Abstract
In this article, we present a numerical solver for simulating district heating networks. The method applies a local time step** 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
Similar content being viewed by others
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 step** 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 step** 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 Step** 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)