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Lax-Wendroff and McCormack Schemes for Numerical Simulation of Unsteady Gradually and Rapidly Varied Open Channel Flow

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EN
Abstrakty
EN
Two explicit schemes of the finite difference method are presented and analyzed in the paper. The applicability of the Lax-Wendroff and McCormack schemes for modeling unsteady rapidly and gradually varied open channel flow is investigated. For simulation of the transcritical flow the original and improved McCormack scheme is used. The schemes are used for numerical solution of one dimensional Saint-Venant equations describing free surface water flow. Two numerical simulations of flow with different hydraulic characteristics were performed – the first one for the extreme flow of the dam-break type and the second one for the simplified flood wave propagation problem. The computational results are compared to each other and to arbitrary solutions.
Twórcy
  • University of Technology, Faculty of Civil and Environmental Engineering, ul. Narutowicza 11/12, 80–233
  • University of Technology, Faculty of Civil and Environmental Engineering, ul. Narutowicza 11/12, 80–233
Bibliografia
  • Cunge J. A., Holly Jr F. M. and Verwey A. (1980) Practical Aspects of Computational River Hydraulics, Pitman, London.
  • Garcia-Navarro P., Alcrudo F. and Saviron J. M. (1992) 1-D open-channel flow simulation using TVD-McCormack scheme, Journal of Hydraulic Engineering, 118 (10), 1359–1372.
  • LeVeque R. J. (2002) Finite volume method for hyperbolic problems, Cambridge University Press, New York.
  • McCormack R.W. (1971) Numerical solution of the interaction of a shock wave with a laminar boundary layer, Proc. 2nd Int. Conf. on Numerical Methods in Fluid Dynamics, Springer-Verlag, Berlin, 151–163.
  • Potter D. (1973) Computational Physics, Wiley and Sons, London.
  • Roe P. L. (1981) Approximate Riemann solvers, parameters vectors and difference schemes, Journal of Computational Physics, 43, 357–372.
  • Stoker J. J. (1957) Water Waves, Interscience Publishers, Wiley, New York.
  • Szymkiewicz R. (1995) Method to solve 1D unsteady transport and flowequations, Journal of Hydraulic Engineering, 121 (5), 396–403.
  • Szymkiewicz R. (2010) Numerical Modeling in Open Channel Hydraulics, Springer, London, New York.
  • Toro E. F. (1997) Riemann solvers and numerical methods for fluid dynamics, Springer-Verlag, Berlin.
  • Tseng M. H. (2003) The improved surface gradient method for flows simulation in variable bed topography channel using TVD-McCormack scheme, International Journal for Numerical Methods in Fluids, 43, 71–91.
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Bibliografia
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bwmeta1.element.baztech-a108ffb0-a23f-460f-8216-ab18984efd8e
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