IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i16p1885-d610525.html
   My bibliography  Save this article

Alternating Polynomial Reconstruction Method for Hyperbolic Conservation Laws

Author

Listed:
  • Shijian Lin

    (College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410000, China)

  • Qi Luo

    (Department of Mathematics, National University of Defense Technology, Changsha 410000, China)

  • Hongze Leng

    (College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410000, China)

  • Junqiang Song

    (College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410000, China)

Abstract

We propose a new multi-moment numerical solver for hyperbolic conservation laws by using the alternating polynomial reconstruction approach. Unlike existing multi-moment schemes, our approach updates model variables by implementing two polynomial reconstructions alternately. First, Hermite interpolation reconstructs the solution within the cell by matching the point-based variables containing both physical values and their spatial derivatives. Then the reconstructed solution is updated by the Euler method. Second, we solve a constrained least-squares problem to correct the updated solution to preserve the conservation laws. Our method enjoys the advantages of a compact numerical stencil and high-order accuracy. Fourier analysis also indicates that our method allows a larger CFL number compared with many other high-order schemes. By adding a proper amount of artificial viscosity, shock waves and other discontinuities can also be computed accurately and sharply without solving an approximated Riemann problem.

Suggested Citation

  • Shijian Lin & Qi Luo & Hongze Leng & Junqiang Song, 2021. "Alternating Polynomial Reconstruction Method for Hyperbolic Conservation Laws," Mathematics, MDPI, vol. 9(16), pages 1-24, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1885-:d:610525
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/16/1885/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/16/1885/
    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:9:y:2021:i:16:p:1885-:d:610525. 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.