Publication at Faculty of Mathematics and Physics |
2023
Abstract
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.
The scheme also requires limiters which prevent spurious oscillations in the numerical solution and keep the numerical traffic density in an admissible interval. In order to solve traffic flows on networks, we construct suitable numerical fluxes at junctions based on preferences of the drivers.
We prove that our semi-discrete DG solution is L^2 stable. We present numerical experiments, including a junction with complicated traffic light patterns with multiple phases.