Contents
xv
9.3
Model Analysis......................................................................... 301
9.3.1 General......................................................................... 301
9.3.2 Complété similarity................................................... 302
9.3.3 Applications of model analysis................................ 302
9.4
Principles of Similitude......................................................... 303
9.4.1 General......................................................................... 303
9.4.2 Similitude in hydrodynamic problems................... 303
9.4.3 Types of similitude................................................... 303
9.5
Scale Effects............................................................................ 305
9.6
Model Laws ............................................................................ 305
9.7
Case Studies............................................................................ 307
Refer ences............................................................................................ 314
10. Numerical Modelling
315
10.1 Introduction............................................................................ 315
10.2 Need for Numerical Models.................................................. 315
10.3 Mathematical Description of Flows:
Governing Equations ............................................................ 317
10.3.1 Continuity équation.................................................. 317
10.3.2 Momentum équation............................................... 317
10.4 Discretization ........................................................................ 318
10.4.1 Discretization techniques........................................ 319
10.4.1.1 Finite différence method (FDM)........... 319
10.4.1.2 Finite volume method (FVM).............. 319
10.4.1.3 Finite element method (FEM).............. 319
10.5 Numerical Wave Modelling.................................................. 320
10.5.1 Wave spectral models............................................... 320
10.5.2 Test case: Wave propagation over constant
depth bathymetry........................................ 321
10.5.3 Test case: Wave prédiction over Bay of Bengal
during a cyclone............................................ 323
10.6 Mild-Slope Equation (MSE) Wave Models ...................... 327
10.6.1 Solution of MSE........................................................ 329
10.7 Boussinesq Approximation.................................................. 333
10.7.1 Boussinesq équations............................................... 334
10.7.2 Shallow-water équation wave models..................... 336
References............................................................................................ 336
Index
339