**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