IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i9p1482-d805376.html
   My bibliography  Save this article

A High–Order WENO Scheme Based on Different Numerical Fluxes for the Savage–Hutter Equations

Author

Listed:
  • Min Wang

    (College of Civil Engineering & Architecture, China Three Gorges University, Yichang 443002, China
    Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, China
    College of Science, China Three Gorges University, Yichang 443002, China
    These authors contributed equally to this work.)

  • Xiaohua Zhang

    (Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, China
    College of Science, China Three Gorges University, Yichang 443002, China
    These authors contributed equally to this work.)

Abstract

The study of rapid free surface granular avalanche flows has attracted much attention in recent years, which is widely modeled using the Savage–Hutter equations. The model is closely related to shallow water equations. We employ a high-order shock-capturing numerical model based on the weighted essential non-oscillatory (WENO) reconstruction method for solving Savage–Hutter equations. Three numerical fluxes, i.e., Lax–Friedrichs (LF), Harten–Lax–van Leer (HLL), and HLL contact (HLLC) numerical fluxes, are considered with the WENO finite volume method and TVD Runge–Kutta time discretization for the Savage–Hutter equations. Numerical examples in 1D and 2D space are presented to compare the resolution of shock waves and free surface capture. The numerical results show that the method proposed provides excellent performance with high accuracy and robustness.

Suggested Citation

  • Min Wang & Xiaohua Zhang, 2022. "A High–Order WENO Scheme Based on Different Numerical Fluxes for the Savage–Hutter Equations," Mathematics, MDPI, vol. 10(9), pages 1-18, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1482-:d:805376
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/9/1482/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/9/1482/
    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:9:p:1482-:d:805376. 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.