IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v215y2024icp607-627.html
   My bibliography  Save this article

Decoupled, linear, unconditionally energy stable and charge-conservative finite element method for an inductionless magnetohydrodynamic phase-field model

Author

Listed:
  • Wang, Xiaorong
  • Zhang, Xiaodi

Abstract

In this paper, we consider the numerical approximation for a diffuse interface model of the two-phase incompressible inductionless magnetohydrodynamics (MHD) problem. This model consists of Cahn–Hilliard equations, Navier–Stokes equations and Poisson equation. We propose a linear and decoupled finite element method to solve this highly nonlinear and multi-physics system. For the time variable, the discretization is a combination of the first order Euler semi-implicit scheme, several first-order stabilization terms and implicit–explicit treatments for coupling terms. For the space variables, we adopt the finite element discretization. Especially, we approximate the current density and electric potential by inf–sup stable face-volume mixed finite element pairs. With these techniques, the scheme only involves a sequence of decoupled linear equations to solve at each time step. We show that the scheme is provably mass-conservative, charge-conservative and unconditionally energy stable. Numerical experiments are performed to illustrate the properties, accuracy and efficiency of the proposed scheme.

Suggested Citation

  • Wang, Xiaorong & Zhang, Xiaodi, 2024. "Decoupled, linear, unconditionally energy stable and charge-conservative finite element method for an inductionless magnetohydrodynamic phase-field model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 607-627.
    • Handle: RePEc:eee:matcom:v:215:y:2024:i:c:p:607-627
    DOI: 10.1016/j.matcom.2023.08.039
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475423003750
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2023.08.039?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. Chen, Chuanjun & Zhang, Tong, 2022. "Unconditional stability and optimal error estimates of first order semi-implicit stabilized finite element method for two phase magnetohydrodynamic diffuse interface model," Applied Mathematics and Computation, Elsevier, vol. 429(C).
    Full references (including those not matched with items on IDEAS)

    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:matcom:v:215:y:2024:i:c:p:607-627. 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: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

      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.