viii Contents
8 Contaminant and sediment transport by advection
and diffusion
197
8.1 Introduction to mathematical modelling
of transport processes 197
8.1.1 General concepts 197
8.1.2 Mathematical formulation 198
8.2 Numerical solutions of the transport model 201
8.3 Lagrangian modelling of mass transport 210
8.3.1 Application of the random-walk method 211
8.4 Mechanics of sediment transport 220
8.4.1 General concepts of sediment transport 220
8.4.2 Quantification of sediment transport 222
8.4.2.1 Meyer-Peter and Muller formula
for bed load transport 223
8.4.2.2 Engelund and Hansen method
for total load sediment transport 223
8.4.3 Alongshore sediment transport 231
8.4.3.1 One-line model 231
8.4.4 Cross-shore sediment transport by waves 235
8.4.4.1 Conceptual description 235
8.4.4.2 Mathematical formulation 236
8.5 Tracer method applied to active particles 244
8.5.1 Qualitative description 244
8.5.2 Mathematical formulation 245
9 Other numerical methods
255
9.1 Overview 255
9.2 Weighted residual methods 255
9.2.1 Collocation method 256
9.2.2 Sub-domain method 256
9.2.3 Least squares method 257
9.2.4 Method of moments 257
9.2.5 Galerkin method 257
9.3 Finite elements method 262
9.3.1 Rayleigh-Ritz method 262
9.3.2 Finite elements method 264