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A New Total Variation Diminishing Predictor Corrector Approach for Two-Dimensional Shallow Water Flow

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  • Hriday Mani Kalita

    (National Institute of Technology Meghalaya)

Abstract

This paper presents a new efficient and robust hydrodynamic model for simulation of unsteady shallow water flow. The governing equations of shallow water flows in two dimensional forms are solved using a new total variation diminishing (TVD) MacCormack predictor corrector scheme. In this numerical technique an additional TVD term is added after the traditional predictor corrector steps. The advantage of the present TVD term is that it is very simple and gives accurate results at the same time removing the numerical oscillations. Further, application of semi implicit treatment of the friction slope term helps in flow simulation even with very low water depth. Finally the model is used to analyze a wide variety of hydraulic problems including quiescent water above irregular bed, steady flow over irregular bed, steady flow over irregular bed with a shock, dam break flow over dry bed and dam break flow over wet bed. For each of the cases numerical results are compared with available analytical solution and known experimental data. The agreements between the results are satisfactory.

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  • Hriday Mani Kalita, 2016. "A New Total Variation Diminishing Predictor Corrector Approach for Two-Dimensional Shallow Water Flow," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(4), pages 1481-1497, March.
    • Handle: RePEc:spr:waterr:v:30:y:2016:i:4:d:10.1007_s11269-016-1234-9
    DOI: 10.1007/s11269-016-1234-9
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    References listed on IDEAS

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    1. P. Sreeja & Kapil Gupta, 2007. "An alternate approach for transient flow modeling in urban drainage systems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 21(7), pages 1225-1244, July.
    2. Vasilis Bellos & George Tsakiris, 2015. "Comparing Various Methods of Building Representation for 2D Flood Modelling In Built-Up Areas," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(2), pages 379-397, January.
    3. George Tsakiris & Vasilis Bellos, 2014. "A Numerical Model for Two-Dimensional Flood Routing in Complex Terrains," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(5), pages 1277-1291, March.
    4. Pierfranco Costabile & Francesco Macchione, 2012. "Analysis of One-Dimensional Modelling for Flood Routing in Compound Channels," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(5), pages 1065-1087, March.
    5. Joy Sanyal & Alexander Densmore & Patrice Carbonneau, 2014. "2D Finite Element Inundation Modelling in Anabranching Channels with Sparse Data: Examination of Uncertainties," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(8), pages 2351-2366, June.
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    Cited by:

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