Flow Division at a Free-Surface, Three-Channel Intersection Using 1D Shallow Water Equations

  • Sajjad HaiderEmail author
  • Hamza Farooq Gabriel
  • Ammara Mubeen
Research Article - Civil Engineering


One of the numerical techniques to treat the problem of free-surface flow division at a 90°, equal-width, three-channel junction is based on using a 1D shallow water equations model in tandem with a zero-crest height side weir model to simulate the outflow to the side channel (Kesserwani et al. in J Hydraul Eng 136(9):662–668, 2010; Ghostine et al. in Appl Math Comput 219:5070–5082, 2013). This method in subcritical flow case is put to test because of downstream backwater effect from the side channel which requires using the Villemonte equation to suitably reduce the flow due to weir submergence. This methodology is problematic as VE requires the downstream flow depth which lies outside the domain modeled. To overcome it, we proposed a new methodology which used the lateral weir height in the side channel as weir crest height at the junction instead of zero-crest height, thus obviating the need to use the Villemont equation. As the flow conditions at the junction can vary, the study uses a robust model based on an explicit, finite-volume technique, employing approximate Riemann solver of Roe for the simulation. The model is evaluated by comparing it with experimental, theoretical and 3D numerical model data in super-, trans- and subcritical flow regimes. For all the cases, the maximum error in the model predicted outflow ratio to side channel remained below 8%, while the max root-mean-squared error did not exceed 3.53%. The model performed satisfactorily, combining accuracy and computational efficiency.


Shallow water equations Flow bifurcation T-junction Free-surface flow Side weir 


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© King Fahd University of Petroleum & Minerals 2019

Authors and Affiliations

  1. 1.NUST Institute of Civil EngineeringNational University of Sciences and Technology (NUST)IslamabadPakistan

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