IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v314y2017icp408-421.html
   My bibliography  Save this article

Algebraic construction and numerical behavior of a new s-consistent difference scheme for the 2D Navier–Stokes equations

Author

Listed:
  • Amodio, Pierluigi
  • Blinkov, Yuri
  • Gerdt, Vladimir
  • La Scala, Roberto

Abstract

In this paper, we consider a regular grid with equal spatial spacings and construct a new finite difference approximation (difference scheme) for the system of two-dimensional Navier–Stokes equations describing the unsteady motion of an incompressible viscous liquid of constant viscosity. In so doing, we use earlier constructed discretization of the system of three equations: the continuity equation and the proper Navier–Stokes equations. Then, we compute the canonical Gröbner basis form for the obtained discrete system. It gives one more difference equation which is equivalent to the pressure Poisson equation modulo difference ideal generated by the Navier–Stokes equations, and thereby comprises a new finite difference approximation (scheme). We show that the new scheme is strongly consistent. Besides, our computational experiments demonstrate much better numerical behavior of the new scheme in comparison with the other strongly consistent schemes we constructed earlier and with the scheme which is not strongly consistent.

Suggested Citation

  • Amodio, Pierluigi & Blinkov, Yuri & Gerdt, Vladimir & La Scala, Roberto, 2017. "Algebraic construction and numerical behavior of a new s-consistent difference scheme for the 2D Navier–Stokes equations," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 408-421.
    • Handle: RePEc:eee:apmaco:v:314:y:2017:i:c:p:408-421
    DOI: 10.1016/j.amc.2017.06.037
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317304502
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.06.037?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:eee:apmaco:v:314:y:2017:i:c:p:408-421. 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.