Stochastic modelling of a diffusive wave for flood propagation using the random walk particle tracking method in a hypothetical city

Abstract

Deterministic numerical schemes have been widely used for the solution of the diffusive wave (DW) equation, however, these schemes are computationally costly and suffer instability issues. This paper presents a stochastic random walk particle tracking (RWPT) method to solve such an equation for a dam-break flow problem. Three different wave duration scenarios are presented for simulations of the DW for flood flows in a hypothetical city. The hypothetical city is represented by a domain of size 2,000 m by 500 m in x and y directions, respectively. The domain is divided into 25 m by 25 m cells. A dam is located at the upstream of the hypothetical city. Each scenario has a distinct propagation pattern after the dam is breached. Analysed and presented are 18 different simulations, which are composed of three different building configurations, two different bed slopes, and three different shapes of hydrographs. In this method, the flood volume is divided into a large number of particles where each particle carries a fixed amount of the flood volume. These particles undergo convective and diffusive movements, and their superposition represents propagation of the DW in the flow domain. The solution algorithm of the RWPTbased equations is used to compute flood inundation depths in the hypothetical city.Comparison is drawn among the simulated results from three different shapes of the inflow hydrographs. The proposed stochastic method has two major advantages over traditional deterministic schemes: (a) greater efficiency, thus lesser computational costs, and (b) no instability issues.