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

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  • Hriday Kalita

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. Copyright Springer Science+Business Media Dordrecht 2016

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  • Hriday 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:p:1481-1497
    DOI: 10.1007/s11269-016-1234-9
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    1. 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.
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    6. 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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    2. Vasilis Bellos & Ino Papageorgaki & Ioannis Kourtis & Harris Vangelis & Ioannis Kalogiros & George Tsakiris, 2020. "Reconstruction of a flash flood event using a 2D hydrodynamic model under spatial and temporal variability of storm," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 101(3), pages 711-726, April.

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