IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v325y2018icp252-270.html
   My bibliography  Save this article

On a third order CWENO boundary treatment with application to networks of hyperbolic conservation laws

Author

Listed:
  • Naumann, Alexander
  • Kolb, Oliver
  • Semplice, Matteo

Abstract

High order numerical methods for networks of hyperbolic conservation laws have recently gained increasing popularity. Here, the crucial part is to treat the boundaries of the single (one-dimensional) computational domains in such a way that the desired convergence rate is achieved in the smooth case but also stability criterions are fulfilled, in particular in the presence of discontinuities. Most of the recently proposed methods rely on a WENO extrapolation technique introduced by Tan and Shu (2010). Within this work, we refine and in a sense generalize these results for the case of a third order scheme. Numerical evidence for the analytically found parameter bounds is given as well as results for a complete third order scheme based on the proposed boundary treatment.

Suggested Citation

  • Naumann, Alexander & Kolb, Oliver & Semplice, Matteo, 2018. "On a third order CWENO boundary treatment with application to networks of hyperbolic conservation laws," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 252-270.
    • Handle: RePEc:eee:apmaco:v:325:y:2018:i:c:p:252-270
    DOI: 10.1016/j.amc.2017.12.041
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317309086
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.12.041?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.

    References listed on IDEAS

    as
    1. Domschke, Pia & Kolb, Oliver & Lang, Jens, 2015. "Adjoint-based error control for the simulation and optimization of gas and water supply networks," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 1003-1018.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Borsche, Raul & Eimer, Matthias & Siedow, Norbert, 2019. "A local time stepping method for thermal energy transport in district heating networks," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 215-229.
    2. Zuo, Hujian & Zhao, Weifeng & Lin, Ping, 2022. "Boundary treatment of linear multistep methods for hyperbolic conservation laws," Applied Mathematics and Computation, Elsevier, vol. 425(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Terrence W. K. Mak & Pascal Van Hentenryck & Anatoly Zlotnik & Russell Bent, 2019. "Dynamic Compressor Optimization in Natural Gas Pipeline Systems," INFORMS Journal on Computing, INFORMS, vol. 31(1), pages 40-65, February.
    2. Pia Domschke & Oliver Kolb & Jens Lang, 2022. "Fast and reliable transient simulation and continuous optimization of large-scale gas networks," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(3), pages 475-501, June.
    3. Borsche, Raul & Eimer, Matthias & Siedow, Norbert, 2019. "A local time stepping method for thermal energy transport in district heating networks," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 215-229.

    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:325:y:2018:i:c:p:252-270. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.