Well-balanced scheme for modeling open-channel and surcharged flows in steep-slope closed conduit systems

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  • The model presented herein is the same as that of Leon et al. (2010b), except that it has been modified to preserve "lake at rest" conditions in sloped prismatic conduits. The results of the new model (present paper) are identical to those of Leon et al. (2010b) for non-rest conditions. These schemes are based on the two-governing equation model, where open channel flows are simulated using the Saint-Venant equations and pressurized flows using the compressible water hammer equations. The new model preserves "lake at rest" conditions (horizontal still water) regardless of the conduit slope, resolves moving jump discontinuities over dry-beds in sloped conduits, and resolves small perturbations from steady-states, even when adjacent to dry regions. The preserving steady-state capability of the new model is of particular importance in continuous long simulations when the conduits are relatively steep (|S₀|>∼0.5%). Two main contributions are presented here, namely: (1) a new method for water stage reconstruction that preserves "lake at rest" conditions regardless of the pipe slope, and (2) a horizontal system of coordinates, instead of the commonly used inclined coordinate system, is used for facilitating the implementation of the proposed well-balanced scheme to complex systems. In the horizontal coordinate system, the cross-section of a circular pipe becomes an ellipse. The hydraulic characteristics of an ellipse are presented. Good results are achieved in the test cases.
  • Keywords: Transient flow, Unsteady flow, Surcharged flow, Well-balanced scheme, Open-channel flow, Storm water system, Finite-volume method, Combined sewer system
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  • Leon, A., Gifford-Miears, C., and Choi, Y. (2013). ”Well-Balanced Scheme for Modeling Open-Channel and Surcharged Flows in Steep-Slope Closed Conduit Systems.” Journal of Hydraulic Engineering, 139(4), 374–384.
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  • 139
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  • 4
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  • The authors gratefully acknowledge the financial support of the School of Civil and Construction Engineering at Oregon State University (OSU) and Northwest Hydraulic Consultants (NHC), Pasadena, CA.



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