Volume 12 Issue 5
Dec.  2021
Turn off MathJax
Article Contents
Weiqi Wang, Wenjie Chen, Guoru Huang. Urban Stormwater Modeling with Local Inertial Approximation Form of Shallow Water Equations: A Comparative Study[J]. International Journal of Disaster Risk Science, 2021, 12(5): 745-763. doi: 10.1007/s13753-021-00368-0
Citation: Weiqi Wang, Wenjie Chen, Guoru Huang. Urban Stormwater Modeling with Local Inertial Approximation Form of Shallow Water Equations: A Comparative Study[J]. International Journal of Disaster Risk Science, 2021, 12(5): 745-763. doi: 10.1007/s13753-021-00368-0

Urban Stormwater Modeling with Local Inertial Approximation Form of Shallow Water Equations: A Comparative Study

doi: 10.1007/s13753-021-00368-0

This work was supported by the National Natural Science Foundation of China (Grant Numbers 51739011 and 51879108).

  • Available Online: 2021-12-25
  • This study focused on the performance and limitations of the local inertial approximation form model (LIM) of the shallow water equations (SWEs) when applied in urban flood modeling. A numerical scheme of the LIM equations was created using finite volume method with a first-order spatiotemporal Roe Riemann solver. A simplified urban stormwater model (SUSM) considering surface and underground dual drainage system was constructed based on LIM and the US Environmental Protection Agency Storm Water Management Model. Moreover, a complete urban stormwater model (USM) based on the SWEs with the same solution algorithm was used as the evaluation benchmark. Numerical results of the SUSM and USM in a highly urbanized area under four rainfall return periods were analyzed and compared. The results reveal that the performance of the SUSM is highly consistent with that of the USM but with an improvement in computational efficiency of approximately 140%. In terms of the accuracy of the model, the SUSM slightly underestimates the water depth and velocity and is less accurate when dealing with supercritical flow in urban stormwater flood modeling. Overall, the SUSM can produce comparable results to USM with higher computational efficiency, which provides a simplified and alternative method for urban flood modeling.
  • loading
  • Apel, H., G.T. Aronica, H. Kreibich, and A.H. Thieken. 2009. Flood risk analyses—How detailed do we need to be?. Natural Hazards 49(1): 79–98.
    Audusse, E., F. Bouchut, M.-O. Bristeau, R. Klein, and B. Perthame. 2004. A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. SIAM Journal on Scientific Computing 25(6): 2050–2065.
    Bates, P.D., M.S. Horritt, and T.J. Fewtrell. 2010. A simple inertial formulation of the shallow water equations for efficient two-dimensional flood inundation modelling. Journal of Hydrology 387(1): 33–45.
    Brufau, P., M.E. Vázquez-Cendón, and P. García-Navarro. 2002. A numerical model for the flooding and drying of irregular domains. International Journal for Numerical Methods in Fluids 39(3): 247–275.
    Carsell, K.M., N.D. Pingel, and D.T. Ford. 2004. Quantifying the benefit of a flood warning system. Natural Hazards Review 5(3): 131–140.
    Castro, M.J., A.M. Ferreiro Ferreiro, J.A. García-Rodríguez, J.M. González-Vida, J. Macías, C. Parés, and M.E. Vázquez-Cendón. 2005. The numerical treatment of wet/dry fronts in shallow flows: Application to one-layer and two-layer systems. Mathematical and Computer Modelling 42(3): 419–439.
    Chen, C.W., and R.P. Shubinski. 1971. Computer simulation of urban storm water runoff. Journal of the Hydraulics Division 97(2): 289–301.
    Chen, A.S., M.H. Hsu, T.S. Chen, and T.J. Chang. 2005. An integrated inundation model for highly developed urban areas. Water Science and Technology 51(2): 221–229.
    Chen, A.S., S. Djordjevic, J. Leandro, and D. Savic. 2007. The urban inundation model with bidirectional flow interaction between 2D overland surface and 1D sewer networks. In Proceedings of the Sixth International Conference on Sustainable Techniques and Strategies in Urban Water Management, June 2007, Lyon, France.
    Chen, W., G. Huang, H. Zhang, and W. Wang. 2018. Urban inundation response to rainstorm patterns with a coupled hydrodynamic model: A case study in Haidian Island, China. Journal of Hydrology 564: 1022–1035.
    Chen, W., W. Wang, G. Huang, Z. Wang, C. Lai, and Z. Yang. 2021. The capacity of grey infrastructure in urban flood management: A comprehensive analysis of grey infrastructure and the green-grey approach. International Journal of Disaster Risk Reduction 54: Article 102045.
    Dazzi, S., R. Vacondio, and P. Mignosa. 2020. Internal boundary conditions for a GPU-accelerated 2D shallow water model: Implementation and applications. Advances in Water Resources 137: Article 103525.
    de Almeida, G.A.M., and P. Bates. 2013. Applicability of the local inertial approximation of the shallow water equations to flood modeling. Water Resources Research 49(8): 4833–4844.
    Gironás, J., L.A. Roesner, L.A. Rossman, and J. Davis. 2010. A new applications manual for the Storm Water Management Model (SWMM). Environmental Modelling & Software 25(6): 813–814.
    Hsu, M.H., S.H. Chen, and T.J. Chang. 2000. Inundation simulation for urban drainage basin with storm sewer system. Journal of Hydrology 234(1): 21–37.
    Kaspersen, P.S., N.H. Ravn, K. Arnbjerg-Nielsen, H. Madsen, and M. Drews. 2017. Comparison of the impacts of urban development and climate change on exposing European cities to pluvial flooding. Hydrology and Earth System Sciences 21(8): 4131–4147.
    Leandro, J., A.S. Chen, S. Djordjević, and D.A. Savić. 2009. Comparison of 1D/1D and 1D/2D coupled (sewer/surface) hydraulic models for urban flood simulation. Journal of Hydraulic Engineering 135(6): 495–504.
    Leandro, J., P. Lopes, R. Carvalho, P. Páscoa, R. Martins, and M. Romagnoli. 2014. Numerical and experimental characterization of the 2D vertical average-velocity plane at the center-profile and qualitative air entrainment inside a gully for drainage and reverse flow. Computers & Fluids 102: 52–61.
    Liang, Q., X. Xia, and J. Hou. 2015. Efficient urban flood simulation using a GPU-accelerated SPH model. Environmental Earth Sciences 74(11): 7285–7294.
    Martins, R., J. Leandro, and S. Djordjević. 2015. A well balanced Roe scheme for the local inertial equations with an unstructured mesh. Advances in Water Resources 83: 351–363.
    McCallum, I., W. Liu, L. See, R. Mechler, A. Keating, S. Hochrainer-Stigler, J. Mochizuki, and S. Fritz et al. 2016. Technologies to support community flood disaster risk reduction. International Journal of Disaster Risk Science 7(2): 198–204.
    Neal, J., I. Villanueva, N. Wright, T. Willis, T. Fewtrell, and P. Bates. 2012. How much physical complexity is needed to model flood inundation?. Hydrological Processes 26(15): 2264–2282.
    Néelz, S., and G. Pender. 2013. Benchmarking the latest generation of 2D hydraulic modelling packages. Bristol, UK: Environment Agency.
    Ponce, V.M. 1990. Generalized diffusion wave equation with inertial effects. Water Resources Research 26(5): 1099–1101.
    Roe, P.L. 1981. Approximate Riemann solvers, parameter vectors, and difference schemes. Journal of Computational Physics 43(2): 357–372.
    Rossman, L.A., and W. Huber. 2017. Storm Water Management Model reference manual volume II—Hydraulics. Washington, DC: US Environmental Protection Agency.
    Santos, P.P., and E. Reis. 2018. Assessment of stream flood susceptibility: A cross-analysis between model results and flood losses. Journal of Flood Risk Management 11(S2): S1038–S1050.
    Xia, X., and Q. Liang. 2018. A new efficient implicit scheme for discretising the stiff friction terms in the shallow water equations. Advances in Water Resources 117: 87–97.
    Xia, X., Q. Liang, X. Ming, and J. Hou. 2017. An efficient and stable hydrodynamic model with novel source term discretization schemes for overland flow and flood simulations. Water Resources Research 53(5): 3730–3759.
    Xia, X., Q. Liang, and X. Ming. 2019. A full-scale fluvial flood modelling framework based on a high-performance integrated hydrodynamic modelling system (HiPIMS). Advances in Water Resources 132: Article 103392.
    Yang, Y., L. Sun, R. Li, J. Yin, and D. Yu. 2020. Linking a Storm Water Management Model to a novel two-dimensional model for urban pluvial flood modeling. International Journal of Disaster Risk Science 11(4): 508–518.
  • 加载中


    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (88) PDF downloads(0) Cited by()
    Proportional views


    DownLoad:  Full-Size Img  PowerPoint