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Godunov-like numerical fluxes for conservation laws on networks

Vacek, Lukáš;  Kučera, Václav — 2023

Programs and Algorithms of Numerical Mathematics

We describe a numerical technique for the solution of macroscopic traffic flow models on networks of roads. On individual roads, we consider the standard Lighthill-Whitham-Richards model which is discretized using the discontinuous Galerkin method along with suitable limiters. In order to solve traffic flows on networks, we construct suitable numerical fluxes at junctions based on preferences of the drivers. Numerical experiment comparing different approaches is presented.

Construction of fluxes at junctions for the numerical solution of traffic flow models on networks

Vacek, Lukáš;  Kučera, Václav — 2021

Programs and Algorithms of Numerical Mathematics

We deal with the simulation of traffic flow on networks. On individual roads we use standard macroscopic traffic models. The discontinuous Galerkin method in space and explicit Euler method in time is used for the numerical solution. We apply limiters to keep the density in an admissible interval as well as prevent spurious oscillations in the numerical solution. To solve traffic networks, we construct suitable numerical fluxes at junctions. Numerical experiments are presented.

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