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

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  • 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
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    References listed on IDEAS

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    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.
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    Cited by:

    1. 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).
    2. 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.

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