Mathematical and Numerical Modelling for Environmental Applications
Author(s):
Miglio Edie
Title:
Mathematical and Numerical Modelling for Environmental Applications
Date:
Thursday 30th November 2000
Advisor:
Prof. A. Quarteroni
Advisor II:
Co-advisor:
Prof. F. Saleri
Abstract:
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.