Fully Coupled Discontinuous Galerkin Modeling of Dam-Break Flows over Movable Bed with Sediment Transport
Publication: Journal of Hydraulic Engineering
Volume 140, Issue 4
Abstract
A one-dimensional (1D) discontinuous Galerkin morphodynamic model has been devised with application to simulate of dam-break flows over erodible beds with suspended sediment transport. The morphodynamic equations adopt the shallow-water equations (SWE) considering the interaction of sediment transport and bed changes on the flow. A local second-order Runge-Kutta discontinuous Galerkin (RKDG2) model has been reformulated to numerically solve the morphodynamic equations in a fully coupled manner and with a noncapacity sediment model. The model’s implementation is thoroughly detailed with focus on the discretization of the complex source terms, the treatment of wetting and drying, and other stabilizing issues pertaining to high-solution gradients and the transient character of the topography. The model has been favorably applied to replicate experimental dam-break flow over erodible sediment beds.
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References
Ali, M., Sterk, G., Seeger, M., Boersema, M., and Peters, P. (2012). “Effect of hydraulic parameters on sediment transport capacity in overland flow over erodible beds.” Hydrol. Earth Syst. Sci., 16(2), 591–601.
Benkhaldoun, F., Sari, S., and Seaid, M. (2012). “A flux-limiter method for dam-break flows over erodible sediment beds.” Appl. Math. Modell., 36(10), 4847–4862.
Bunya, S., Kubatko, E. J., Westerink, J. J., and Dawson, C. (2009). “A wetting and drying treatment for the Runge-Kutta discontinuous Galerkin solution to the shallow water equations.” Comput. Meth. Appl. Mech. Eng., 198(17–20), 1548–1562.
Cao, Z., Day, R., and Egashira, S. (2002). “Coupled and decoupled numerical modeling of flow and morphological evolution in alluvial rivers.” J. Hydraul. Eng., 306–321.
Cao, Z., Pender, G., Wallis, S., and Carling, P. (2004). “Computational dam-break hydraulics over erodible sediment bed.” J. Hydraul. Eng., 689–703.
Cao, Z., Pender, G., and Meng, G. (2006). “Explicit formulation of the shields diagram for incipient motion of sediment.” J. Hydraul. Eng., 1097–1099.
Cao, Z., Li, Z., Pender, G., and Hu, P. (2012). “Non-capacity or capacity model for fluvial sediment transport.” Water Manage., 165(4), 193–211.
Capart, H., and Young, D. L. (1998). “Formation of jump by the dam-break wave over a granular bed.” J. Fluid Mech., 372(1), 165–187.
Cockburn, B., and Shu, C. W. (2001). “Runge-Kutta discontinuous Galerkin methods for convection- dominated problems.” J. Sci. Comput., 16(3), 173–261.
El Kadi Abderrezzak, K., and Paquier, A. (2009). “One-dimensional numerical modeling of sediment transport and bed deformation in open channels.” Water Resour. Res., 45(5), W05404.
El Kadi Abderrezzak, K., and Paquier, A. (2011). “Applicability of sediment transport capacity formulas to dam-break flows over movable beds” J. Hydraul. Eng., 209–221.
Fagherazzi, S., and Sun, T. (2003). “Numerical simulations of transportational cyclic step.” Comput. Geosci., 29(9), 1071–1201.
Formann, E., Habersack, H. M., and Schober, St. (2007). “Morphodynamic river processes and techniques for assessment of channel evolution in Alpine gravel bed rivers.” Geomorphol., 90(3–4), 340–355.
Fraccarollo, L., and Capart, H. (2002). “Riemann wave description of erosional dam-break flows.” J. Fluid Mech., 461, 183–228.
Kesserwani, G. (2013). “Topography discretization techniques for Godunov-type shallow water numerical models: a comparative study.” J. Hydraul. Res., 51(4), 351–367.
Kesserwani, G., and Liang, Q. (2011). “A conservative high-order discontinuous Galerkin method for the shallow water equations with arbitrary topography.” Int. J. Numer. Methods Eng., 86(1), 47–67.
Kesserwani, G., and Liang, Q. (2012a). “Influence of total-variation-diminishing slope limiting on local discontinuous Galerkin solutions of the shallow water equations.” J. Hydraul. Eng., 216–222.
Kesserwani, G., and Liang, Q. (2012b). “Locally limited and fully conserved RKDG2 shallow water solutions with wetting and drying.” J. Sci. Comput., 50(1), 120–144.
Kesserwani, G., Liang, Q., Mosé, R., and Vazquez, J. (2010). “Well balancing issues related to the RKDG2 scheme for the shallow water equations.” Int. J. Numer. Method Fluids, 62(4), 428–448.
Lai, W., and Khan, A. A. (2012). “Discontinuous Galerkin method for 1D shallow water flow in nonrectangular and nonprismatic channels.” J. Hydraul. Eng., 285–296.
Li, S., and Duffy, C. J. (2011). “Fully coupled approach to modeling shallow water flow, sediment transport, and bed evolution in rivers.” Water Resour. Res., 47(3), W03508.
Liang, Q. (2010). “Flood simulation using a well-balanced shallow flow model.” J. Hydraul. Eng., 136(9), 669–675.
Li, W., Vriend, H. J., Wang, Z., and Maren, D. S. (2013). “Morphological modeling using a fully coupled, TVD upwind-biased centered scheme.” Water Resour. Res., 49(6), 3547–3565.
Mirabito, C., Dawson, C., Kubatko, E. J., Westerink, J. J., and Bunya, S. (2011). “Implementation of a discontinuous Galerkin morphological model on two-dimensional unstructured meshes.” Comput. Methods Appl. Mech. Eng., 200(1–4), 189–207.
Pasquale, N., Perona, P., Schneider, P., Shrestha, J., Wombacher, A., and Burlando, P. (2011). “Modern comprehensive approach to monitor the morphodynamic evolution of a restored river corridor.” Hydrol. Earth Syst. Sci., 15(4), 1197–1212.
Tassi, P. A., Rhebergen, S., Vionnet, C. A., and Bokhove, O. (2008). “A discontinuous Galerkin finite element model for river bed evolution under shallow flows.” Comput. Methods Appl. Mech. Eng., 197(33–40), 2930–2947.
Toro, E. F. (2001). Shock-capturing methods for free-surface shallow flows, Wiley, Chichester, U.K.
Toro, E. F., and García-Navarro, P. (2007). “Godunov-type methods for free-surface shallow flows: A review.” J. Hydr. Res., 45(6), 736–751.
Toro, E. F., Spruce, M., and Speares, W. (1994). “Restoration of the contact surface in the HLL-Riemann solver.” Shock Waves, 4(1), 25–34.
Wu, W. (2007). Computational river dynamics, CRC.
Wu, W., Vieira, D. A., and Wang, S. S. Y. (2004). “One-dimensional numerical model for nonuniform sediment transport under unsteady flows in channel networks.” J. Hydraul. Eng., 914–923.
Wu, W., and Wang, S. S. Y. (2007). “One-dimensional modeling of dam-break flow over movable beds.” J. Hydraul. Eng., 48–58.
Xia, J. Q., Lin, B. L., Falconer, R. A., and Wang, G. Q. (2010). “Modelling dam-break flows over mobile beds using a 2D coupled approach.” Adv. Water Resour., 33(2), 171–183.
Xing, Y., Zhang, X., and Shu, C.-W. (2010). “Positivity preserving high-order well-balanced discontinuous Galerkin methods for the shallow water equations.” Adv. Water Resour., 33(12), 1476–1493.
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Published In
Journal of Hydraulic Engineering
Volume 140 • Issue 4 • April 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: May 30, 2013
Accepted: Dec 10, 2013
Published online: Jan 23, 2014
Published in print: Apr 1, 2014
Discussion open until: Jun 23, 2014
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