The one-dimensional (1D) pipe drainage network plays an important role in the modeling of urban dual drainage systems. Many 1D sewer software packages have been extensively developed and widely used, including the Simulation of Interaction between Pipe flow and Surface Overland flow in Networks (SIPSON) package and the US Environmental Protection Agency (EPA) Storm Water Management Model (SWMM) (Gironás et al. 2010). Due to its powerful functions and robust algorithms, the SWMM, a set of open-source codes, has become the most widely used 1D hydraulic model in the world. In addition, as a distributed hydrological model, the SWMM also provides a powerful rainfall-runoff calculation capability. Therefore, it has been widely used in various urban flood studies (Yang et al. 2020; Chen et al. 2021), and has become the computational core of 1D pipe models in many commercial software, such as Infoworks-ICM, PCSWMM, and XP-SWMM.
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In the past decades, regarding the solution of two-dimensional (2D) shallow water equations (SWEs), great progress has been made in terms of the development of both numerical discretization schemes and robust algorithms to address the key challenges encountered in flood modeling, such as wet/dry fronts (Castro et al. 2005), Riemann problem (Roe 1981), and sheet flow over steep slope source terms and stiff source terms (Audusse et al. 2004; Xia et al. 2017; Xia and Liang 2018). Nevertheless, there exist prevailing challenges, especially in terms of computational efficiency, which is relevant for real-time urban flood forecasting. Although GPU parallel computing technology can be used to reduce the computational time cost (Xia et al. 2019; Dazzi et al. 2020), several simplified forms of the complete SWEs, which has accuracy similar to that of the SWEs but with a less intensive flux calculation process, have been proposed, such as the diffusive wave model (DWM) and the kinematic wave model (Ponce 1990; Apel et al. 2009). As a simplified form of the complete SWEs, the local inertial approximation form model (LIM) proposed by Bates et al. (2010), which was derived by neglecting the convective acceleration term in the momentum equation, has attracted the interest of other researchers (Neal et al. 2012; de Almeida and Bates 2013; Martins et al. 2015). Via UK Environment Agency (EA) model benchmark tests, Neal et al. (2012) found that the LIM was often the most efficient model of the three main computational engines (the DWM, LIM, and full SWEs) of the LISFLOOD-FP model, and achieved good accuracy in most of the test cases. Furthermore, de Almeida and Bates (2013) pointed out that in a range of floodplain and lowland channels, the performance of the LIM becomes increasingly relevant with the increase of the Froude number and depth gradients. However, these studies were based on the finite difference method with structured grids, and were aimed at the flood characteristics of floodplains. Comparatively few studies have analyzed the performance of the LIM in urban stormwater simulation, especially in urban stormwater modeling considering a dual drainage system.
where superscript \(j\) and \(j+1\) respectively represent the current time step and next time step, and \(\Delta t\) is the calculation time step. Benefiting from the novel scheme of the friction source term, the time step is only strictly limited by the Courant-Friedrichs-Levy (CFL) condition. As the stability criterion in this study, the CFL condition is slightly different from that of the SWEs because the LIM only includes the information of momentum (-c and c), and, as shown by Bates et al. (2010): 2ff7e9595c
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