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Shallow Water Flows in Channels

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Abstract

We consider the shallow water equations for flows through channels with arbitrary cross section. The system forms a hyperbolic set of balance laws. Exact steady-state solutions are available and are controlled by the relation between the bottom topography and the channel geometry. We use a Roe-type upwind scheme for the system. Considerations of conservation, near steady-state accuracy, velocity regularization and positivity near dry states are discussed. Numerical solutions are presented illustrating the merits of the scheme for a variety of flows and demonstrating the effect of the interplay between the topography and the geometry on the solution.

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Authors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109-1043, USA

    Gerardo Hernández-Dueñas & Smadar Karni

Authors
  1. Gerardo Hernández-Dueñas
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  2. Smadar Karni
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Correspondence to Smadar Karni.

Additional information

Work supported in part by NSF, award number DMS 0609766, and by Conacyt #160147.

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Hernández-Dueñas, G., Karni, S. Shallow Water Flows in Channels. J Sci Comput 48, 190–208 (2011). https://doi.org/10.1007/s10915-010-9430-x

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  • DOI: https://doi.org/10.1007/s10915-010-9430-x

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