High-order Finite Volume WENO schemes for non-local multi-class traffic flow models

Felisia Angela Chiarello (1, 2) , Paola Goatin (3, 2) , Luis Miguel Villada (4)

1 COMUE UCA - COMUE Université Côte d'Azur (2015-2019)
2 ACUMES - Analysis and Control of Unsteady Models for Engineering Sciences
3 LJAD - Laboratoire Jean Alexandre Dieudonné
4 Universidad de Concepción - University of Concepcion [Chile]

This paper focuses on the numerical approximation of a class of non-local systems of conservation laws in one space dimension, arising in traffic modeling, proposed by [F. A. Chiarello and P. Goatin. Non-local multi-class traffic flow models. Networks and Heterogeneous Media, to appear, Aug. 2018]. We present the multi-class version of the Finite Volume WENO (FV-WENO) schemes [C. Chalons, P. Goatin, and L. M. Villada. High-order numerical schemes for one-dimensional non-local conservation laws. SIAM Journal on Scientific Computing, 40(1):A288-A305, 2018.], with quadratic polynomial reconstruction in each cell to evaluate the non-local terms in order to obtain high-order of accuracy. Simulations using FV-WENO schemes for a multi-class model for autonomous and human-driven traffic flow are presented for M = 3 .

Domaines: Analyse numérique [math.NA]

Felisia Angela Chiarello, Paola Goatin, Luis Miguel Villada. High-order Finite Volume WENO schemes for non-local multi-class traffic flow models. Hyperbolic Problems: Theory, Numerics, Applications. Proceedings of the XVII international conference in Penn State., Jun 2018, University Park, Pennsylvania, United States. pp.353-560. ⟨hal-01979543⟩