In the past 15 years the field of general purpose computing on graphics processing units, or GPUs, has become well developed and the practice is becoming more mainstream. Computational demands of simulation software are continuously increasing. As such for many applications traditionally computed on the central processing unit the question arises of whether moving to GPU computing is a possible cost effective way of meeting these demands. The fundamental nature of GPU architecture that makes it so cost effective at doing bulk computation also poses restrictions on which applications are suitable for it. The shallow water equations are a simplified form of the Navier-Stokes equations and describe water levels and flow currents in suitably shallow water such as rivers, estuaries and the North sea. The main research goal of this thesis project was to determine whether the shallow water equations are suitable for implementation on a GPU. Two options exist, the equations may be solved with either an explicit or implicit time integration method. First, a literature study was conducted to familiarize with the tools required to build explicit and implicit shallow water models on a GPU. Then both an explicit and implicit shallow water solver were developed first in the MATLAB programming language and later in CUDA C++ on both CPU and GPU. The main findings are that both explicit and implicit methods are well suited for GPU implementation. Both methods proved to be compatible with a wetting and drying mechanism of numerical cells. The Cuda C++ implementation was in the order of 10 times as fast as a MATLAB implementation for both CPU and GPU. For the benchmark cases tested, the Cuda C++ GPU implementation was in the order of 50 times faster than the equivalent multithreaded CPU implementation. The implicit implementation was benchmarked using the conjugate gradient method to solve the linear system. Various preconditioners were tested and a Repeated Red Black preconditioner was found to be the most effective. The computation time of the RRB preconditioned implicit method was compared with the explicit method and it was found that the two methods reached parity in computation time when the implicit time step was taken roughly 50 times as large as the explicit time step. For implicit time steps smaller than that the explicit method was faster and when the implicit time step was larger the implicit method was faster. For the benchmark cases tested, the implicit method using a time step 50 times larger than the explicit method was found to be less accurate and less stable than the explicit method. The conclusion is that for cases similar to the benchmark cases an explicit method is the fastest, most stable and most accurate method and thus the preferred choice.

Ice loads on the bridge piers can be one of the major components for the Extreme Limit State (ELS) combinations, specified in the Euro Code. In arctic and sub-arctic regions, the ice action on infrastructures such as platforms, lighthouses, sub-sea pipelines, or wind turbines may exceed the total forces of wind, waves and currents and may, therefore, determine the design. For example, in regions such as Beitstad in Norway, ice loads can be the predominant lateral force in the design of bridge sub-structures. Therefore, accurate estimation of ice forces that can act on bridge piers in northern climates is critical in both cases – the design of new bridges and the structural evaluation of existing bridges. Different design codes provide empirical formulae to calculate the design ice forces, based on the effective ice strength, thickness and other important empirical environmental or climatic coefficients. Ice forces must be considered in the design of the coastal and hydraulic structures. Both the ice conditions and the environmental factors are combined in a formula to calculate the magnitude of ice forces that a structure is expected to withstand in the future and over its lifetime. The existing standards for estimation of the ice loads on vertical and sloping structures adopt different analysis methods, and to determine the global ice loads on these structures, the ice-structure interaction scenarios must be identified. In this study, most of the focus will be on fjord and lake ice conditions and their loading on a bridge pier will be assessed and compared by using different shapes of structure and standards of different countries, followed by the deterministic extreme value analysis , probabilistic assessment and uncertainty analysis of the ice loading during the design lifetime of the bridge sub-structure.