IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v333y2018icp376-400.html
   My bibliography  Save this article

Implicit finite element methodology for the numerical modeling of incompressible two-fluid flows with moving hyperelastic interface

Author

Listed:
  • Laadhari, Aymen

Abstract

We present a numerical methodology based on the use of the Newton and level set methods and tailored for the simulation of incompressible immiscible two-fluid flows with moving hyperelastic membrane. The method features the use of implicit time integration schemes and is based on a consistent Newton–Raphson linearization. The performances are enhanced by using the Kou’s method (Kou et al., 2006) which features a third-order convergence behavior without requiring higher order derivatives. To overcome numerical instability issues related to the explicit decoupling, a fully monolithic strategy and a partitioned implicit strategy are devised. We investigate the main features of the proposed strategies, and we report several numerical experiments with the aim of illustrating their robustness and accuracy. We show numerically that the monolithic strategy performs better and remains stable when considering relatively small viscosities or large stiffness, for which the partitioned approach depicts a slow convergence or even fails to converge. However, the partitioned strategy features significant computational savings when it converges within a reasonable number of sub-iterations.

Suggested Citation

  • Laadhari, Aymen, 2018. "Implicit finite element methodology for the numerical modeling of incompressible two-fluid flows with moving hyperelastic interface," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 376-400.
    • Handle: RePEc:eee:apmaco:v:333:y:2018:i:c:p:376-400
    DOI: 10.1016/j.amc.2018.03.074
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318302558
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.03.074?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. Franck J. Vernerey & Mehdi Farsad, 2011. "An Eulerian/XFEM formulation for the large deformation of cortical cell membrane," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 14(05), pages 433-445.
    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. Aymen Laadhari, 2023. "Finite-Element Method for the Simulation of Lipid Vesicle/Fluid Interactions in a Quasi–Newtonian Fluid Flow," Mathematics, MDPI, vol. 11(8), pages 1-18, April.

    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:apmaco:v:333:y:2018:i:c:p:376-400. 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: 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.