Abstract
The Discrete Boltzmann Equation (DBE) is a versatile simulation method, consisting of linear advection equations, which can be applied to the Shallow Water Equations (SWE).\\ The aim of this study is to assess the accuracy of the DBE to simulate dam-break of shallow water flows in presence of obstacles.\\ Dam-break flows in presence of obstacles can be regarded as simplified models for floods in urban areas.\\ In this study three cases of dam-break flows in presence of obstacles are considered: two with an isolated obstacle and the third in presence of an idealised city.\\ The comparison between DBE and benchmark results shows a fair agreement, confirming the validity of the DBE as simulation method for the SWE.
Highlights
Flooding is considered one of the most significant hazards society is facing
The multispeed Discrete Boltzmann Equation (DBE) is a method recently developed to simulate transcritical shallow water flows, and the main advantage is the simplicity of the mathematical model: a set of linear, uncoupled, purely advective equations
The DBE has been assessed as solution method for the Shallow Water Equation (SWE) when dam-break flows impacting on obstacles are considered
Summary
Flooding is considered one of the most significant hazards society is facing. Huge losses in terms of human lives, damages to buildings, houses, and civil infrastructures are caused every year by hurricanes and flooding. Great attention has been paid to the development of numerical solvers for the SWE (Toro and Garcia-Navarro, 2007; Toro, 2009). The latter tackle directly the SWE by means of the finite volumes discretization and have reached a sufficient level of complexity so that they are able to account for crucial issues such as to cite just a few, the treatment of topography source terms (Duran and Marche, 2014; Hou et al, 2018), the use of unstructured grids (Zhao et al, 2019), and the evolution of wet-dry fronts (Ferrari et al, 2019)
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