C2.1 Mathematical Models in the Coastal Zone

Overview of basic numerical methods for solving elliptic, parabolic and hyperbolic equations and relevant applications. Stability and accuracy analysis, numerical diffusion. Computational grids. Mathematical models of coastal circulation: shallow water equations, model classification, boundary conditions, simulation of wind-induced and wave-induced circulation, applications using computational codes, model calibration and verification. Simulation of bottom roughness and bottom shear stresses. Effect of the wave breaking on the eddy viscosity coefficient. Secondary currents at the solid boundary of the coastline. Simulation of pollutant dispersion in the coastal zone. Coastal water circulation due to long waves and circulation induced by wave breaking. Simulation of erosion/bottom sediments deposition, sediment motion along and transversely to the coast, coastline evolution at different time scales. The above topics are covered with the following order:

1. Introduction, basic concepts, discretization methods, overview of basic numerical methods for solving elliptic, parabolic and hyperbolic partial differential equations, stability and accuracy analysis, numerical diffusion, applications and exercises.
2. Introduction to mathematical modeling of coastal water circulation: principles for solving problems, model classification, calibration and verification.
3. Simulation of wind-induced and tide-induced circulation: model construction, application.
4. Simulation of pollutant dispersion in the coastal zone and application.
5. Simulation of wave-induced circulation: radiation stresses, secondary currents, application.
6. Bottom roughness and bottom shear stresses.
7. Sediment transport and coastline morphodynamics: simulation of erosion, sediment transport models, application in sediment transport and bottom morphology, coastline evolution and application.