Abstract
We describe the simulation of traffic flows on networks. On individual roads we use standard macroscopic traffic models. The discontinuous Galerkin method in space and a multistep method in time is used for the numerical solution. We introduce limiters to keep the density in an admissible interval as well as prevent spurious oscillations in the numerical solution. To simulate traffic on networks, one should construct suitable numerical fluxes at junctions.
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Acknowledgements
The research of L. Vacek is supported by the Charles University, project GA UK No. 20-01074S. The work of V. Kučera was supported by the research project No. 20-01747S of the Czech Science Foundation.
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Vacek, L., Kučera, V. (2021). Numerical Solution of Traffic Flow Models. In: Vermolen, F.J., Vuik, C. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, vol 139. Springer, Cham. https://doi.org/10.1007/978-3-030-55874-1_106
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DOI: https://doi.org/10.1007/978-3-030-55874-1_106
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