IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-031-61395-1_12.html

Second-Order Non-linear Methods

In: Computational Algorithms for Shallow Water Equations

Author

Listed:
  • Eleuterio F. Toro

    (University of Trento, DICAM)

Abstract

This chapter is devoted to the construction of second-order accurate numerical methods as applied to the shallow water equations. The schemes are non-linear, in order to circumvent Godunov’s theorem, which is concerned with the phenomenon of spurious oscillations in the vicinity of large spatial gradients, shocks in particular. For the class of flux limiter methods considered, the non-linear character of the schemes results from enforcing total variation diminishing (TVD) criteria. A second class of non-linear second-order methods is based either on TVD criteria or on non-linear spatial reconstruction of the Essentially Non-Oscillatory (ENO) type. Regarding the underlying first-order methods, two classes of methods are constructed, namely upwind methods based on the Riemann solvers studied in previous chapters and centred methods based on the FORCE framework. Numerical results from some of the methods are shown, followed by analysis and discussion on the performance of the methods tested.

Suggested Citation

  • Eleuterio F. Toro, 2024. "Second-Order Non-linear Methods," Springer Books, in: Computational Algorithms for Shallow Water Equations, edition 2, chapter 0, pages 261-281, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-61395-1_12
    DOI: 10.1007/978-3-031-61395-1_12
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    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:spr:sprchp:978-3-031-61395-1_12. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.