High-performance numerical model for large-scale flood inundation problems

Abstract

The simulation of large-scale flood inundation problems requires numerical models that are both accurate and have high computational performance. Over the past decades giant achievements have been attained in computational hydraulics and a number of accurate models have emerged. However, the accurate simulations of these models require high-resolution meshes, resulting in high computational cost. Thus, the models providing a rational trade-off between accuracy and time cost are highly demanded. The lack of such tools substantially limits our ability to understand and predict floods that extend over large areas. In this research a new model is presented, which falls into this line. The model solves the two dimensional shallow water equations (SWE) by a Godunov type finite volume (FV) method that makes use of two nested meshes. Runtime computations are performed at a coarse computational mesh (thus increasing computational performance), while a fine mesh is used to incorporate finely resolved information into the solution at pre-processing level (thus substantially reducing the loss of accuracy that would otherwise result). The proposed model presents new upscaling methods that are separately derived for each of the terms in the SWE based on the integration of the governing equations over subdomains defined by the coarse resolution grid cells, such as friction and bed slope source terms. This research also sheds light onto the limitations of some of the widely used assumptions in nested meshes models, such as constant friction slope for upscaling the friction effects. The accuracy and performance of the model are tested through six artificial and a real-world test problems, namely one-dimensional steady flow over a hump, dam-break problem, dam-break wave propagating over three humps, open channel flow around a bend, 1D flow over an irregular bed, compound channel, and the River Tiber. These test cases cover a wide range of hydraulic issues, such as steady and unsteady flows, hydraulic jump, 1D and 2D flood propagation, (mild, large or no) variation of topography and roughness coefficient across the domain of study, propagation of waves with continuous (rarefaction) and discontinuous (shock) water surface. It is shown that that i) in general the proposed model provides more accurate results than traditional FV models currently available and ii) for the same accuracy and at low resolution, the proposed methods substantially increase computational performance. These attributions make the proposed model suitable for large-scale real-life problems and those artificial cases with significant changes in topography’s features and roughness properties.

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ORCID for Gustavo De Almeida: orcid.org/0000-0002-3291-3985

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