Flood Wave Modeling Based on a Two-Dimensional Modified Wave Propagation Algorithm Coupled to a Full-Pipe Network Solver
Publication: Journal of Hydraulic Engineering
Volume 138, Issue 3
Abstract
Flood propagation over urban areas can cause an interaction between the free-surface flow and large underground pipe networks used for sewage and storm drainage, causing outflows and inflows at the bed. The waves resulting from these bed discharges may collide with each other and the surface waves, increasing water depths, velocities and accelerations, and their interaction thus affects flood risk. The authors previously introduced a one-dimensional (1D) shallow-water model for simulating free-surface interaction with the flows issuing vertically through finite gaps, referred to as efflux. This model used a modified wave propagation algorithm and was validated by comparing results with the full Navier-Stokes equation solver (STAR-CD) based on the volume-of-fluid method, which models free-surface motion quite generally, although at considerable computational expense. The present paper extends the shallow-water scheme to two dimensions, including source terms for pipe outflow/inflow (efflux/influx) and bed friction and bathymetry gradients. A general pipe network solver for full flow is coupled with the free-surface flow. The methodology is first tested with idealized cases. Two-dimensional (2D) dam-break flow over a complex bed profile without efflux/influx at the bed is first modeled. Next, efflux discharge is modeled in isolation over a dry bed and then with dam-break interaction, comparing with 3D STAR-CD results. Results for these idealized cases are in good agreement. Finally dam-break interaction with a pipe network of 25 nodes demonstrates the complex bore interaction.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors are grateful to the anonymous reviewers for their careful reviews and many useful suggestions.
References
Audusse, E., Bouchut, F., Bristeau, M. O., Klein, R., and Perthame, B. (2004). “A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows.” SIAM J. Sci. Comput., 25(6), 2050–2065.
Bale, D. S., LeVeque, R. J., Mitran, S., and Rossmanith, J. A. (2002). “A wave propagation method for conservation laws and balance laws with spatially varying flux functions.” SIAM J. Sci. Comput., 24(3), 955–978.
Bolle, A. et al. (2006). “Hydraulic modelling of the two-directional interaction between sewer and river systems.” Proc., Urban Drainage Modelling and Water Sensitive Urban Design, Monash Univ., Melbourne, Australia.
Brufau, P., Vázquez-Cendón, M. E., and Garcia-Navarro, P. (2002). “A numerical model for the flooding and drying of irregular domains.” Int. J. Numer. Methods Fluids, 39(3), 247–275.
Carr, R. W., and Smith, G. P. (2006). “Linking of 2D and pipe hydraulic models at fine spatial scales.” Proc., Urban Drainage Modelling and Water Sensitive Urban Design, Monash Univ., Melbourne, Australia.
Chen, A. S., Hsu, M. H., Chen, T. S., and Chang, T. J. (2005). “An integrated inundation model for highly developed urban areas.” Water Sci. Technol., 51(2), 221–229.
Danish Hydraulic Institute (DHI). (2009). “Mike 21 flow model.” 〈http://www.dhigroup.com〉.
Delft Hydraulics Software (2010). “SOBEK, 1D/2D modelling suite for integral water.” 〈http://delftsoftware.wldelft.nl〉.
Delis, A. I., Kazolea, M., and Kampanis, N. A. (2008). “A robust high-resolution finite volume scheme for the simulation of long waves over complex domains.” Int. J. Numer. Methods Fluids, 56(4), 419–452.
Djordjević, S., Prodanović, D., Maksimović, C., Ivetić, M., and Savić, D. (2005). “SIPSON—Simulation of interaction between pipe flow and surface overland flow in networks.” Water Sci. Technol., 52(5), 275–283.
Djordjević, S., Prodanović, D., and Walters, G. A. (2004). “Simulation of transcritical flow in pipe/channel networks.” J. Hydraul. Eng., 130(12), 1167–1178.
George, D. L. (2008). “Augmented Riemann solvers for the shallow water equations over variable topography with steady states and inundation.” J. Comput. Phys., 227(6), 3089–3113.
Godunov, S. K. (1959). “A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics.” Mat. Sb., 47, 271–306.
Hsu, M. H., Chen, S. H., and Chang, T. J. (2002). “Dynamic inundation simulation of storm water interaction between sewer system and overland flows.” J. Chin. Inst. Eng., 25(2), 171–177.
Kawahara, M., and Umetsu, T. (1986). “Finite-element method for moving boundary problems in river fow.” Int. J. Numer. Methods Fluids, 6(6), 365–386.
Larock, B. E., Jeppson, R. W., and Watters, G. Z. (1999). Hydraulics of Pipeline Systems, CRC Press, New York.
Leandro, J., Chen, A. S., Djordjevic, S., and Savic, D. A. (2009). “Comparison of 1D/2D coupled (sewer/surface) hydraulic models for urban flood simulation.” J. Hydraul. Eng., 135(6), 495–504.
León, A. S., Ghidaoui, M. S., Schmidt, A. R., and García, M. H. (2006). “Godunov-type solutions for transient flows in sewers.” J. Hydraul. Eng., 132(8), 800–813.
León, A. S., Liu, X., Ghidaoui, M. S., Schmidt, A. R., and García, M. H. (2010). “Junction and drop-shaft boundary conditions for modeling free-surface, pressurized, and mixed free-surface pressurized transient flows.” J. Hydraul. Eng., 136(10), 705–715.
LeVeque, R. J. (1997). “Wave propagation algorithms for multidimensional hyperbolic systems.” J. Comput. Phys., 131(2), 327–353.
LeVeque, R. J. (1998). “Balancing source terms and flux gradients in high-resolution Godunov methods: The quasi-steady wave-propagation algorithm.” J. Comput. Phys., 146(1), 346–365.
LeVeque, R. J. (2002). Finite volume methods for hyperbolic problems, Cambridge Univ. Press, Cambridge, UK.
Liang, Q. H., and Borthwick, A. G. L. (2009). “Adaptive quadtree simulation of shallow flows with wet-dry fronts over complex topography.” Comput. Fluids, 38(2), 221–234.
Liang, Q. H., and Marche, F. (2009). “Numerical resolution of well-balanced shallow water equations with complex source terms.” Adv. Water Resour., 32(6), 873–884.
Mahdizadeh, H. (2010). “Modelling of flood waves based on wave propagation algorithms with bed efflux and influx including a coupled pipe network solver.” Ph.D. thesis, Univ. of Manchester, Manchester, UK.
Mahdizadeh, H., Stansby, P. K., and Rogers, B. D. (2011). “On the approximation of local efflux/influx bed discharge in the shallow water equations based on a wave propagation algorithm.” Int. J. Numer. Methods Fluids, 66(10), 1295–1314.
MWH Soft Website. (2010). “InfoWwaorks Cs technical review.” 〈www.mwhsoft.com〉.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (1992). Numerical recipes in Fortran 77, Second Ed., Cambridge University Press.
Rogers, B. D., Alistair, A. G., and Taylor, P. H. (2003). “Mathematical balancing of flux gradient and source terms prior to using Roe’s approximate Riemann solver.” J. Comput. Phys., 192, 422–451.
Rossman, L. A., Dickinson, R. E., Schade, T., Chan, C., Burgess, E. H., and Huber, W. C. (2005). “The US EPA’s newest tool for urban drainage analysis.” Proc., 10th International Conf. on Urban Drainage, Technical University of Denmark, Copenhagen, Denamark.
Swamee, P. K., and Jain, A. K. (1976). “Explicit equations for pipe-flow problems.” J. Hydraul. Div., 102(5), 657–664.
Toro, E. F. (1997). Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer, Tokyo.
Toro, E. F. (2001). Shock Capturing Methods for Free Surface Shallow Flows, Wiley, UK.
Vázquez-Cendón, M. E. (1999). “Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry.” J. Comput. Phys., 148, 497–526.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 138 • Issue 3 • March 2012
Pages: 247 - 259
Copyright
© 2012 American Society of Civil Engineers.
History
Received: Oct 21, 2010
Accepted: Sep 26, 2011
Published online: Sep 28, 2011
Published in print: Mar 1, 2012
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.