Accuracy analysis of Lagrangian Godunov scheme using variational theory
VAN WAGENINGEN-KESSELS ; LECLERCQ ; VUIK ; HOOGENDOORN ; VAN LIT
Type de document
COMMUNICATION AVEC ACTES INTERNATIONAL (ACTI)
Langue
anglais
Auteur
VAN WAGENINGEN-KESSELS ; LECLERCQ ; VUIK ; HOOGENDOORN ; VAN LIT
Résumé / Abstract
The kinematic wave model is used to describe dynamic traffic flow. The model equations are solved using the Lagrangian Godunov scheme. Previously, this scheme has been found to be more accurate than the traditional Eulerian Godunov scheme. Furthermore, the variational theory has been applied to solve the model equations even more accurately and under certain conditions exactly. Therefore, it can be used as a benchmark. We analyse the global error of the Lagrangian Godunov scheme. This is the error after a certain simulated time, which is influenced by all local errors made in previous time steps. We use the exact solution of a Riemann initial value problem obtained with variational theory to determine the error introduced by the Lagrangian Godunov scheme. We show that the global error for a fixed vehicle number goes to zero as time goes to infinity. However, the global error on certain characteristic waves does not converge to zero. We define four error measures based on absolute and relative vehicle position, spacing and velocity. Dependent on the error measure, the error increases on certain characteristic waves. Furthermore, the accuracy depends on the discretization step size. These errors can have a great impact if one wants to extend the model for example with lane-changing, if the computed velocities are used for traffic control such as ramp metering or if the simulations are used for travel time prediction.
Editeur
Elsevier
