dimensional non-hydrostatic model for free-surface flows

International Journal for Numerical Methods in Fluids

Volumn 54, Issue 9, 2007, Pages 1055-1074

  Ahmadi, Afshin ^a   Badiei, Peyman ^a   Namin, Masoud M ^a  

^a UNIVERSITY OF TEHRAN   (Iran)

Author keywords

Free surface flow; Implicit finite volume method; Non hydrostatic pressure; Projection method; Sigma coordinate; Top layer treatment

Indexed keywords

ADVECTION-DIFFUSION EQUATION; FREE-SURFACE FLOW; MOMENTUM EQUATIONS; NON-HYDROSTATIC PRESSURE DISTRIBUTION;

ADVECTION; DIFFUSION; FINITE VOLUME METHOD; HYDRODYNAMICS; MATRIX ALGEBRA; MOMENTUM; NAVIER STOKES EQUATIONS; PRESSURE DISTRIBUTION; TWO DIMENSIONAL;

FLOW OF WATER;

ADVECTION; DIFFUSION; FINITE VOLUME METHOD; FLOW OF WATER; HYDRODYNAMICS; MATRIX ALGEBRA; MOMENTUM; NAVIER STOKES EQUATIONS; PRESSURE DISTRIBUTION; TWO DIMENSIONAL;

EID: 34447519056     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1414     Document Type: Article

References (23)

1. Chorin AJ. Numerical solution of the Navier-Stokes equations. Mathematics of Computation 1968; 22:745-762.
2. Guermond JL, Quartapelle L. On stability and convergence of projection methods based on pressure Poisson equation. International Journal for Numerical Methods in Fluids 1998; 26:1039-1053.
3. Mahadevan A, Oliger J, Street R. A non-hydrostatic mesoscale ocean model. Part 1: Well posedness and scaling. Journal of Physical Oceanography 1996; 26(9):1868-1880.
4. 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.
5. Casulli V. A semi-implicit finite difference method for non-hydrostatic, free-surface flows. International Journal for Numerical Methods in Fluids 1999; 30:425-440.
6. Li B, Fleming C. Three-dimensional model of Navier-Stokes equations for water waves. Journal of Waterway, Port, Coastal, and Ocean Engineering (ASCE) 2001; 16-25.
7. Lin P, Li C. A σ-coordinate three-dimensional numerical model for surface wave propagation. International Journal for Numerical Methods in Fluids 2002; 38:1045-1068.
8. Kocyigit MB, Falconer RA, Lin B. Three-dimensional numerical modeling of free surface flows with nonhydrostatic pressure. International Journal for Numerical Methods in Fluids 2002; 40:1145-1162.
9. Chen X. A fully hydrodynamic model for three-dimensional, free-surface flows. International Journal for Numerical Methods in Fluids 2003; 42(9):929-952.
10. Namin M, Lin B, Falconer R. An implicit numerical algorithm for solving non-hydrostatic free-surface flow problems. International Journal for Numerical Methods in Fluids 2001; 35:341-356.
11. Namin M. A fully three-dimensional non-hydrostatic free surface flow model for hydro-environmental prediction. Ph.D. Thesis, Cardiff School of Engineering, Cardiff University, 2003.
12. Yuan HL, Wu CH. A two-dimensional vertical non-hydrostatic σ model with an implicit method for free-surface flows. International Journal for Numerical Methods in Fluids 2004; 44:811-835.
13. Yuan HL, Wu CH. An implicit three-dimensional fully non-hydrostatic model for free-surface flows. International Journal for Numerical Methods in Fluids 2004; 46:709-733.
14. Casulli V, Stelling GS. Numerical simulation of 3D quasi-hydrostatic free-surface flows. Journal of Hydraulic Engineering (ASCE) 1998; 124(7):678-686.
15. Stelling G, 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.
16. Casulli V, Zanolli P. Semi-implicit numerical modeling of nonhydrostatic free-surface flows for environmental problems. Mathematical and Computer Modeling 2002; 36(9-10):1131-1149.
17. Fromm JE. A method of reducing dispersion in convective difference scheme. Journal of Computational Physics 1968; 3:176-184.
18. Dean RG, Dalrymple RA. Water Wave Mechanics for Engineers and Scientists. World Scientific: Singapore, 2000.
19. Mei CC. The Applied Dynamics of Ocean Surface Waves. Wiley Inter-science: New York, 1983.
20. Sorensen RM. Basic Coastal Engineering. Kluwer Academic Publishers: New York, 1997.
21. Madsen OS, Mel CC. The transformation of a solitary wave over an uneven bottom. Journal of Fluid Mechanics 1969; 39(4):781-791.
22. Woo SB, Liu PLF. A Petrov-Galerkin finite element model for one-dimensional fully non-linear and weakly dispersive wave propagation. International Journal for Numerical Methods in Fluids 2001; 37:541-575.
23. Chapalain G, Cointe R, Temperville A. Observed and modeled resonantly interacting progressive water-waves. Coastal Engineering 1992; 16:267-300.