PhD Thesis Author: Edie Miglio Title: "Mathematical and Numerical Modelling for Environmental Applications"
In this thesis the numerical approximation of free surface and groundwater flows is addressed: in particular the 3D Shallow Water equations and the 3D motion of a fluid in a porous media are considered. As for the Shallow Water flows a particular nonhydrostatic system has been proposed which is useful in presence of short waves. In the framework of inexact algebraic factorization two methods has been proposed for the efficient solution of this nonhydrostatic system. Some numerical results for test cases for real problems are presented. A linearized 3D hydrostatic model is also introduced and studied from the theoretical point of view. In the second part of the thesis the numerical approximation of the Darcy's law describing the 3D motion of a fluid in a porous media is considered. Finally the problem of coupling the equations for Shallow Water flows and groudwater flows is addressed. From the applicative side this coupling is important for the simulation of the transport and diffusion of pollutants into the ground due to effects of surface flows. Suitable interface conditions are introduced and an iterative scheme for the decoupling of solution of the two problems is proposed.
