IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i14p1604-d590357.html
   My bibliography  Save this article

A Solution of Richards’ Equation by Generalized Finite Differences for Stationary Flow in a Dam

Author

Listed:
  • Carlos Chávez-Negrete

    (Facultad de Ingeniería Civil, Universidad Michoacana de San Nicolás de Hidalgo, Santiago Tapia 403, Morelia 58000, Mexico)

  • Daniel Santana-Quinteros

    (Centro de Ciencias Matemáticas, UNAM Campus Morelia, Antigua Carretera a Pátzcuaro 8701, Morelia 58089, Mexico)

  • Francisco Domínguez-Mota

    (Facultad de Ciencias Físico Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Santiago Tapia 403, Morelia 58000, Mexico)

Abstract

The accurate description of the flow of water in porous media is of the greatest importance due to its numerous applications in several areas (groundwater, soil mechanics, etc.). The nonlinear Richards equation is often used as the governing equation that describes this phenomenon and a large number of research studies aimed to solve it numerically. However, due to the nonlinearity of the constitutive expressions for permeability, it remains a challenging modeling problem. In this paper, the stationary form of Richards’ equation used in saturated soils is solved by two numerical methods: generalized finite differences, an emerging method that has been successfully applied to the transient case, and a finite element method, for benchmarking. The nonlinearity of the solution in both cases is handled using a Newtonian iteration. The comparative results show that a generalized finite difference iteration yields satisfactory results in a standard test problem with a singularity at the boundary.

Suggested Citation

  • Carlos Chávez-Negrete & Daniel Santana-Quinteros & Francisco Domínguez-Mota, 2021. "A Solution of Richards’ Equation by Generalized Finite Differences for Stationary Flow in a Dam," Mathematics, MDPI, vol. 9(14), pages 1-14, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:14:p:1604-:d:590357
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/14/1604/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/14/1604/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Domínguez-Mota, Francisco J. & Armenta, Sanzon Mendoza & Tinoco-Guerrero, G. & Tinoco-Ruiz, J.G., 2014. "Finite difference schemes satisfying an optimality condition for the unsteady heat equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 106(C), pages 76-83.
    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. Qiang Wang & Pyeoungkee Kim & Wenzhen Qu, 2022. "A Hybrid Localized Meshless Method for the Solution of Transient Groundwater Flow in Two Dimensions," Mathematics, MDPI, vol. 10(3), pages 1-14, February.

    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.

      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:gam:jmathe:v:9:y:2021:i:14:p:1604-:d:590357. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.