Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Borsche, R., Kall, J.: ADER schemes and high order coupling on networks of hyperbolic conservation laws. J. Comput. Phys. 273, 658–670 (2014)
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)
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)
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) https://www.mathematik.hu-berlin.de/de/forschung/pub/P-13-11
Jiang, G., Shu, C.: Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202–228 (1996)
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)
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)
Acknowledgements
This research was supported by Verbundprojekt 05M2018-EiFer: Energieeffizienz durch intelligente Fernwärmenetze. 05M18AMB-810303892568
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Eimer, M., Borsche, R., Siedow, N. (2019). Local Time Stepping Method for District Heating Networks. In: Faragó, I., Izsák, F., Simon, P. (eds) Progress in Industrial Mathematics at ECMI 2018. Mathematics in Industry(), vol 30. Springer, Cham. https://doi.org/10.1007/978-3-030-27550-1_50
Download citation
DOI: https://doi.org/10.1007/978-3-030-27550-1_50
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-27549-5
Online ISBN: 978-3-030-27550-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)