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Numerical Discretization of Coupling Conditions by High-Order Schemes

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Abstract

We consider numerical schemes for \(2\times 2\) hyperbolic conservation laws on graphs. The hyperbolic equations are given on arcs which are one-dimensional in space and are coupled at a single point, the node, by a nonlinear coupling condition. We develop high-order finite volume discretizations for the coupled problem. The reconstruction of the fluxes at the node is obtained using derivatives of the parameterized algebraic conditions imposed at the nodal points in the network. Numerical results illustrate the expected theoretical behavior.

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Acknowledgments

This work has been partly supported by DFG ‘Integrated Production in High-Wage Countries’ and the BMBF KinOpt project. This work is also based on the research supported in part by the National Research Foundation of South Africa (Grant No. 93476) and the Research Development Programme of the University of Pretoria.

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Authors and Affiliations

  1. University of Pretoria, Pretoria, South Africa

    Mapundi K. Banda

  2. RWTH Aachen University, Aachen, Germany

    Axel-Stefan Häck & Michael Herty

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  1. Mapundi K. Banda
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  2. Axel-Stefan Häck
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  3. Michael Herty
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Correspondence to Axel-Stefan Häck.

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Banda, M.K., Häck, AS. & Herty, M. Numerical Discretization of Coupling Conditions by High-Order Schemes. J Sci Comput 69, 122–145 (2016). https://doi.org/10.1007/s10915-016-0185-x

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  • DOI: https://doi.org/10.1007/s10915-016-0185-x

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