IDEAS home Printed from https://ideas.repec.org/a/spr/waterr/v30y2016i4d10.1007_s11269-016-1234-9.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11269-016-1234-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11269-016-1234-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alibek Issakhov & Medina Imanberdiyeva, 2020. "Numerical Simulation of the Water Surface Movement with Macroscopic Particles of Dam Break Flow for Various Obstacles," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(9), pages 2625-2640, July.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Francesco Macchione & Gianluca De Lorenzo & Pierfranco Costabile & Babak Razdar, 2016. "The Power Function for Representing the Reservoir Rating Curve: Morphological Meaning and Suitability for Dam Breach Modelling," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(13), pages 4861-4881, October.
    3. 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.
    4. Ting Zhang & Ping Feng & Čedo Maksimović & Paul Bates, 2016. "Application of a Three-Dimensional Unstructured-Mesh Finite-Element Flooding Model and Comparison with Two-Dimensional Approaches," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(2), pages 823-841, January.
    5. Ting Zhang & Ping Feng & Čedo Maksimović & Paul D. Bates, 2016. "Application of a Three-Dimensional Unstructured-Mesh Finite-Element Flooding Model and Comparison with Two-Dimensional Approaches," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(2), pages 823-841, January.
    6. Ismail Haltas & Sebnem Elçi & Gokmen Tayfur, 2016. "Numerical Simulation of Flood Wave Propagation in Two-Dimensions in Densely Populated Urban Areas due to Dam Break," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(15), pages 5699-5721, December.
    7. Hriday Mani Kalita, 2020. "A Numerical Model for 1D Bed Morphology Calculations," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(15), pages 4975-4989, December.
    8. Ismail Haltas & Gokmen Tayfur & Sebnem Elci, 2016. "Two-dimensional numerical modeling of flood wave propagation in an urban area due to Ürkmez dam-break, İzmir, Turkey," 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. 81(3), pages 2103-2119, April.
    9. Song-Yue Yang & Shaohua Marko Hsu & Ching Hsiao & Che-Hao Chang, 2023. "Digital elevation models for high-resolution base flood elevation mapping in a densely populated city," 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. 116(2), pages 2693-2716, March.
    10. Shouhong Zhang & Yiping Guo, 2014. "Stormwater Capture Efficiency of Bioretention Systems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(1), pages 149-168, January.
    11. José Pinho & Rui Ferreira & Luís Vieira & Dirk Schwanenberg, 2015. "Comparison Between Two Hydrodynamic Models for Flooding Simulations at River Lima Basin," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(2), pages 431-444, January.
    12. Fahad, Md Golam Rabbani & Nazari, Rouzbeh & Motamedi, M.H. & Karimi, Maryam, 2022. "A Decision-Making Framework Integrating Fluid and Solid Systems to Assess Resilience of Coastal Communities Experiencing Extreme Storm Events," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    13. J. Teng & J. Vaze & D. Dutta & S. Marvanek, 2015. "Rapid Inundation Modelling in Large Floodplains Using LiDAR DEM," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(8), pages 2619-2636, June.
    14. 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.
    15. Santiago Gaitan & Marie-claire ten Veldhuis & Nick Giesen, 2015. "Spatial Distribution of Flood Incidents Along Urban Overland Flow-Paths," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(9), pages 3387-3399, July.
    16. G. Papaioannou & A. Loukas & L. Vasiliades & G. T. Aronica, 2016. "Flood inundation mapping sensitivity to riverine spatial resolution and modelling approach," 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. 83(1), pages 117-132, October.
    17. Xiaoling Wang & Wenlong Chen & Zhengyin Zhou & Yushan Zhu & Cheng Wang & Zhen Liu, 2017. "Three-dimensional flood routing of a dam break based on a high-precision digital model of a dense urban area," 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. 86(3), pages 1147-1174, April.
    18. Pierfranco Costabile & Francesco Macchione & Luigi Natale & Gabriella Petaccia, 2015. "Flood mapping using LIDAR DEM. Limitations of the 1-D modeling highlighted by the 2-D approach," 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. 77(1), pages 181-204, May.
    19. María Bermúdez & Andreas Paul Zischg, 2018. "Sensitivity of flood loss estimates to building representation and flow depth attribution methods in micro-scale flood modelling," 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. 92(3), pages 1633-1648, July.
    20. P. Sreeja & Kapil Gupta, 2008. "Transfer Function Formulation of Saint-Venant’s Equations for Modeling Drainage Channel Flow: An Experimental Evaluation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 22(12), pages 1881-1898, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:waterr:v:30:y:2016:i:4:d:10.1007_s11269-016-1234-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.