IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v433y2022ics0096300322004520.html
   My bibliography  Save this article

Hyperbolic relaxation models for thin films down an inclined plane

Author

Listed:
  • Dhaouadi, Firas
  • Gavrilyuk, Sergey
  • Vila, Jean-Paul

Abstract

We present a family of relaxation models for thin films flows where both viscosity and surface tension effects are inherent. In a first step, a first-order hyperbolic approximation to the dissipationless part of the system is presented. The method is based on an augmented Lagrangian approach, where a classical penalty method is used and high-order derivatives in the Lagrangian are promoted to new independent variables, for which hyperbolic closure equations are sought. Then, we show that the viscous terms can be treated either by plugging them directly to the obtained system, making it of the hyperbolic-parabolic type or by casting them into an approximate algebraic source term that is asymptotically equivalent to the former formulation. Finally, the extension of the method to a classical nonlinear surface tension model is also presented. Numerical results, for all the proposed models are shown and compared with experimental results and reference solutions.

Suggested Citation

  • Dhaouadi, Firas & Gavrilyuk, Sergey & Vila, Jean-Paul, 2022. "Hyperbolic relaxation models for thin films down an inclined plane," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    • Handle: RePEc:eee:apmaco:v:433:y:2022:i:c:s0096300322004520
    DOI: 10.1016/j.amc.2022.127378
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322004520
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.127378?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Firas Dhaouadi & Michael Dumbser, 2023. "A Structure-Preserving Finite Volume Scheme for a Hyperbolic Reformulation of the Navier–Stokes–Korteweg Equations," Mathematics, MDPI, vol. 11(4), pages 1-25, February.

    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:433:y:2022:i:c:s0096300322004520. 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.