One-Dimensional Riemann Solver Involving Variable Horizontal Density to Compute Unsteady Sediment Transport
Publication: Journal of Hydraulic Engineering
Volume 142, Issue 3
Abstract
Intense transient shallow flows over erodible bed imply the appearance of a changing horizontal density attributable to the presence of sediment particles in the water layer. The lack of consideration of the variability of the bulking density of the mixture is not admissible when modeling severe types of erosional flow such as the release of a dam break wave over a sedimentary bottom. Such events can lead to significant changes in the wave hydrodynamics, since the inertia of the flow can be larger and consequently its erosion/deposition capacity can be altered. From a numerical point of view a new complex erosion/deposition source term appears. For the integration of these source terms two strategies have been explored in this work: upwind and pointwise. Hence, this work is focused on the development and validation of a novel numerical scheme based on an approximate augmented Riemann solver, where the erosion/deposition rates play an important role in the variation of mixture density. Several analytical test cases have been derived in order to validate the computational tool. The numerical predictions have also been compared against experimental data.
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Acknowledgments
This work has been partially funded by the Spanish Ministry of Science and Technology under research projects CGL2011-28590.
References
Armanini, A., and Di Silvio, G. (1988). “A one-dimensional model for the transport of a sediment mixture in non-equilibrium conditions.” J. Hydraul. Res., 26(3), 275–292.
Armanini, A., and Fraccarollo, L. (1997). “Critical conditions for debris flows.” Proc., 1st Int. Conf. on Debris-Flow Hazards Mitigation, D. Rickenmann, and G. F. Wieczorek, eds., Mill Press, Rotterdam, Netherlands, 434–443.
Begnudelli, L., Valiani, A., and Sanders, B. F. (2010). “A balanced treatment of secondary currents, turbulence and dispersion in a depth-integrated hydrodynamic and bed deformation model for channel bends.” Adv. Water Resour., 33(1), 17–33.
Canelas, R., Murillo, J., and Ferreira, R. (2013). “Two-dimensional depth-averaged modelling of dam-break flows over mobile beds.” J. Hydraul. Res., 51(4), 392–407.
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., and Carling, P. (2006). “Shallow water hydrodynamic models for hyperconcentrated sediment-laden flows over erodible bed.” Adv. Water Resour., 29(4), 546–557.
Capart, H., and Young, D. (1998). “Formation of a jump by the dam-break wave over a granular bed.” J. Fluid Mech., 372, 165–187.
Castro Diaz, M., Fernandez Nieto, E., and Ferreiro, A. (2008). “Sediment transport models in shallow water equations and numerical approach by high order finite volume methods.” J. Comput. Fluids, 37(3), 299–316.
De Vries, M., Klaassen, G., and Struiksma, N. (1990). “On the use of movable-bed models for river problems: A state of the art.” Int. J. Sediment Res., 5(1), 183–228.
Fraccarollo, L., and Capart, H. (2002). “Riemann wave description of erosional dam-break flows.” J. Fluid Mech., 461, 115–133.
Fraccarollo, L., Capart, H., and Zech, Y. (2003). “A Godunov method for the computation of erosional shallow water transients.” Int. J. Numer. Methods Fluids, 41(9), 951–976.
Garegnani, G., Rosatti, G., and Bonaventura, L. (2013). “On the range of validity of the Exner-based models for mobile-bed river flow simulations.” J. Hydraul. Res., 51(4), 380–391.
Godunov, S. (1959). “A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics.” Matematicheskii Sbornik, 47, 271–306.
Grass, A. (1981). “Sediments transport by waves and currents.”, SERC London Cent. Mar. Technol, FL.
Harten, A., and Hyman, J. M. (1983). “Self adjusting grid methods for one-dimensional hyperbolic conservation laws.” J. Comput. Phys., 50(2), 235–269.
Hudson, J., and Sweby, P. K. (2005). “A high-resolution scheme for the equations governing 2D bed-load sediment transport.” Int. J. Numer. Methods Fluids, 47(10–11), 1085–1091.
Jiang, L., Borthwick, A. G. L., Kramer, T., and Jozsa, J. (2011). “Variable density bore interactions with block obstacles.” Int. J. Comput. Fluid Dyn., 25(4), 223–237.
Juez, C., Murillo, J., and Garca-Navarro, P. (2013). “2D simulation of granular flow over irregular steep slopes using global and local coordinates.” J. Comput. Phys., 255(4), 166–204.
Juez, C., Murillo, J., and Garca-Navarro, P. (2014). “A 2D weakly-coupled and efficient numerical model for transient shallow flow and movable bed.” Adv. Water Resour., 71, 93–109.
Kalinske, A. (1947). “Movement of sediment as bed load in rivers.” Trans. AGU, 28(4), 615–620.
Lai, C. (1991). “Modelling alluvial channel flow by multimode characteristic method.” J. Eng. Mech., 117(1), 32–53.
Leighton, F. Z., Borthwick, A. G. L., and Taylor, P. H. (2010). “1D numerical modeling of shallow flows with variable horizontal density.” Int. J. Numer. Methods Fluids, 62(11), 1209–1231.
Leveque, R. (2002). Finite volume methods for hyperbolic problems, Cambridge University Press, New York.
Liu, X., Landry, B., and Garca, M. (2008). “Two-dimensional scour simulations based on coupled model of shallow water equations and sediment transport on unstructured meshes.” Coastal Eng., 55(10), 800–810.
Meyer-Peter, E., and Müller, R. (1948). “Formulae for bed-load transport.” Proc., 2nd Meeting Int. Association Hydraulic Structure Research, Delft, Netherlands.
Murillo, J., and Garca-Navarro, P. (2010a). “An Exner-based coupled model for two-dimensional transient flow over erodible bed.” J. Comput. Phys., 229(23), 8704–8732.
Murillo, J., and Garca-Navarro, P. (2010b). “Weak solutions for partial differential equations with source terms: Application to the shallow water equations.” J. Comput. Phys., 229(11), 4327–4368.
Murillo, J., and Garca-Navarro, P. (2011). “Improved Riemann solvers for complex transport in two-dimensional unsteady shallow flow.” J. Comput. Phys., 230(19), 7202–7239.
Murillo, J., Latorre, B., and Garca-Navarro, P. (2012). “A Riemann solver for unsteady computation of 2D shallow flows with variable density.” J. Comput. Phys., 231(4), 1963–2001.
Palumbo, A., Soares-Frazao, S., Goutiere, L., Pianese, D., and Zech, Y. (2008). “Dam-break flow on mobile bed in a channel with a sudden enlargement.” Proc., River Flow 2008 Int. Conf. on Fluvial Hydraulics, Taylor & Francis Group, London.
Rosatti, G., Murillo, J., and Fraccarollo, L. (2007). “Generalized Roe schemes for 1D two-phase, free-surface flows over a mobile bed.” J. Comput. Phys., 54(24), 543–590.
Siviglia, A., Stecca, G., Vanzo, D., Zolezzi, G., Toro, E., and Tubino, M. (2013). “Numerical modelling of two-dimensional morphodynamics with applications to river bars and bifurcations.” Adv. Water Resour., 52, 243–260.
Smart, G. (1984). “Sediment transport formula for steep channels.” J. Hydraul. Eng., 267–276.
Soares-Frazao, S., and Zech, Y. (2010). “HLLC scheme with novel wave-speed estimators appropriate for two-dimensional shallow-water flow on erodible bed.” Int. J. Numer. Methods Fluids, 66(8), 1019–1036.
Spinewine, B., and Zech, Y. (2007). “Small-scale laboratory dam-break waves on movable beds.” J. Hydraul. Res., 45, 73–86.
Toro, E. (1994). “Restoration of the contact surface in the HLL Riemann solver.” Shock Waves, 4(1), 25–34.
Wu, W. (2004). “Depth-averaged two-dimensional numerical modeling of unsteady flow and nonuniform sediment transport in open channels.” J. Hydraul. Eng., 1013–1024.
Wu, W. (2007). Computational river dynamics, CRC Press, London.
Wu, W., and Wang, S. (2007). “One-dimensional modeling of Dam-break flow over movable beds.” J. Hydraul. Eng., 48–58.
Wu, W., and Wang, S. (2008). “One-dimensional explicit finite-volume model for sediment transport with transient flows over movable beds.” J. Hydraul. Res., 46(1), 87–98.
Xia, J., Lin, B., Falconer, R., and Wang, G. (2010). “Modelling dam-break flows over mobile beds using a 2D coupled approach.” Adv. Water Resour., 33(2), 171–183.
Zhang, S., Duan, J. G., and Strelkoff, T. S. (2013). “Grain-scale nonequilibrium sediment transport model for unsteady flow.” J. Hydraul. Eng., 22–36.
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Published In
Journal of Hydraulic Engineering
Volume 142 • Issue 3 • March 2016
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Jan 29, 2015
Accepted: Jul 20, 2015
Published online: Oct 12, 2015
Published in print: Mar 1, 2016
Discussion open until: Mar 12, 2016
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