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139 Numerical Modeling of Unsteady Flows in Rivers

Part 12. Open-Channel Flow

  1. Bommanna G Krishnappan1,
  2. Mustafa S Altinakar2

Published Online: 15 APR 2006

DOI: 10.1002/0470848944.hsa146

Encyclopedia of Hydrological Sciences

Encyclopedia of Hydrological Sciences

How to Cite

Krishnappan, B. G. and Altinakar, M. S. 2006. Numerical Modeling of Unsteady Flows in Rivers. Encyclopedia of Hydrological Sciences. 12:139.

Author Information

  1. 1

    Environment Canada, Canada Centre for Inland Waters, Aquatic Ecosystem Impacts Research Branch, National Water Research Institute, Burlington, ON, Canada

  2. 2

    National Center for Computational Hydroscience and Engineering, The University of Mississippi, MS, US

Publication History

  1. Published Online: 15 APR 2006


Solution methods to solve the unsteady flow equations are reviewed in this article. The basis of the method of characteristics is outlined. Some of the commonly used finite difference schemes are reviewed. A detailed description of an unsteady flow model called MOBED is given to highlight the various assumptions and simplifications that are involved in the development of an unsteady flow model. Testing of the model using a laboratory data set measured by Treske is described. Such a data set can serve as a benchmark data for the testing of unsteady flow models. Integral form of governing equations and their properties are introduced. High-resolution conservative finite-volume schemes for modeling flows with discontinuities are briefly discussed. Examples of numerical solutions using a robust one-dimensional upwind finite-volume code are presented.


  • conservative equations;
  • discontinuous solutions;
  • equations of Saint Venant;
  • explicit methods;
  • implicit methods;
  • method of characteristics;
  • open-channel flow;
  • unsteady flow;
  • TVD schemes;
  • unsteady flow;
  • upwind schemes