Local Time Stepping Method for District Heating Networks

  • Matthias EimerEmail author
  • Raul Borsche
  • Norbert Siedow
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 30)


In this article, we present a numerical solver for simulating district heating networks. The method applies a local time stepping to networks of linear advection equations. Numerical diffusion as well as the computational effort on each edge is reduced significantly. The combination with high order coupling and reconstruction techniques leads to a very efficient scheme.



This research was supported by Verbundprojekt 05M2018-EiFer: Energieeffizienz durch intelligente Fernwärmenetze. 05M18AMB-810303892568


  1. 1.
    Borsche, R., Kall, J.: ADER schemes and high order coupling on networks of hyperbolic conservation laws. J. Comput. Phys. 273, 658–670 (2014)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Dumbser, M., Käser, M., Toro, E.F.: An arbitrary high-order Discontinuous Galerkin method for elastic waves on unstructured meshes-V. Local time stepping and p-adaptivity. Geophys. J. Int. 171 695–717 (2007)Google Scholar
  3. 3.
    Dumbser, M., Zanotti, O., Loubère, R., Diot, S.: A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws. J. Comput. Phys. 278 47–75 (2014)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Jansen, L., Pade, J.: Global unique solvability for a quasi-stationary water network model. In: Preprint series: Institut für Mathematik. Humboldt-Universität zu, Berlin (2013)
  5. 5.
    Jiang, G., Shu, C.: Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202–228 (1996)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Müller, L.O., Blanco, P.J., Watanabe, S.M, Feijóo, R.A.: A high-order local time stepping finite volume solver for one-dimensional blood flow simulations: application to the ADAN model. Int. J. Numer. Methods Biomed. Eng. 32, e02761, 36 (2016)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Toro, E.F., Millington, R.C., Nejad, L.A.M.: Towards very high order Godunov schemes. In: Godunov methods (Oxford, 1999), pp. 907–940. Kluwer/Plenum, New York (2001)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.TU KaiserslauternKaiserslauternGermany
  2. 2.Fraunhofer Institute for Industrial Mathematics ITWMKaiserslauternGermany

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