IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v190y2021icp1275-1293.html
   My bibliography  Save this article

Well-balanced central schemes for pollutants transport in shallow water equations

Author

Listed:
  • Touma, R.
  • Saleh, M.A.

Abstract

We present a new one-dimensional hybrid second-order accurate well-balanced unstaggered central scheme/particle method (WBUCS-P) for computing the transport of pollutant in water flows. The shallow water equations are employed to model the free-surface water flow, and the transport equation is employed to model pollutant propagation. Our proposed scheme employs the particle method and avoids the resolution of Riemann problems occurring at the boundaries of neighboring cells. Furthermore, the proposed hybrid method is second-order accurate both in space and time; it evolves a piecewise linear numerical solution on a single grid, and benefits from the non-dissipativeness property of the particle method. Our scheme is also well-balanced due to a unique integration of the source term and to the application of the surface gradient method. We implement the proposed scheme and solve some selected problems featuring the transport of pollutants. Accurate pollutant’s location and concentration are observed and reported in the numerical test cases.

Suggested Citation

  • Touma, R. & Saleh, M.A., 2021. "Well-balanced central schemes for pollutants transport in shallow water equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1275-1293.
  • Handle: RePEc:eee:matcom:v:190:y:2021:i:c:p:1275-1293
    DOI: 10.1016/j.matcom.2021.07.021
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475421002718
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2021.07.021?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.

    Citations

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


    Cited by:

    1. Yan, Ruifang & Tong, Wei & Chen, Guoxian, 2023. "An efficient invariant-region-preserving central scheme for hyperbolic conservation laws," Applied Mathematics and Computation, Elsevier, vol. 436(C).

    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:eee:matcom:v:190:y:2021:i:c:p:1275-1293. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.