Fast flood finite volume model for the shallow water equations using high-resolution bathymetry data 

Abstract

Fast and precise flood predictions are crucial in preventing disastrous outcomes associated with flooding. However, creating accurate flood predictions based on numerical models is extremely time-consuming, posing challenges for early warning systems. Consequently, less accurate models are often employed in practical applications due to the importance of simulation time. This is far from ideal as accuracy is key to get the predictions correct, jeopardizing the reliability of the predictions. The shallow water equations (SWEs), which are physics-based depth-integrated differential equations, are commonly used to accurately simulate floods on land. These models remain time-consuming for large-scale simulations, leading to the frequent use of coarse meshes in practical settings. Unfortunately, using coarse meshes presents difficulties in accurately representing bottom resistance, which is a non-linear function of water depth. Solving this problem traditionally requires overestimating the friction coefficients and a lot of practical experience.   Advancements in the field of sub-grid resolution [1] and [2] have addressed this challenge by linking the source term and fluxes to the bathymetry at a sub-grid level. The sub-grid method involves dividing each cell into multiple sub-cells that store bathymetry data and roughness coefficients. This approach evaluates water depth and bottom resistances at the sub-cell level, resulting in a more precise representation at reduced computational cost. Additionally, this method accommodates flood and dry treatments by allowing cells to be partially wet, enabling them to adapt to the wet domain.  At the session, we intend to introduce a new explicit finite volume scheme that leverages high-resolution bathymetry data to more accurately incorporate non-linear bottom resistance effects. Show preliminary results of how the conveyance is improved for large meshes and what that means for the total simulation time. This scheme is a step toward an explicit depth-dependent flood and dry method for the SWEs, enabling the use of coarse meshes while retaining critical physical effects. Ultimately, this innovation will drastically reduce simulation time for flood predictions, facilitating more accurate simulations within shorter durations.   [1] V. Casulli. A high-resolution wetting and drying algorithm for free-surface hydrodynamics. International Journal for Numerical Methods in Fluids, 60:391–408, 2009.  [2] N. D. Volp, B. C. Van Prooijen, and G. S. Stelling. A finite volume approach for shallow water flow accounting for high-resolution bathymetry and roughness data. Water Resources Research, 49:4126–4135, 2013.