IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v419y2022ics0096300321009371.html
   My bibliography  Save this article

DoD Stabilization for non-linear hyperbolic conservation laws on cut cell meshes in one dimension

Author

Listed:
  • May, Sandra
  • Streitbürger, Florian

Abstract

In this work, we present the Domain of Dependence (DoD) stabilization for systems of hyperbolic conservation laws in one space dimension. The base scheme uses a method of lines approach consisting of a discontinuous Galerkin scheme in space and an explicit strong stability preserving Runge-Kutta scheme in time. When applied on a cut cell mesh with a time step length that is appropriate for the size of the larger background cells, one encounters stability issues. The DoD stabilization consists of penalty terms that are designed to address these problems by redistributing mass between the inflow and outflow neighbors of small cut cells in a physical way. For piecewise constant polynomials in space and explicit Euler in time, the stabilized scheme is monotone for scalar problems. For higher polynomial degrees p, our numerical experiments show convergence orders of p+1 for smooth flow and robust behavior in the presence of shocks.

Suggested Citation

  • May, Sandra & Streitbürger, Florian, 2022. "DoD Stabilization for non-linear hyperbolic conservation laws on cut cell meshes in one dimension," Applied Mathematics and Computation, Elsevier, vol. 419(C).
    • Handle: RePEc:eee:apmaco:v:419:y:2022:i:c:s0096300321009371
    DOI: 10.1016/j.amc.2021.126854
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300321009371
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2021.126854?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:419:y:2022:i:c:s0096300321009371. 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.