Modelling and Simulation of Large Scale Distributed Parameter Systems

Modelling and Simulation of Large Scale Distributed Parameter Systems by Issam Sullivan Strub-Brahimi Doctor of Philosophy in Engineering Science Civil and Environmental Engineering University of California, Berkeley Professor A. M. Bayen, Chair 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