IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i22p4242-d971353.html
   My bibliography  Save this article

Bifurcation and Multiplicity of Solutions of the Navier–Stokes Equations in Driven Semi-Elliptical Cavity Flow

Author

Listed:
  • Ercan Erturk

    (Mechanical Engineering Department, Istanbul Medeniyet University, Istanbul 34700, Turkey)

  • Tofigh Allahviranloo

    (Software Engineering Department, Istinye University, Istanbul 34010, Turkey)

Abstract

In this paper, bifurcations in the solution of the Navier–Stokes equations are studied and multiple solutions of the driven semi-elliptical cavity flow are presented. The two-dimensional steady incompressible driven viscous flow in a semi-elliptical cavity is solved numerically. To this end, the problem is formulated using an elliptic coordinate system that transforms the geometry conformally and provides a body fitted coordinate system. The presented results show that above a bifurcation Reynolds number the solution of the governing flow equations bifurcates and there exist multiple solutions for a particular Reynolds number when the aspect ratio of the semi-elliptical cavity geometry is 0.26 ⩽ D ⩽ 0.8. The bifurcation Reynolds numbers for different aspect ratios and also multiple solutions at different Reynolds numbers are presented in detail.

Suggested Citation

  • Ercan Erturk & Tofigh Allahviranloo, 2022. "Bifurcation and Multiplicity of Solutions of the Navier–Stokes Equations in Driven Semi-Elliptical Cavity Flow," Mathematics, MDPI, vol. 10(22), pages 1-20, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4242-:d:971353
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/22/4242/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/22/4242/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:10:y:2022:i:22:p:4242-:d:971353. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.