Improved Modeling of Flows in Sewer Pipes with a Novel, Well-Balanced MUSCL Scheme
Publication: Journal of Hydraulic Engineering
Volume 148, Issue 12
Abstract
The numerical study in this paper aims at obtaining exact well-balance and improving the computational accuracy, efficiency, and the performance at wet–dry fronts, especially for the flows in ventilated sewer pipes. To this end, a novel numerical model for mixed flows in a circular-shaped sewer is proposed. The major contributions of this study are: (1) a MUSCL scheme (monotonic upstream-centered scheme for conservation laws) is designed so that second-order accuracy is achieved, which leads to accurate solutions even over coarse meshes; (2) a special reconstruction technique and novel source term discretization are proposed for pipe flows to guarantee the exact well-balance in the framework of a MUSCL scheme, thus numerical oscillations at stationary steady states are avoided; (3) the proposed new scheme produces reasonable solutions for kinetic flows in underresolved finite-volume grids with very low water volumes; and (4) it guarantees the positivity of the computed water volume without forcing a minimum wetted area value or reducing the global time step size. The performance and superiorities of the proposed new scheme for sewer flows are verified against previously reported well-balanced numerical models on a number of experiments.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
References
Ackers, P., and A. Harrison. 1964. “Attenuation of flood waves in part-full pipes.” Proc. Inst. Civ. Eng. 28 (3): 361–382. https://doi.org/10.1680/iicep.1964.10089.
Ambrosi, D. 1995. “Approximation of shallow water equations by Roe’s Riemann solver.” Int. J. Numer. Methods Fluids 20 (2): 157–168. https://doi.org/10.1002/fld.1650200205.
Aureli, F., S. Dazzi, A. Maranzoni, and P. Mignosa. 2015. “Validation of single- and two-equation models for transient mixed flows: A laboratory test case.” J. Hydraul. Res. 53 (4): 440–451. https://doi.org/10.1080/00221686.2015.1038324.
Bollermann, A., S. Noelle, and M. Lukáčová-Medvid’ová. 2011. “Finite volume evolution Galerkin methods for the shallow water equations with dry beds.” Commun. Comput. Phys. 10 (2): 371–404. https://doi.org/10.4208/cicp.220210.020710a.
Bousso, S., M. Daynou, and M. Fuamba. 2013. “Numerical modeling of mixed flows in storm water systems: Critical review of literature.” J. Hydraul. Eng. 139 (4): 385–396. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000680.
Burguete, J., and P. García-Navarro. 2001. “Efficient construction of high-resolution TVD conservative schemes for equations with source terms: Application to shallow water flows.” Int. J. Numer. Methods Fluids 37 (2): 209–248. https://doi.org/10.1002/fld.175.
Capart, H., C. Bogaerts, J. Kevers-Leclercq, and Y. Zech. 1999. “Robust numerical treatment of flow transitions at drainage pipe boundaries.” Water Sci. Technol. 39 (9): 113–120. https://doi.org/10.2166/wst.1999.0455.
Capart, H., X. Sillen, and Y. Zech. 1997. “Numerical and experimental water transients in sewer pipes.” J. Hydraul. Res. 35 (5): 659–672. https://doi.org/10.1080/00221689709498400.
Delis, A. I., H. Guillard, and Y.-C. Tai. 2018. “Numerical simulations of hydraulic jumps with the shear shallow water model.” SMAI J. Comput. Math. 4 (Nov): 319–344. https://doi.org/10.5802/smai-jcm.37.
Fraccarollo, L., and E. F. Toro. 1995. “Experimental and numerical assessment of the shallow water model for two-dimensional dam-break type problems.” J. Hydraul. Res. 33 (6): 843–864. https://doi.org/10.1080/00221689509498555.
Garcia-Navarro, P., and M. E. Vazquez-Cendon. 2000. “On numerical treatment of the source terms in the shallow water equations.” Comput. Fluids 29 (8): 951–979. https://doi.org/10.1016/S0045-7930(99)00038-9.
Gottlieb, S., C.-W. Shu, and E. Tadmor. 2001. “Strong stability-preserving high-order time discretization methods.” SIAM Rev. 43 (1): 89–112. https://doi.org/10.1137/S003614450036757X.
Kerger, F., P. Archambeau, S. Erpicum, B. J. Dewals, and M. Pirotton. 2011. “An exact Riemann solver and a Godunov scheme for simulating highly transient mixed flows.” J. Comput. Appl. Math. 235 (8): 2030–2040. https://doi.org/10.1016/j.cam.2010.09.026.
Kurganov, A., and D. Levy. 2002. “Central-upwind schemes for the Saint-Venant system.” ESAIM Math. Model. Numer. Anal. 36 (3): 397–425. https://doi.org/10.1051/m2an:2002019.
Kurganov, A., and C.-T. Lin. 2007. “On the reduction of numerical dissipation in central-upwind schemes.” Commun. Comput. Phys. 2 (1): 141–163.
León, A. S., M. S. Ghidaoui, A. R. Schmidt, and M. H. García. 2006. “Godunov-type solutions for transient flows in sewers.” J. Hydraul. Eng. 132 (8): 800–813. https://doi.org/10.1061/(ASCE)0733-9429(2006)132:8(800).
León, A. S., M. S. Ghidaoui, A. R. Schmidt, and M. H. García. 2009. “Application of Godunov-type schemes to transient mixed flows.” J. Hydraul. Res. 47 (2): 147–156. https://doi.org/10.3826/jhr.2009.3157.
León, A. S., C. Gifford-Miears, and Y. Choi. 2013. “Well-balanced scheme for modeling open-channel and surcharged flows in steep-slope closed conduit systems.” J. Hydraul. Eng. 139 (4): 374–384. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000690.
Li, Q., Q. Liang, and X. Xia. 2020. “A novel 1D-2D coupled model for hydrodynamic simulation of flows in drainage networks.” Adv. Water Resour. 137 (Mar): 103519. https://doi.org/10.1016/j.advwatres.2020.103519.
Liang, Q., and F. Marche. 2009. “Numerical resolution of well-balanced shallow water equations with complex source terms.” Adv. Water Resour. 32 (6): 873–884. https://doi.org/10.1016/j.advwatres.2009.02.010.
Lieb, A. M., C. H. Rycroft, and J. Wilkening. 2016. “Optimizing intermittent water supply in urban pipe distribution networks.” SIAM J. Appl. Math. 76 (4): 1492–1514. https://doi.org/10.1137/15M1038979.
Liu, X. 2020a. “A steady-state-preserving scheme for shallow water flows in channels.” J. Comput. Phys. 423 (Dec): 109803. https://doi.org/10.1016/j.jcp.2020.109803.
Liu, X. 2020b. “A well-balanced asymptotic preserving scheme for the two-dimensional shallow water equations over irregular bottom topography.” SIAM J. Sci. Comput. 42 (5): B1136–B1172. https://doi.org/10.1137/19M1262590.
Liu, X., A. Chertock, A. Kurganov, and K. Wolfkill. 2019. “One-dimensional/two-dimensional coupling approach with quadrilateral confluence region for modeling river systems.” J. Sci. Comput. 81 (3): 1297–1328. https://doi.org/10.1007/s10915-019-00985-4.
Malekpour, A., and B. Karney. 2016. “Spurious numerical oscillations in the Preissmann slot method: Origin and suppression.” J. Hydraul. Eng. 142 (3): 04015060. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001106.
Mao, Z., G. Guan, and Z. Yang. 2020. “Suppress numerical oscillations in transient mixed flow simulations with a modified HLL solver.” Water 12 (5): 1245. https://doi.org/10.3390/w12051245.
Michel-Dansac, V., C. Berthon, S. Clain, and F. Foucher. 2016. “A well-balanced scheme for the shallow-water equations with topography.” Comput. Math. Appl. 72 (3): 568–593. https://doi.org/10.1016/j.camwa.2016.05.015.
Parés, C., and M. Castro. 2004. “On the well-balance property of Roe’s method for nonconservative hyperbolic systems. Applications to shallow-water systems.” ESAIM Math. Model. Numer. Anal. 38 (5): 821–852. https://doi.org/10.1051/m2an:2004041.
Sanders, B. F., and S. F. Bradford. 2011. “Network implementation of the two-component pressure approach for transient flow in storm sewers.” J. Hydraul. Eng. 137 (2): 158–172. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000293.
Sturm, T. W. 2001. Open channel hydraulics. New York: McGraw-Hill.
Sweby, P. K. 1984. “High resolution schemes using flux limiters for hyperbolic conservation laws.” SIAM J. Numer. Anal. 21 (5): 995–1011. https://doi.org/10.1137/0721062.
Toro, E. F. 1992. “Riemann problems and the WAF method for solving the two-dimensional shallow water equations.” Philos. Trans. R. Soc. London, Ser. A 338 (1649): 43–68. https://doi.org/10.1098/rsta.1992.0002.
Van Leer, B. 1979. “Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method.” J. Comput. Phys. 32 (1): 101–136. https://doi.org/10.1016/0021-9991(79)90145-1.
Vasconcelos, J. G., S. J. Wright, and P. L. Roe. 2006. “Improved simulation of flow regime transition in sewers: Two-component pressure approach.” J. Hydraul. Eng. 132 (6): 553–562. https://doi.org/10.1061/(ASCE)0733-9429(2006)132:6(553).
Vasconcelos, J. G., S. J. Wright, and P. L. Roe. 2009. “Numerical oscillations in pipe-filling bore predictions by shock-capturing models.” J. Hydraul. Eng. 135 (4): 296–305. https://doi.org/10.1061/(ASCE)0733-9429(2009)135:4(296).
Zhang, X. 2017. “Modeling transient flow in intermittent water supply system.” M.S. thesis, Dept. of Civil and Environmental Engineering, Massachusetts Institute of Technology.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 148 • Issue 12 • December 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Aug 19, 2021
Accepted: May 24, 2022
Published online: Sep 16, 2022
Published in print: Dec 1, 2022
Discussion open until: Feb 16, 2023
ASCE Technical Topics:
- Analysis (by type)
- Engineering fundamentals
- Flow (fluid dynamics)
- Fluid dynamics
- Fluid mechanics
- Hydrologic engineering
- Infrastructure
- Lifeline systems
- Methodology (by type)
- Model accuracy
- Models (by type)
- Numerical analysis
- Numerical methods
- Numerical models
- Pipe flow
- Pipeline systems
- Pipes
- Sewer pipes
- Sewers
- Steel pipes
- Water and water resources
- Water conservation
- Water management
- Water policy
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