Modelling and simulation of large scale distributed parameter systems

The research presented in this dissertation is motivated by the need for modelling, simulation and optimisation of large scale distributed parameter systems, namely rivers and highways.;The problem of state estimation for two-dimensional river flows is investigated using a novel algorithm for two-dimensional Lagrangian data assimilation of shallow water flows and floating sensors. This algorithm is based on a quadratic programming formulation with the linearised two-dimensional shallow water equations used as constraints. It is compared in computer-based twin experiments with an ensemble Kalman filtering algorithm, and the performance of the two algorithms is evaluated in a number of settings. The sensitivity of the two data assimilation algorithms to the number of drifters, low or high discharge and time sampling frequency is analysed and the respective computational costs of each method compared. One of the conclusion is that the quadratic programming based algorithm introduced by the author presents a good balance of accuracy and low computational cost. The quadratic programming based algorithm is also applied to experimental drifter data collected during field experiments.;Another problem is the estimation of open boundary conditions in situations in which tidal forcing is dominant. A quadratic programming based variational data assimilation algorithm is applied to the estimation of open boundary conditions for tidal flows using one-dimensional shallow water equations and floating sensors. This algorithm is evaluated in computer generated experiments both with and without tidal reversion. The experiments show that during the period of time that observations are available, the inverse model is able to effectively estimate the harmonic constants and reproduce the flows.;The final part of the dissertation deals highway traffic modelling. We prove the existence and uniqueness of a weak solution to a scalar conservation law on a bounded domain through the introduction of a weak formulation of the boundary conditions. This result is applied to the Lighthill-Whitham-Richards model and discretised using a Godunov scheme. This numerical scheme is validated through a comparison with experimentally measured data. Finally, the existence of a minimiser of travel time is obtained, with corresponding optimal boundary control.