Numerical Methods for Shallow-Water Flow

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Springer Science & Business Media, Oct 31, 1994 - Science - 262 pages
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A wide variety of problems are associated with the flow of shallow water, such as atmospheric flows, tides, storm surges, river and coastal flows, lake flows, tsunamis. Numerical simulation is an effective tool in solving them and a great variety of numerical methods are available. The first part of the book summarizes the basic physics of shallow-water flow needed to use numerical methods under various conditions. The second part gives an overview of possible numerical methods, together with their stability and accuracy properties as well as with an assessment of their performance under various conditions. This enables the reader to select a method for particular applications. Correct treatment of boundary conditions (often neglected) is emphasized. The major part of the book is about two-dimensional shallow-water equations but a discussion of the 3-D form is included.
The book is intended for researchers and users of shallow-water models in oceanographic and meteorological institutes, hydraulic engineering and consulting. It also provides a major source of information for applied and numerical mathematicians.
 

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Contents

Shallowwater flows
1
12 Atmospheric flows
2
13 Tidal flows
3
16 Storm surges
6
18 Flows around structures
8
110 Coastal flows
10
113 Internal flows
12
114 Planetary flows
13
Effects of space discretization on wave propagation
117
72 Gravity waves
120
73 Vorticity waves
123
74 Flood waves
126
75 Rossby waves
129
76 Rotated grids
132
77 Irregular grids
133
78 Discrete conservation
134

Equations
15
22 Surface and bottom boundary conditions
18
23 Scales
19
24 Boundarylayer form
21
25 Twodimensional shallowwater equations
22
26 Driving forces
26
27 Bottom stress
29
28 Lateral momentum exchange
36
29 Forms of the shallowwater equations
38
210 Curvilinear coordinates
41
Some properties
47
32 Correspondence with incompressible viscous flow
48
33 Conservation laws
49
34 Discontinuities
53
Behaviour of solutions
56
42 Wave equation
59
44 Harmonic wave propagation
63
Boundary conditions
73
52 Energy arguments
75
53 Initial conditions
81
54 Reflection
82
55 Moving boundaries
88
Discretization in space
89
62 Staggered grids
90
63 Curvilinear grids
95
64 Finite elements
100
65 Finite elements for wave equation
105
66 Grid generation
106
67 Spectral methods
112
Time integration methods
139
83 Implicit methods
142
84 Semiimplicit methods
143
85 ADI methods
149
86 Fractionalstep methods
152
87 Riemann solvers
153
Effects of time discretization on wave propagation
168
92 Gravity waves
171
93 Vorticity waves
175
94 Flood waves
177
95 Rossby waves
179
96 Amount of work
184
97 Evaluation
185
Numerical treatment of boundary conditions
196
102 Examples of boundary schemes
197
103 Stability analysis by the energy method
199
104 Normal mode analysis
203
105 Accuracy of boundary treatment
210
Threedimensional shallowwater flow
217
112 3d Model equations
218
113 Discretization in space
226
114 Discretization in time
230
115 Advectiondiffusion
233
116 Accuracy
238
List of notation
247
References
249
Index
259
Copyright

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Page 258 - ZIMMERMAN, JTF 1978 Topographic generation of residual circulation by oscillatory (tidal) currents. Geophys. Astrophys. Fluid Dyn. 11, 35-47. ZIMMERMAN, JTF 1979 On the Euler-Lagrange transformation and the Stokes drift in the presence of oscillatory and residual currents.
Page 249 - A High-Resolution Godunov-Type Scheme in Finite Volumes for the 2D Shallow-Water Equations...
Page 252 - Forward— backward scheme modified to prevent two-grid-interval noise and its application in sigma coordinate models. Contrib. Atmos. Phys. 52, 69-84. Janjic, ZI, 1984. Non-linear advection schemes and energy cascade on semi-staggered grids.
Page 257 - Vichnevetsky, R. 1987 - Wave propagation analysis of difference schemes for hyperbolic equations: a review, Int. J.
Page 253 - ... zur naherungsweisen Integration totaler Differentialgleichungen. Z. Math. Phys. 46, 435-453. 27. JD LAMBERT (1973). Computational Methods in Ordinary Differential Equations, John Wiley & Sons, London. 28. P. LANCASTER (1969). Theory of Matrices, Academic Press, New York and London. 29. JJ LEENDERTSE (1967). Aspects of a Computational Model for Longperiod Water-wave Propagation, Rand Corp., Mem. RM-5294, Santa Monica. 30. JJ LEENDERTSE (1970). A water-quality simulation model for wellmixed estuaries...
Page 255 - The effect of spatial discretization on the steady-state and transient solutions of a dispersive wave equation.
Page 258 - L. van Stijn, GS Stelling, and GA Fokkema, 1988: A fully implicit splitting method for accurate tidal computations.
Page 256 - Press. Taylor, GI, 1919. Tidal friction in the Irish Sea. Phil. Trans.
Page 255 - Reid, RO, 1957: Modification of the quadratic bottom-stress law for turbulent channel flow in the presence of surface wind-stress. US Army Corps of Engineers, Beach Erosion Board, Tech. Memo.

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