IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v264y2015icp179-197.html
   My bibliography  Save this article

The immersed interface method for axis-symmetric problems and application to the Hele–Shaw flow

Author

Listed:
  • Ruiz Álvarez, Juan
  • Li, Zhilin

Abstract

Many physical application problems are axis-symmetric. Using axis-symmetric properties, many three dimensional problems can be solved efficiently using two dimensional axis-symmetric coordinates. In this paper, the immersed interface method (IIM) in axis-symmetric coordinates is developed for elliptic interface problems that have a discontinuous coefficient, solution or flux. A staggered grid is used to overcome the pole singularity. Other challenges include deriving the jump relations in axis-symmetric coordinates, designing the numerical algorithm when the interface is close to the pole (r = 0); computing interface quantities such as the normal and tangential directions, surface derivatives, curvature information, etc. The numerical algorithm is based on a finite difference discretization and uniform grid in the axis-symmetric coordinates. The finite difference scheme is the standard one away from the interface but is modified at grid points near and on the interface. The method is shown to be second order accurate in the infinity norm. The developed new IIM is applied to the Hele–Shaw flow and compared with the results from the literature.

Suggested Citation

  • Ruiz Álvarez, Juan & Li, Zhilin, 2015. "The immersed interface method for axis-symmetric problems and application to the Hele–Shaw flow," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 179-197.
    • Handle: RePEc:eee:apmaco:v:264:y:2015:i:c:p:179-197
    DOI: 10.1016/j.amc.2015.03.131
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315004506
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.03.131?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.

    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:apmaco:v:264:y:2015:i:c:p:179-197. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.