18.06.2020

DEFENCE Redchyts

Redchyts D.O. "UNSTEADY COUPLED PROBLEMS OF THE DYNAMICS OF A LIQUID, GAS, AND LOW-TEMPERATURE PLASMA" (Doct. Phys.-Math. Sci.)

HYDRODYNAMICS AND ACOUSTICS

2018 ◊ Volume 1 (91) ◊ Issue 2 p. 132-159

I. M. Gorban*

* Institute of Hydromechanics of NAS of Ukraine, Kyiv, Ukraine

Modeling of sandpit dynamics in river flows

Gidrodin. akust. 2018, 1(2):132-159

https://doi.org/10.15407/jha2018.02.132

TEXT LANGUAGE: Ukrainian

ABSTRACT

A two-dimensional numerical method for simulating of coupled evolution of the water flow and the bed in open reservoirs is developed considering the mutual influence of the morphological processes. It combines the Kurganov-Noelle-Petrova central upwind scheme for integration of shallow water equations and the fifth-order Weighted Essentially Non-Oscillatory (WENO) Scheme to describe the evolution of bed surface. The bedload sediment transport rate is estimated by power-law Grass formula. Simulation of the test problem on erosion of a conical sand dune in a water flow revealed the longterm stability of the obtained solution, as well as its relevance to the data presented by other researchers. The method was used to calculate the evolution of deep sand quarries on the river bed. The obtained results demonstrate formation of a compound relief form on the bed when the localized hollow is transformed into the system of pits and small mounds moving with the flow. At the same time, the deepening expands across the flow that leads to the formation of extended erosion zones on the river bottom. The angle of spread characterizing the evolution of the quarry is found to depend on the initial quarry depth and water flow parameters and ranges from 20° to 35°. The obtained estimates of "survivability" of sand quarries indicate the nonlinear dependence of both the intensity of their filling and motion velocity on the flow parameters. Simulation of free surface evolution revealed an intense wave front generation over the unevenness of the bottom. The shape of this front changes in accordance with the processes occurring at the riverbed. The obtained estimates may be used when organizing the activities to prevent the negative technological and natural phenomena in river water areas initiated by interaction of large-scale bed roughness with hydraulic structures and banks.

KEY WORDS

morphological process, bed surface, sediment transport, sand quarry, angle of spread

REFERENCES

  1. W. Wu, Computational river dynamics. London: Taylor and Francis, 2008.
  2. M. J. Castro-Diaz, E. D. Fernandez-Nieto, and A. M. Ferreiro, “Sediment transport models in shallow water equations and numerical approach by high order finite volume methods”, Computers & Fluids, vol. 37, pp. 299–316, 2008. https://doi.org/10.1016/j.compfluid.2007.07.017.
  3. I. M. Gorban, “Numerical simulation of evolution of large-scale irregularities on a river bottom”, Ukrainian, Applied Hydromechanics, vol. 17(89), no. 1, pp. 21–36, 2015.
  4. J. Hudson and P. K. Sweby, “Formulations for numerically approximating hyperbolic systems governing sediment transport”, Journal of Scientific Computing, vol. 19, pp. 225–252, 2003.
  5. L. Goutiere, S. Soares-Frazao, C. Savary, T. Laraichi, and Y. Zech, “One-dimensional model for transient flows involving bed-load sediment transport and changes in flow regimes”, Journal of Hydraulic Engineering, vol. 134, no. 6, pp. 726–735, 2008. https://doi.org/10.1061/(asce)0733-9429(2008)134:6(726).
  6. E. Kubatko, J. Westerink, and C. Dawson, “An unstructured grid morphodynamic model with a discontinuous Galerkin method for bed evolution”, Ocean Modelling, vol. 15, pp. 71–89, 2006. https://doi.org/10.1016/j.ocemod.2005.05.005.
  7. W. Long, J. T. Kirby, and Z. Shao, “A numerical scheme for morphological bed level calculations”, Coastal Engineering, vol. 55, pp. 167–180, 2008. https://doi.org/10.1016/j.coastaleng.2007.09.009.
  8. G. I. Suhomel, A study of hydraulics of open channels and structures. Kiev: Naukova Dumka, 1965.
  9. X.-D. Liu, S. Osher, and T. Chan, “Weighted essentially non-oscillatory schemes”, Journal of Computational Physics, vol. 115, pp. 200–211, 1994. https://doi.org/10.1006/jcph.1994.1187.
  10. A. Kurganov, S. Noelle, and S. Petrova, “Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton—Jacobi equations”, SIAM Journal on Scientific Computing, vol. 23, no. 3, pp. 707–740, 2001. https://doi.org/10.1137/s1064827500373413.
  11. A. Kurganov and C.-T. Lin, “On the reduction of numerical dissipation in central-upwind schemes”, Communications in Computational Physics, vol. 2, no. 1, pp. 141–163, 2007.
  12. S. Gottlieb, C. W. Shu, and E. Tadmor, “Strong stability-preserving high order time discretization methods”, SIAM Review, vol. 43, pp. 89–112, 2001. https://doi.org/10.1137/s003614450036757x.
  13. J. Hudson and P. K. Sweby, “A high-resolution scheme for the equations governing 2D bed-load sediment transport”, International Journal for Numerical Methods in Fluids, vol. 47, pp. 1085–1091, 2005. https://doi.org/10.1002/fld.853.
  14. F. Benkhaldoun, S. Sahmim, and M. Seaid, “A two-dimensional finite volume morphodynamic model on unstructured triangular grids”, International Journal for Numerical Methods in Fluids, vol. 63, pp. 1296–1327, 2010.
  15. A. Kurganov and E. Tadmor, “New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations”, Journal of Computational Physics, vol. 160, pp. 241–282, 2000. https://doi.org/10.1006/jcph.2000.6459.
  16. V. O. Gorban and I. M. Gorban, “Numerical models of non-stationary river processes”, Applied Hydromechanics, vol. 15(87), no. 4, pp. 19–39, 2013.
  17. H. C. Yee, “Construction of explicit and implicit symmetric TVD schemes and their applications”, Journal of Computational Physics, vol. 68, pp. 151–179, 1987. https://doi.org/10.1016/0021-9991(87)90049-0.
  18. A. Kurganov and D. Levy, “Central-upwind schemes for the Saint-Venant system”, ESAIM: Mathematical Modelling and Numerical Analysis, vol. 36, pp. 397–425, 2002. https://doi.org/10.1051/m2an:2002019.
  19. H. K. Johnson and J. A. Zyserman, “Controlling spatial oscillations in bed level update schemes”, Coastal Engineering, vol. 46, pp. 109–126, 2002. https://doi.org/10.1016/s0378-3839(02)00054-6.
  20. J. H. Jensen, E. O. Madsen, and J. Fredsoe, “Oblique flow over dredged channels: II. Sediment transport and morphology”, Journal of Hydraulic Engineering, vol. 125, no. 11, pp. 1190–1198, 1999. https://doi.org/10.1061/(asce)0733-9429(1999)125:11(1190).
  21. A. Hurten, “High resolution schemes for hyperbolic conservation laws”, Journal of Computational Physics, vol. 49, pp. 357–365, 1983.
  22. R. J. LeVeque, “Balancing source terms and flux gradients in high-resolution Godunov methods: The quasi-steady wave-propagation algorithm”, Journal of Computational Physics, vol. 146, pp. 346–356, 1998. https://doi.org/10.1006/jcph.1998.6058.
  23. Y. Hing and C.-W. Shu, “High order finite difference WENO schemes with the exact conservation property for the shallow water equations”, Journal of Computational Physics, vol. 208, pp. 206–227, 2005. https://doi.org/10.1016/j.jcp.2005.02.006.
  24. J. Hudson, “Numerical techniques for morphodynamic modelling”, PhD thesis, University of Reading, 2001.