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The transition from open-channel to surcharged flow creates problems for numerical modeling of stormwater systems. Mathematically, problems arise through a discrete shock at the boundary between the hyperbolic Saint-Venant equations and the elliptic incompressible flow equations at the surcharge transition. Physically, problems arise through trapping of air pockets, creation of bubbly flows, and cavitation in rapid emptying and filling that are difficult to correctly capture in one-dimensional (1D) models. Discussed herein are three approaches for modeling surcharged flow with hyperbolic 1D equations: (i) Preissmann Slot (PS), (ii) Two- component Pressure Approach (TPA) and (iii) Artificial Compressibility (AC). Each provides approximating terms that are controlled by model coefficients to alter the pressure wave celerity through the surcharged system. Commonly, the implementation of these models involve slowing the pressure celerity below physical values, which allows the numerical solution to dissipate the transition shock between the free surface and surcharged flows without resorting to extraordinarily small time-steps. The different methods provide different capabilities and numerical implementations that affect their behavior and suitability for different problems. https://doi.org/10.3850/IAHR-39WC2521711920221370