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Pointwise and Upwind Discretizations of Source Terms in Open-Channel Flood Routing

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Abstract

Upwind algorithms are becoming progressively popular for river flood routing due to their capability of resolving trans-critical flow regimes. For consistency, these algorithms suggest natural upwind discretization of the source term, which may be essential for natural channels with irregular geometry. Yet applications of these upwind algorithms to natural river flows are rare, and in such applications the traditional and simpler pointwise, rather than upwind discretization of the source term is used. Within the framework of a first-order upwind algorithm, this paper presents a comparison of upwind and pointwise discretizations of the source term. Numerical simulations were carried out for a selected irregular channel comprising a pool-riffle sequence in the River Lune, England with observed data. It is shown that the impact of pointwise discretization, compared to the upwind, is appreciable mainly in flow zones with the Froude number closer to or larger than unity. The discrepancy due to pointwise and upwind discretizations of the source term is negligible in flow depth and hence in water surface elevation, but well manifested in mean velocity and derived flow quantities. Also the occurrence of flow reversal and equalisation over the pool-riffle sequence in response to increasing discharges is demonstrated.

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Authors and Affiliations

  1. College of Information Management, Wuhan University, Wuhan, 430072, China

    Jian Meng

  2. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan, 430072, China

    Zhi-xian Cao

  3. School of Geography, University of Southampton, Highfield, SO17 1BJ, UK

    Paul A. Carling

Authors
  1. Jian Meng
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  2. Zhi-xian Cao
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  3. Paul A. Carling
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Corresponding author

Correspondence to Zhi-xian Cao.

Additional information

Project supported by the Open Research Fund of the State Key Laboratory of Water Resources and Hydropower Engineering Science, and the National Natural Science Foundation of China (Grant No: 50459001).

Biography: MENG Jian (1967 -), Female, Master, Associate Professor

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Meng, J., Cao, Zx. & Carling, P.A. Pointwise and Upwind Discretizations of Source Terms in Open-Channel Flood Routing. J Hydrodyn 18, 379–386 (2006). https://doi.org/10.1016/S1001-6058(06)60108-X

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  • DOI: https://doi.org/10.1016/S1001-6058(06)60108-X

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