Asymptotic problems and numerical schemes for traffic flows with unilateral constraints describing the formation of jams

TL;DR

This paper develops numerical schemes for traffic flow PDE models with unilateral constraints, addressing congestion and jam formation by handling stiff terms and large propagation speeds.

Contribution

It introduces stable numerical strategies for asymptotic traffic flow models with density thresholds and congestion constraints.

Findings

Schemes effectively simulate traffic jams and congestion.

Methods handle stiff PDE terms with relaxed stability conditions.

Models accurately reproduce jam formation dynamics.

Abstract

We discuss numerical strategies to deal with PDE systems describing traffic flows, taking into account a density threshold, which restricts the vehicles density in the situation of congestion. These models are obtained through asymptotic arguments. Hence, we are interested in the simulation of approached models that contain stiff terms and large speeds of propagation. We design schemes intended to apply with relaxed stability conditions.