IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v137y2017icp266-285.html
   My bibliography  Save this article

A phase field approach to pressurized fractures using discontinuous Galerkin methods

Author

Listed:
  • Engwer, Christian
  • Schumacher, Liesel

Abstract

Subsurface fractures play an important role in many modern energy technologies (e.g. geothermal energy, fracking, nuclear waste management). Real world experiments concerning fracture propagation are usually expensive and time consuming, therefore numerical simulations become more and more important in this area. The main challenge for numerical methods is the evolving domain. Standard finite element (FE) methods require remeshing to resolve the crack surface once a fracture starts propagating. To overcome this problem we use a phase field approach to regularize the crack surface. Thereby we consider quasi static evolution in fluid filled media. For the one-dimensional case Γ-convergence of the approximating functional to the potential energy of the system is shown. Based on this model we propose a discontinuous Galerkin (DG) formulation for the displacement. This takes into account displacement jumps at the crack surface. Numerical experiments compare our method with a standard FE approach.

Suggested Citation

  • Engwer, Christian & Schumacher, Liesel, 2017. "A phase field approach to pressurized fractures using discontinuous Galerkin methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 137(C), pages 266-285.
    • Handle: RePEc:eee:matcom:v:137:y:2017:i:c:p:266-285
    DOI: 10.1016/j.matcom.2016.11.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475416302075
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2016.11.001?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. Bastian, Peter & Engwer, Christian & Fahlke, Jorrit & Ippisch, Olaf, 2011. "An Unfitted Discontinuous Galerkin method for pore-scale simulations of solute transport," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(10), pages 2051-2061.
    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.

      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:137:y:2017:i:c:p:266-285. 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.