Numerical improvements for large-scale flood simulation

Abstract

This work assesses two numerical approaches that are most commonly used nowadays for large-scale flood simulation. For this purpose, two different numerical models are developed, i.e. a finite volume Godunov-type model that solves the fully 2D shallow water equations and a simplified model that is based on the zero-inertia formula. The fully 2D model employs an explicit finite volume Godunov-type scheme to solve a pre-balanced formulation of the 2D shallow water equations (SWEs). The interface fluxes are calculated by an HLLC approximate Riemann solver with the local Riemann problems defined by the Riemann states that are reconstructed using a depth-positivity-preserving approach. The second order accuracy is achieved using a Runge-Kutta integrated method in time and a slope limited linear reconstruction (MUSCL) scheme in space. For the explicit scheme, the adaptive time step controlled by the Courant-Friedrichs-Lewy (CFL) criterion is implemented to maintain the computational stability. After being validated against several theoretical benchmark tests, this fully 2D model is applied to simulate different types of flood waves, including rapidly-varying dam breaks, slow-evolving inundations and coastal applications. In all of the tests, the numerical results are found to agree well with the analytical solutions, laboratory measurements, previously published predictions and field data whenever available. Closely related to the reliability of the numerical solutions, the effects of the mesh resolution and the numerical accuracy are also investigated in this work. The flood extent, water depth and arrival time are found to be sensitive to the change of the mesh resolution. However, the sensitive response of the numerical accuracy is only restricted to those simple analytical tests but not found in any of the realistic simulations. A new zero-inertia model is developed for predicting slow-varying flood inundations, where the governing equation is solved by an explicit finite volume scheme implemented with a depth-positivity-preserving condition. The new zero-inertia model is validated against analytical tests and a realistic flood inundation event in Thamesmead, England. The numerical results present good agreement with the analytical solutions and predictions produced by the aforementioned fully 2D shallow flow model. The mass conservation is strictly maintained throughout the computations. However, the computational cost is found to be much more expensive than the fully 2D model due to the use of much smaller time step in maintaining numerical stability.