IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v221y2024icp435-460.html
   My bibliography  Save this article

A numerical investigation on coupling of conforming and hybridizable interior penalty discontinuous Galerkin methods for fractured groundwater flow problems

Author

Listed:
  • Etangsale, Grégory
  • Fahs, Marwan
  • Fontaine, Vincent
  • Hoteit, Hussein

Abstract

The present paper focuses on the numerical modeling of groundwater flows in fractured porous media using the codimensional model description. Therefore, fractures are defined explicitly as a (d−1)-dimensional geometric object immersed in a d-dimensional region and can act arbitrarily as a drain or a barrier. We numerically investigate a novel numerical strategy combining distinctive classes of conforming and nonconforming high-order Galerkin methods, both eligible for static condensation. This procedure is here particularly relevant, leading to a smaller and sparser final system with coupled degrees of freedom solely on the mesh skeleton. Precisely, we combine an inspired hybridizable interior penalty discontinuous Galerkin (HIP) formulation inside the bulk region and a standard continuous Galerkin (CG) approximation on the fracture network. The distinctive discretization of corresponding PDEs and the coupling strategy are rigorously exposed, and the local and global matrix assemblies are detailed. Extensive numerical experiments are then achieved to prove the model’s performances for 2D/3D analytic and realistic benchmarks. Qualitative comparisons are also considered with other discretization methods and commercial software, such as comsol.

Suggested Citation

  • Etangsale, Grégory & Fahs, Marwan & Fontaine, Vincent & Hoteit, Hussein, 2024. "A numerical investigation on coupling of conforming and hybridizable interior penalty discontinuous Galerkin methods for fractured groundwater flow problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 435-460.
  • Handle: RePEc:eee:matcom:v:221:y:2024:i:c:p:435-460
    DOI: 10.1016/j.matcom.2024.03.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475424000740
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2024.03.003?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. Etangsale, Grégory & Fahs, Marwan & Fontaine, Vincent, 2023. "Families of hybridized interior penalty discontinuous Galerkin methods for locally degenerate advection-diffusion-reaction problems," Applied Mathematics and Computation, Elsevier, vol. 456(C).
    2. Mozolevski, Igor & Murad, Marcio A. & Schuh, Luciane A., 2021. "High order discontinuous Galerkin method for reduced flow models in fractured porous media," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1317-1341.
    Full references (including those not matched with items on IDEAS)

    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. Yunqi Jiang & Huaqing Zhang & Kai Zhang & Jian Wang & Shiti Cui & Jianfa Han & Liming Zhang & Jun Yao, 2022. "Reservoir Characterization and Productivity Forecast Based on Knowledge Interaction Neural Network," Mathematics, MDPI, vol. 10(9), pages 1-22, May.

    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:221:y:2024:i:c:p:435-460. 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: 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.