Optimal control for studying wave energy in hydraulic
systems

Abstract

A class of novel models for water waves induced by elastic deformation in the topography is
developed and analyzed. The depth-averaged shallow water equations including friction terms
for the water free-surface and the well-known second-order elastostatic formulation for the bed
deformation have been implemented. Friction forces and water hydrostatic pressure distribution
are also accounted for in this model. At the interface between the water
ow and the bed
topography, transfer conditions are implemented. Furthermore, a hybrid nite element/nite
volume method for solving free-surface run-up
ow problems over deformable beds has been
proposed. The deformations in the topography have been generated by a localized force which
causes propagations of the water waves with dierent amplitudes and frequencies. Two dierent
methods have been proposed for the transfer of informations through the interface. The
rst one is the two-mesh procedure; in this method a proper interpolation has been implemented
to transfer the data between the surface nodes and the control volumes using uniform
nite volume meshes. In the second method, and to avoid the interpolation at the interface,
a nite volume method using non-uniform meshes has been implemented. When the shallow
water waves approach the coastline they begin to transform as they enter shallow water regime.
As each wave begins to experience the seabed, both run-up and overtopping occur. To solve
for this, a class of stable, accurate and simple numerical model for moving wet/dry fronts in
shallow water equations using the parametrization concept and the point-wise Riemann solver
has been proposed.
Many parameters of shallow water equations are subject to uncertainties to the inherit randomness
of natural processes. To incorporate uncertain parameters into the stochastic shallow
water equations, the stochastic properties of dierent parameters that are considered uncertain,
namely in
ow boundary condition, the bed friction coecients and the domain topography are
added to the system. Development of accurate and ecient tools for uncertainty quantication
in shallow water
ows has been proposed and carefully examined for single-layer, two-layer -
nite volume models. To further quantify the uncertainty in shallow water
ows the proposed
methods have been extended to multi-layer shallow water
ows with mass exchange terms
subject to stochastic topography, uncertain friction and viscosity coecients. Several test
examples and well-established benchmark problems have been used to assess the numerical
performance of the proposed models and methods. Comparisons to experimental measurements
have also been carried out in this thesis. Finally, an optimal control technique for bed
reconstruction has been presented as in many engineering applications this information is not
entirely provided.