Simulation of flooding in cities using the Shallow water equations

Abstract

This thesis studies the simulation of wave propagation in simplified urban environments using the shallow water equations. Urban flooding can cause significant damage to infrastructure and society, and numerical models can be useful tools for studying how water moves through complex city geometries. The aim of this work is to develop and evaluate a Runge-Kutta discontinuous Galerkin method for solving the two-dimensional shallow water equations and to investigate its use in both idealized and urban computational domains. The method utilizes RKDG time stepping together with a Lax-Friedrichs numerical flux and reflective boundary conditions. For the urban simulations, a mesh representing the Avenyn area in Gothenburg is used, where building regions are treated as reflective internal wall interfaces. A total variation bounded slope limiter is also implemented in order to reduce non-physical oscillations near steep gradients and hence increase the stability of the solver. The model is first tested and compared against benchmark cases generated with pyswashes, which is a Python package containing several analytic reference solutions. Additional simulations are performed on square, rectangular, and urban domains. The results show that the RKDG method successfully captures wave propagation, reflection, and interaction with building geometries. Without slope limiting, the urban simulation may develop non-physical oscillations and become unstable, whereas the simulation with the slope limiter activated remains more stable, and the waves retain their propagation pattern. The results indicate that the RKDG method is suitable for studying simplified wave propagation in urban environments. It is, however, in need of further development and improvement before the model can be used for realistic flood prediction. Future work could include incorporating non-flat terrain, wetting and drying, and improving computational efficiency.