Two-dimensional dispersion analyses of finite element approximations to the shallow water equations

International Journal for Numerical Methods in Fluids

Volumn 45, Issue 7, 2004, Pages 715-749

  Atkinson, J H ^a   Westerink, J J ^a   Luettich Jr , R A ^b  

^a UNIVERSITY OF NOTRE DAME   (United States)

^b UNIVERSITY OF NORTH CAROLINA   (United States)

Author keywords

Dispersion analysis; Finite element models; Shallow water equations

Indexed keywords

ALGORITHMS; FINITE ELEMENT METHOD; FLUID DYNAMICS; FREQUENCIES; GALERKIN METHODS; HARMONIC ANALYSIS; WAVE EFFECTS;

DISCRETIZATIONS; DISPERSION ANALYSIS; SHALLOW WATER EQUATIONS; WAVE NUMBER;

DISPERSION (WAVES);

DISPERSION; SHALLOW WATER;

EID: 3042819205     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/fld.701     Document Type: Article

References (20)

1. Gray WG, Lynch DR. Time stepping schemes for finite element tidal model computations. Advances in Water Resources 1977; 1:83-95.
2. Walters RA, Carey GF. Analysis of spurious oscillation modes for the shallow water and Navier-Stokes equations. Computers and Fluids 1983; 11:51-68.
3. Williams RT, Zienkiewicz OC. Improved finite element forms for the shallow-water wave equations. International Journal for Numerical Methods in Fluids 1981; 1:81-97.
4. Laible JP, Lillys TP. A filtered solution of the primitive shallow-water equations. Advances in Water Resources 1997; 20:23-35.
5. Lynch DR, Gray WG. A wave equation model for finite element tidal computations. Computers and Fluids 1979; 7:207-228.
6. Platzman GW. Some response characteristics of finite element tidal models. Journal of Computational Physics 1981; 40:36-63.
7. Foreman MGG. An analysis of two-step time discretizations in the solution of the linearized shallow water equations. Journal of Computational Physics 1983; 51:454-483.
8. Foreman MGG. An analysis of the 'wave equation' model for finite element tidal computations. Journal of Computational Physics 1983; 52:290-312.
9. Walters RA, Carey GF. Numerical noise in ocean and estuarine models. Advances in Water Resources 1984; 7:15-20.
10. Kinnmark IP. The Shallow Water Wave Equations: Formulation, Analysis and Application. Springer Berlin, 1986.
11. Foreman MGG. A two-dimensional dispersion analysis of selected methods for solving the linearized shallow water equations. Journal of Computational Physics 1984; 56:287-323.
12. Mullen R, Belytschko T. Dispersion analysis of finite element semidiscretizations of the two-dimensional wave equation. International Journal for Numerical Methods in Fluids 1982; 18:11-29.
13. Lynch DR, Paulsen KD. Origin of vector parasits in numerical maxwell solutions. IEEE Transactions on Microwave Theory and Techniques 1991; 39(3):383-394.
14. Gray WG, Lynch DR. On the control of noise in finite element tidal computations. Computers and Fluids 1979; 7:47-67.
15. Atkinson JH. Two-dimensional dispersion analysis. Ph.D. Thesis, University of Notre Dame, October 2002.
16. Kolar RL, Westerink JJ, Cantekin ME, Blain CA. Aspects of nonlinear simulations using shallow-water models based on the wave continuity equation. Computers and Fluids 1994; 23:523-538.
17. Di Giammarco P, Todini F. A control volume finite element method for the solution of 2d overland flow problems. In Modelling of Flood Propagation Over Initially Dry Areas, Proceedings of the ASCE, American Society of Civil Engineers, 1994.
18. Lynch DR, Gray WG. Analytical solutions for computer flow model testing. Journal of the Hydraulics Division (ASCE) 1978; 104:1409-1428.
19. Luettich RA, Westerink JJ, Scheffner NW. Adcirc, an advanced three-dimensional circulation model for shelves, coasts, and estuaries. Technical Report, U.S. Army Corps of Engineers, 1992.
20. Westerink JJ, Luettich RA, Wu JK, Kolar RL. The influence of normal flow boundary conditions on spurious modes in finite element solutions to the shallow water equations. International Journal for Numerical Methods in Fluids 1994; 18:1021-1060.