1st module

Prof. Vincenzo Casulli

A.A. 1998/99

PROGRAMME

MATHEMATICAL MODELS:
the Navier-Stokes equations, a three-dimensional hydrostatic model, the vertically averaged model (2Dxy), the laterally averaged model (2Dxz), the open channel equations (1D).

EULER-LAGRANGE METHODS:
convection-diffusion equations, explicit upwind method, implicit upwind method, Euler-Lagrange methods, semi-implicit methods, the conjugate gradient method.

NUMERICAL METHODS FOR THE 1D MODEL:
characteristic analysis, semi-implicit finite difference methods, an equation for the free surface, stability analysis.

NUMERICAL METHODS FOR THE 2Dxz MODEL:
semi-implicit finite difference methods, derivation of the free surface equation, a particular case: the 1D model, stability analysis.

NUMERICAL METHODS FOR THE 2Dxy MODEL:
characteristic analysis, alternating direction semi-implicit, semi-implicit finite difference methods, an equation for the free surface, fully implicit splitting methods, stability analysis.

NUMERICAL METHODS FOR THE 3D MODEL:
extension of the 2D methods, alternating direction semi-implicit, semi-implicit finite difference methods, an equation for the free surface, fully implicit splitting methods, stability analysis.
 

REFERENCE TEXTS

Lecture notes