Improving the stability of a simple formulation of the shallow water equations for 2-D flood modeling

The ability of two-dimensional hydrodynamic models to accurately and efficiently predict the propagation of floods over large urban areas is of paramount importance for flood risk assessment and management. Paradoxically, it is in these highly relevant urban domains where flood modeling faces some of the most challenging obstacles. This is because of the very high-resolution topography that is typically required to capture key hydraulic features, which significantly increases the computational time of the model. One particularly interesting solution to this difficulty was recently proposed in the form of a numerical scheme for the solution of a simplified version of the shallow water equations, which yields a system of two explicit equations that captures the most relevant hydraulic processes at very high computational efficiency. However, some stability problems were reported, especially when this formulation is applied to low friction areas. This is of particular importance in urban areas, where smooth surfaces are usually abundant. This paper proposes and tests two modifications of this previous numerical scheme that considerably improves the numerical stability of the model. Model improvements were assessed against a structured set of idealized test cases and finally in the simulation of flood propagation over complex topography in a highly urbanized area in London, United Kingdom. The enhanced stability achieved by the new formulation comes at no significant additional computational cost and, in fact, the model performance can benefit from the longer time steps that are allowed by the new scheme.