IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-642-33134-3_15.html
   My bibliography  Save this book chapter

Application of the Level-Set Method to a Mixed-Mode and Curvature Driven Stefan Problem

In: Numerical Mathematics and Advanced Applications 2011

Author

Listed:
  • D. den Ouden

    (Materials innovation institute)

  • F. J. Vermolen

    (Delft University of Technology, DIAM)

  • L. Zhao

    (Materials innovation institute)

  • C. Vuik

    (Delft University of Technology, DIAM)

  • J. Sietsma

    (Delft University of Technology, MS&E)

Abstract

This study focuses on the dissolution and growth of small possibly initially non-smooth particles within a diffusive phase. The dissolution or growth of the particle is assumed to be affected by concentration gradients of a single chemical element within the diffusive phase at the particle boundary caused by diffusion and by an interface reaction. The combined formulation results in a mixed-mode formulation. The moving boundary problem is solved using a level-set method and finite-element techniques such as SUPG. The appropriate meshes are derived using a fixed background mesh and the level-set function. We experimentally show that these techniques give mass-conserving solutions in the limit of infinite resolution, give a linear experimental order of convergence, can handle arbitrary particles and give the possibility to incorporate surface tensions using the Gibbs-Thomson effect and the local curvature.

Suggested Citation

  • D. den Ouden & F. J. Vermolen & L. Zhao & C. Vuik & J. Sietsma, 2013. "Application of the Level-Set Method to a Mixed-Mode and Curvature Driven Stefan Problem," Springer Books, in: Andrea Cangiani & Ruslan L. Davidchack & Emmanuil Georgoulis & Alexander N. Gorban & Jeremy Levesley (ed.), Numerical Mathematics and Advanced Applications 2011, edition 127, pages 141-148, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-33134-3_15
    DOI: 10.1007/978-3-642-33134-3_15
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:spr:sprchp:978-3-642-33134-3_15. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.