# Traffic flow model on networks using numerical fluxes at the junctions

## Main Article Content

## 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 the explicit Euler 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 flow on networks, we construct suitable numerical fluxes at junctions.

## Article Details

How to Cite

Vacek, L., & Kučera, V.
(2020).
Traffic flow model on networks using numerical fluxes at the junctions.

*Proceedings Of The Conference Algoritmy,*, 41 - 50. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/1551/813
Section

Articles

## References

[1] F. van Wageningen–Kessels, H. van Lint, K. Vuik and S. Hoogendoorn, Genealogy of traffic flow models, EURO Journal on Transportation and Logistics, 4 (2015), pp. 445–473.

[2] P. Kachroo and S. Sastry, Traffic Flow Theory: Mathematical Framework, University of California Berkeley, https://www.scribd.com/doc/316334815/Traffic-Flow-Theory (cited 16th April 2020).

[3] B. D. Greenshields, A Study of Traffic Capacity, Highway Research Board, 14 (1935), pp. 448– 477.

[4] M. Garavello and B. Piccoli, Traffic flow on networks, AIMS Series on Applied Mathematics, 1 (2006), pp. 1–243.

[5] V. Dolejšı́ and M. Feistauer, Discontinuous Galerkin Method – Analysis and Applications to Compressible Flow, Analysis and Applications to Compressible Flow, 48 (2015).

[6] C.–W. Shu, Discontinuous Galerkin methods: general approach and stability, Numerical solutions of partial differential equations, 201 (2009).

[7] S. Čanić, B. Piccoli, J. Qiu and T. Ren, Runge–Kutta Discontinuous Galerkin Method for Traffic Flow Model on Networks, Journal of Scientific Computing, 63 (2014).

[2] P. Kachroo and S. Sastry, Traffic Flow Theory: Mathematical Framework, University of California Berkeley, https://www.scribd.com/doc/316334815/Traffic-Flow-Theory (cited 16th April 2020).

[3] B. D. Greenshields, A Study of Traffic Capacity, Highway Research Board, 14 (1935), pp. 448– 477.

[4] M. Garavello and B. Piccoli, Traffic flow on networks, AIMS Series on Applied Mathematics, 1 (2006), pp. 1–243.

[5] V. Dolejšı́ and M. Feistauer, Discontinuous Galerkin Method – Analysis and Applications to Compressible Flow, Analysis and Applications to Compressible Flow, 48 (2015).

[6] C.–W. Shu, Discontinuous Galerkin methods: general approach and stability, Numerical solutions of partial differential equations, 201 (2009).

[7] S. Čanić, B. Piccoli, J. Qiu and T. Ren, Runge–Kutta Discontinuous Galerkin Method for Traffic Flow Model on Networks, Journal of Scientific Computing, 63 (2014).