IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v199y2022icp1-24.html
   My bibliography  Save this article

A pseudo-spectral based efficient volume penalization scheme for Cahn–Hilliard equation in complex geometries

Author

Listed:
  • Sinhababu, Arijit
  • Bhattacharya, Anirban

Abstract

In this paper, we have developed an efficient volume penalization based diffuse-filtering scheme to solve variable mobility based Cahn–Hilliard equation in complex geometries. The main novelty of the work is that a dealiased pseudo-spectral scheme with immersed interface method (IIM) is proposed for solving any generalized concentration-dependent mobility function-based Cahn–Hilliard (CH) equation in complicated computational domains. An indicator function based mobility parameter is introduced to perform simulation of binary spinodal decomposition problem at a lower computational expense in complex geometries by solving a single phase field equation. Due to the smooth removal of high frequency Fourier components, the solution of the present RK4 based diffuse-filtering scheme does not display spurious currents when suitable low-pass filtering strategy and adequately resolved mobility indicator are incorporated. The traditional and memory optimized zero padding schemes are also implemented to show the comparative performance of different dealiasing schemes for the variable mobility based Cahn–Hilliard equation. It is found that the diffuse-filtering scheme displays reasonable accuracy similar to the zero padding based schemes but its average CPU time is significantly lower, which indicates better computational performance of the scheme for the variable mobility Cahn–Hilliard equation. Time variation of the characteristic length scale during spinodal decomposition of a binary mixture agrees well with the analytical prediction. The optimal three stage SSPRK3 temporal scheme is employed and it is found that time step size can be increased approximately 1.4 times than the classical RK4 scheme reducing total CPU time. Oscillation free numerical solution and conservation of order parameter are obtained for the complex geometry based spinodal decomposition problem. A radially-averaged structure factor is introduced to quantify resolution issues of the dealiasing schemes for the spinodal decomposition problem in different complex geometries.

Suggested Citation

  • Sinhababu, Arijit & Bhattacharya, Anirban, 2022. "A pseudo-spectral based efficient volume penalization scheme for Cahn–Hilliard equation in complex geometries," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 1-24.
  • Handle: RePEc:eee:matcom:v:199:y:2022:i:c:p:1-24
    DOI: 10.1016/j.matcom.2022.03.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422001148
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2022.03.015?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. Lee, Chaeyoung & Jeong, Darae & Shin, Jaemin & Li, Yibao & Kim, Junseok, 2014. "A fourth-order spatial accurate and practically stable compact scheme for the Cahn–Hilliard equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 17-28.
    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.
    1. Qiming Huang & Junxiang Yang, 2022. "Linear and Energy-Stable Method with Enhanced Consistency for the Incompressible Cahn–Hilliard–Navier–Stokes Two-Phase Flow Model," Mathematics, MDPI, vol. 10(24), pages 1-16, December.
    2. Chaeyoung Lee & Darae Jeong & Junxiang Yang & Junseok Kim, 2020. "Nonlinear Multigrid Implementation for the Two-Dimensional Cahn–Hilliard Equation," Mathematics, MDPI, vol. 8(1), pages 1-23, January.
    3. Koike, Yukito & Nakamula, Atsushi & Nishie, Akihiro & Obuse, Kiori & Sawado, Nobuyuki & Suda, Yamato & Toda, Kouichi, 2022. "Mock-integrability and stable solitary vortices," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).

    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:199:y:2022:i:c:p:1-24. 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.