IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i1p119-d308266.html
   My bibliography  Save this article

Improving Initial Guess for the Iterative Solution of Linear Equation Systems in Incompressible Flow

Author

Listed:
  • Shuai Ye

    (State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 410073, China
    Current address: No.109 Deya Rd, Kaifu District, Changsha, Hunan, China.)

  • Yufei Lin

    (National Innovation Institute of Defense Technology, Beijing 100071, China)

  • Liyang Xu

    (State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 410073, China)

  • Jiaming Wu

    (Advanced Institute of Engineering Science for Intelligent Manufacturing, Guangzhou University, Guangzhou 510006, China)

Abstract

The pressure equation, generated while solving the incompressible Navier–Stokes equations with the segregated iterative algorithm such as PISO, produces a series of linear equation systems as the time step advances. In this paper, we target at accelerating the iterative solution of these linear systems by improving their initial guesses. We propose a weighted group extrapolation method to obtain a superior initial guess instead of a general one, the solution of the previous linear equation system. In this method, the previous solutions that are used to extrapolate the predicted solutions are carefully organized to address the oscillatory solution on each grid. The proposed method uses a weighted average of the predicted solutions as the new initial guess to avoid over extrapolating. Three numerical test results show that the proposed method can accelerate the iterative solution of most linear equation systems and reduce the simulation time up to 61.3%.

Suggested Citation

  • Shuai Ye & Yufei Lin & Liyang Xu & Jiaming Wu, 2020. "Improving Initial Guess for the Iterative Solution of Linear Equation Systems in Incompressible Flow," Mathematics, MDPI, vol. 8(1), pages 1-20, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:119-:d:308266
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/1/119/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/1/119/
    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:8:y:2020:i:1:p:119-:d:308266. 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.