Comparative analysis of overland flow models using finite volume schemes

Abstract

In this paper attention is first focused on a comparative analysis of three hydraulic models for overland flow simulations. In particular, the overland flow was considered as a 2D unsteady flow and was mathematically described using three approaches (fully dynamic, diffusive and kinematic waves). Numerical results highlighted that the differences among the simulations were not very important when the simulations referred to commonly used ideal tests found in the literature in which the topography is reduced to plane surface. Significant differences were observed in more complicated tests for which only the fully dynamic model was able to provide a good prediction of the observed discharges and water depths. Then, attention is focused on the fully dynamic model and in particular on the analysis of two numerical schemes (TVD-MacCormack and HLL) and the influence of the grid size. Numerical tests carried out on irregular topography show that, as the grid size decreases, the performance of the HLL scheme becomes closer to that of the TVD-MacCormack scheme in shorter computational times at least for high rainfall intensity. P. Costabile

A simple and efficient unstructured finite volume scheme for solving the shallow water equations in overland flow applications

“…Two-dimensional shallow water models (also known as dynamic wave models) are increasingly used in the computation of overland flow and rainfall-runoff transformation in urban and meso-scale rural basins [Cea et al, 2010b;Costabile et al, 2012;Howes et al, 2006;Hunter et al, 2007Hunter et al, , 2008Kivva and Zheleznyak, 2005;Sanders et al, 2008;Schubert et al, 2008]. Although kinematic and diffusive wave models have been traditionally preferred for these applications due to their lower computational cost when applied at the catchment scale, it has been recognized that the diffusive wave (DW) equation presents a series of inconveniences in comparison to the dynamic wave equation due to the fact of neglecting the inertial terms in the momentum balance Costabile et al, 2012]. Dimensional analysis shows that the relative importance of the inertial terms increases with the Froude number and with the small-scale features of the flow [Hunter et al, 2007].…”

Hydraulic Characterization of River Networks Based on Flow Patterns Simulated by 2‐D Shallow Water Modeling: Scaling Properties, Multifractal Interpretation, and Perspectives for Channel Heads Detection

“…Except in some theoretical cases, it is not possible to derive analytical solutions for the 2-D SWEs, and therefore, numerical schemes have to be used in order to obtain a solution for these equations. In particular, on the basis of the authors' experience on these kind of simulations (Costabile & Macchione, 2015;Costabile et al, 2012Costabile et al, , 2013Costabile et al, , 2017Macchione, Costabile, Costanzo, & De Santis 2019;Macchione, Costabile, Costanzo, & De Lorenzo, 2019), the first-order shock-capturing scheme reported in Appendix A has been used here. It is important to observe that this numerical model used here is characterized by well-balanced properties.…”

“…Moreover, the increasing availability of high-topographic detail offered by Light Detection and Ranging (LiDAR) surveys allows the use of fine meshes that, in turn, gives the opportunity for the resolution of small-scale flow patterns, increasing the relevance of inertial terms in the hydrodynamic simulation of the surface runoff (Cea & Bladé, 2015). Considering the added value that they can provide in terms of the physical representation of the overland flow phenomenon using high-resolution digital elevation model (DEM), the SWEs are increasingly recognized as the most suitable approach for the description of hydrodynamic-based surface runoff computations in rainfall-runoff simulations at the catchment scale (Bellos & Tsakiris, 2016;Bout & Jetten, 2018;Caviedes-Voullième et al, 2012;Cea & Bladé, 2015;Cea et al, 2010;Costabile et al, 2012Costabile et al, , 2013Fernández-Pato et al, 2016;Hou et al, 2018;Huang et al, 2015;Liang et al, 2015;Simons et al, 2014;Singh et al, 2015;Xia et al, 2017;Xia & Liang, 2018;Yeh et al, 2011).…”

An efficient and stable hydrodynamic model with novel source term discretization schemes for overland flow and flood simulations

“…Traditionally, hydrological models or simplified hydrodynamic models [ Lighthill and Whitham , ; Govindaraju , ; Bates et al ., ] are usually used for overland flow simulations at a catchment scale. However, most of these simplified models are not capable of depicting the rapid catchment responses and the highly transient surface flow processes to accurately predict water depths and velocities the flood waves [e.g., Cea et al ., ; Costabile et al ., ]. Moreover, their reduced representation of physical complexity may lead to increased sensitivity to parameterization.…”