Skip to main content
SpringerLink
Log in

1-D coupled non-equilibrium sediment transport modeling for unsteady flows in the discontinuous Galerkin framework

  • Published:
Journal of Hydrodynamics Aims and scope Submit manuscript

Abstract

A high-resolution, 1-D numerical model has been developed in the discontinuous Galerkin framework to simulate 1-D flow behavior, sediment transport, and morphological evaluation under unsteady flow conditions. The flow and sediment concentration variables are computed based on the one-dimensional shallow water flow equations, while empirical equations are used for entrainment and deposition processes. The sediment transport model includes the bed load and suspended load components. New formulations for Harten-Lax-van Leer (HLL) and Harten-Lax-van Contact (HLLC) are presented for shallow water flow equations that include the bed load and suspended load fluxes. The computational results for the flow and morphological changes after two dam break events are compared with the physical model tests. Results show that the modified HLL and HLLC formulations are robust and can accurately predict morphological changes in highly unsteady flows.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. GRAHAM W. J., MAJOR U. S. dam failures: Their cause, resultant losses, and impact on dam safety programs and engineering practice[C]. Great River History Symposium at World Environmental and Water Resources Congress. Kansas City, Missouri, USA, 2009.

    Google Scholar 

  2. COZZOLINO L., MORTE R. D. and GIUDICE G. D. et al. A well-balanced spectral volume scheme with the wetting-drying property for the shallow-water equations[J]. Journal of Hydroinformatics, 2012, 14(3): 745–760.

    Article  Google Scholar 

  3. DÜBEN P. D., KORN P. and AIZINGER V. A discontinuous/continuous low order finite element shallow water model on the sphere[J]. Journal of Computational Physics, 2012, 231(6): 2396–2413.

    Article  MathSciNet  Google Scholar 

  4. KHAN A. A., BARKDOLL B. Two-dimensional depthaveraged models for flow simulation in river bends[J]. International Journal of computational Engineering Science, 2001, 2(3): 453–467.

    Article  Google Scholar 

  5. WU W., WANG S. S. One-dimensional modeling of dambreak flow over movable beds[J]. Journal of Hydraulic Engineering, ASCE, 2007, 133(1): 48–58.

    Article  Google Scholar 

  6. CAO Z., LI Z. and PENDER G. et al. Non-capacity or capacity model for fluvial sediment transport[J]. Proceedings of the ICE-Water Management, 2012, 165(4): 193–211.

    Google Scholar 

  7. WU W., VIEIRA D. and WANG S. One-dimensional numerical model for nonuniform sediment transport under unsteady flows in channel networks[J]. Journal of Hydraulic Engineering, ASCE, 2004, 130(9): 914–923.

    Article  Google Scholar 

  8. FRACCAROLLO L., CAPART H. Riemann wave description of erosional dam-break flows[J]. Journal of Fluid Mechanics, 2002, 461: 183–228.

    Article  MathSciNet  Google Scholar 

  9. CAO Z., PENDER G. and WALLIS S. et al. Computational dam-break hydraulics over erodible sediment bed[J]. Journal of Hydraulic Engineering, ASCE, 2004, 130(7): 689–703.

    Article  Google Scholar 

  10. SIMPSON G., CASTELLTORT S. Coupled model of surface water flow, sediment transport and morphological evolution[J]. Computers and Geosciences, 2006, 32(10): 1600–1614.

    Article  Google Scholar 

  11. YING X., KHAN A. A. and WANG S. S. Y. An upwind method for one-dimensional dam break flows[C]. Proceedings of XXX IAHR Congress. Thessaloniki, Greece, 2003.

    Google Scholar 

  12. YING X., KHAN A. A. and WANG S. S. Y. Upwind conservative scheme for the Saint Venant equations[J]. Journal of Hydraulic Engineering, ASCE, 2004, 130(10): 977–987.

    Article  Google Scholar 

  13. ABDERREZZAK K. E., PAQUIER A. One-dimensional numerical modeling of sediment transport and bed deformation in open channels[J]. Water Resources Research, 2009, 45(5): 641–648.

    Google Scholar 

  14. WU W. Computational river dynamics[M]. Abingdon, UK: CRC Press, Taylor and Francis Group, 2007.

    Book  Google Scholar 

  15. CUI Y., PAOLA C. and PARKER G. Numerical simulation of aggradation and downstream fining[J]. Journal of Hydraulic Research, 1996, 34(2): 185–204.

    Article  Google Scholar 

  16. GOUTI ÈRE L., SOARES-FRAZÃO S. and SAVARY C. et al. One-dimensional model for transient flows involving bed-load sediment transport and changes in flow regimes[J]. Journal of Hydraulic Engineering, ASCE, 2008, 134(6): 726–735.

    Article  Google Scholar 

  17. ZHANG S. Numerical study of sediment transport under unsteady flow[D]. Doctoral Thesis, Tucson, USA: The University of Arizona, 2011.

    Google Scholar 

  18. Van RIJN L. Sediment transport, Part II: Suspended load transport[J]. Journal of Hydraulic Engineering, ASCE, 1984, 110(11): 1613–1641.

    Article  Google Scholar 

  19. ZYSERMAN J., FREDSØE J. Data analysis of bed concentration of suspended sediment[J]. Journal of Hydraulic Engineering, ASCE, 1994, 120(9): 1021–1042.

    Article  Google Scholar 

  20. WU W., WANG S. Formulas for sediment porosity and settling velocity[J]. Journal of Hydraulic Engineering, ASCE, 2006, 132(8): 858–862.

    Article  Google Scholar 

  21. ZHOU J. G., CAUSON D. M. and MINGHAM C. G. et al. The surface gradient method for the treatment of source terms in the shallow-water equations[J]. Journal of Computational Physics, 2001, 168(1): 1–25.

    Article  MathSciNet  Google Scholar 

  22. LAI W., KHAN A. A. Discontinuous Galerkin method for 1-D shallow water flow in nonrectangular and nonprismatic channels[J]. Journal of Hydraulic Engineering, ASCE, 2012, 138(3): 285–296.

    Article  Google Scholar 

  23. LAI W., KHAN A. A. A discontinuous Galerkin method for two-dimensional shallow water flows[J]. International Journal of Numerical Methods in Fluids, 2012, 70(8): 939–960.

    Article  MathSciNet  Google Scholar 

  24. LAI Wencong, KHAN Abdul A. Modeling dam-break flood over natural rivers using discontinuous Galerkin method[J]. Journal of Hydrodynamics, 2012, 24(4): 467–478.

    Article  Google Scholar 

  25. LAI W., KHAN A. A. Discontinuous Galerkin method for 1D shallow water flows in natural rivers[J]. Engineering Applications of Computational Fluid Mechanics, 2012, 6(1): 74–86.

    Article  Google Scholar 

  26. HARTEN A., LAX P. and Van LEER B. On upstream differencing and Godunov type methods for hyperbolic conservation laws[J]. SIAM Review, 1983, 25(1): 35–61.

    Article  MathSciNet  Google Scholar 

  27. TORO E. F. Riemann solvers and numerical methods for fluid dynamics: A practical introduction[M]. Dordrecht, The Netherlands: Springer Science+ Business Media, 2009.

    Book  Google Scholar 

  28. MALEKI Farzam Safarzadeh, KHAN Abdul A. Effect of channel shape on selection of time marching scheme in the discontinuous galerkin method for 1-D open channel flow[J]. Journal of Hydrodynamics, 2015, 27(3): 413–426.

    Article  Google Scholar 

  29. KHAN A. A., LAI W. Modeling shallow water flows using the discontinuous Galerkin method[M]. Abingdon, UK: CRCPress, Taylor and Francis Group, 2014.

    Book  Google Scholar 

  30. CAPART H., YOUNG D. L. Formation of a jump by the dam-break wave over a granular bed[J]. Journal of Fluid Mechanics, 1998, 372: 165–187.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Engineering Department, Massachusetts Maritime Academy, Buzzards Bay, MA, 02532, USA

    Farzam Safarzadeh Maleki

  2. Glenn Department of Civil Engineering, Clemson University, Clemson, SC, 29634, USA

    Abdul A. Khan

Authors
  1. Farzam Safarzadeh Maleki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abdul A. Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abdul A. Khan.

Additional information

Biography: Farzam Safarzadeh MALEKI (1983-), Male, Ph. D., Assistant Professor

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Maleki, F.S., Khan, A.A. 1-D coupled non-equilibrium sediment transport modeling for unsteady flows in the discontinuous Galerkin framework. J Hydrodyn 28, 534–543 (2016). https://doi.org/10.1016/S1001-6058(16)60658-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1016/S1001-6058(16)60658-3

Key words

Search

Navigation