Modelling flood events with a cumulant CO lattice Boltzmann shallow water model
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Modelling flood events with a cumulant CO lattice Boltzmann shallow water model Sara Venturi1 · Silvia Di Francesco2 · Martin Geier3 · Piergiorgio Manciola1 Received: 15 April 2020 / Accepted: 10 October 2020 © Springer Nature B.V. 2020
Abstract In this work the development of a semiautomatic procedure based on the coupled use of a GIS subroutine and a two-dimensional hydraulic lattice Boltzmann model solving the shallow water equations is presented. A C code implementing the cumulant collision operator and a limiter velocity strategy to model the wave front on a wet–dry bed is discussed and validated against literature test cases. Finally an application to a real test case, the Malpasset dam break, is shown, highlighting the good performances of the model through a comparison with results from surveys and data from literature. Keywords Wet–dry · Parallel processing · Cumulant · Dam break
1 Introduction This research aims at implementing, validating and applying a fast and efficient procedure to model large-scale hydraulic events and in particular floods (Venturi 2018). The hydrodynamic problem is solved through a kinetic approach based on lattice Boltzmann method with a cumulant collision operator (CO). The chosen mesoscopic model has been proven to be more accurate and stable in simulating low-viscosity flows (e.g. water), relative to other discrete models (Venturi 2019). Moreover, it could be refined to run efficiently in parallel. This characteristic could allow accurate flood wave modelling in a lower computation time, making real-time hydraulic risk assessment possible. Most of the events involving free surface flows (dam break, flooding, tsunami, etc.) has to deal with the wave propagation over dry beds: the simulation of wet–dry position and run-up/run-down processes represent a decisive step for hydraulic engineering studies. Several models were developed using continuous numerical methods, suggesting the use of an ad hoc boundary condition at the wet–dry interface: Lynett et al. (2002) applied a linear * Silvia Di Francesco [email protected] 1
Civil and Environmental Engineering Department, University of Perugia, Via G Duranti 93, Perugia, Italy
2
Niccolò Cusano University, Via Don C. Gnocchi 3, Rome, Italy
3
Institute for Computational Modeling in Civil Engineering (iRMB), TU Braunschweig, Brunswick, Germany
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Natural Hazards
extrapolation technique for water depths, Madsen et al. (1997) a low porous permeable beach, Que and Xu (2006) a thin film for dry areas. In this work, the wetting–drying process is integrated in a cumulant CO lattice Boltzmann shallow water model presented by Venturi (2019). To this end, a procedure based on a threshold value of the water depth and Froude number is defined and implemented. The paper is organized as follows: Sect. 2.1 describes the main features of the mathematical model; Sect. 2.2 is devoted to the implementation of the wet–dry limiter, Sect. 2.3 to the code parallelization and Sect. 2.4 to GIS procedures. Sec
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