IDEAS home Printed from https://ideas.repec.org/a/wsi/ijmpcx/v35y2024i03ns0129183124500359.html
   My bibliography  Save this article

A linear mass and energy conserving numerical scheme for two-phase flows with thermocapillary effects

Author

Listed:
  • Lihua Shao

    (Beijing Key Laboratory for Magneto-Photoelectrical Composite and Interface Science, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, P. R. China)

  • Zhenlin Guo

    (Mechanics Division, Beijing Computational Science Research Center, Building 9, East Zone ZPark II, No. 10, East Xibeiwang Road, Haidian District, Beijing 100193, P. R. China)

  • Yanxiao Sun

    (Mechanics Division, Beijing Computational Science Research Center, Building 9, East Zone ZPark II, No. 10, East Xibeiwang Road, Haidian District, Beijing 100193, P. R. China)

Abstract

In this paper, a thermodynamically consistent phase-field model is employed to simulate the thermocapillary migration of a droplet. The model equations consist of a general Navier–Stokes equation for the two-phase flows, a Cahn–Hilliard equation for the diffuse interface, and a heat equation, and meanwhile satisfy the balance laws of mass, energy and entropy. In particular, the total energy of the system includes kinetic energy, potential energy and internal energy, which leads to a highly coupled and nonlinear equation system. We therefore develop a linear mass and energy conserving, semi-decoupled numerical method for the numerical simulations. As the model contains a heat (energy) equation, a simple error term introduced by the temporal discretization of the momentum equation can be absorbed into the heat equation, such that the numerical solutions satisfy the conservation laws of mass and energy exactly at the temporal discrete level. Several numerical tests are carried out to validate our numerical method.

Suggested Citation

  • Lihua Shao & Zhenlin Guo & Yanxiao Sun, 2024. "A linear mass and energy conserving numerical scheme for two-phase flows with thermocapillary effects," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 35(03), pages 1-12, March.
    • Handle: RePEc:wsi:ijmpcx:v:35:y:2024:i:03:n:s0129183124500359
    DOI: 10.1142/S0129183124500359
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0129183124500359
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0129183124500359?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:wsi:ijmpcx:v:35:y:2024:i:03:n:s0129183124500359. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijmpc/ijmpc.shtml .

    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.