Shallow water theory and its application to the Venice lagoon

We analyze the computational methods for the shallow water equations. First we derive the shallow water equations from the Navier-Stokes equations and then we discuss the weak formulation of a differential problem and its discretization by the finite element method. parallel computations are performed by domain decomposition methods. Finally, we present st finite element model to solve the motion problem of the shallow water due to the tides into the Venice lagoon. A comparison has been made between the numerical simulation and the real data on the internal measurement stations of the lagoon. The experimental and simulated data present a good agreement in all the measurement stations.