A novel Riemann solver for modelling partial barriers to flow within 2-D hydrodynamic models

Abstract

Flooding, exacerbated by anthropogenic climate change, is a pervasive natural phenomenon with profound and widespread implications that necessitates effective flood risk management. Within contemporary flood risk management practice, hydrodynamic modelling comprises a key tool, providing a means for producing crucial quantitative evidence upon which informed decisions can be based. The analysis of flood risk, hazards and exposure is predicated by the accurate determination of the hydrodynamic flow characteristics however, there is great potential for complex interactions which necessitates a more holistic approach. There is therefore a desire for the next generation of flood models to not only accurately simulate the flow dynamics but also possess the capability to effectively account for the myriad of associated events. This thesis therefore presents novel contributions towards the advancement of contemporary hydrodynamic modelling practice via the development of new numerical solutions. Specifically, it addresses limitations in accurately capturing transient flow interactions with partial barriers to flow; within urban environments, obstacles to flow can significantly influence the local flow characteristics and the accurate modelling of the flow interactions is therefore required. This is achieved via the development of two novel Riemann solvers, which enable the flexible and general treatment of partial barriers to flow. The predictive capacity of the solvers is validated via laboratory experiments, demonstrating their capability to resolve numerical fluxes across a range of flow and barrier configurations. The first solver is simple and easy to implement, with a focus on compatibility with existing numerical schemes to enhance the likelihood of implementation and immediate impact. The second solver addresses the limitations of the first, sacrificing simplicity in favour of greater accuracy and complexity. Furthermore, to account for the desired flexible future requirements of hydrodynamic models, the potential for flood flows to transport scalar quantities is also considered. Flood events have the potential to pollute water bodies and degrade water quality, particularly when the capacity of the sewage system is exceeded. In such events, hazardous substances may be transported within the urban catchment, compounding the associated risk. As a consequence, the advection and diffusion of a well mixed scalar quantity is also considered within the context of partial barriers to flow. The unique validation procedure based upon hydro-optical theory, enables the nonintrusive determination of the fieldwise concentration via the observation of the scattering and absorption of incident light by an injected fluorescent tracer mass. The collected data enables validation of the predictive capacity of the model to model the advection diffusion process through a partial barrier to flow whilst also providing a valuable insight into a otherwise seldom explored phenomena. It is hoped that the presented advances will contribute positively towards the development of the next generation of flood models and the implementation of effective flood risk management practice.