From Traffic and Pedestrian Follow-the-Leader Models with Reaction Time to First Order Convection-Diffusion Flow Models

From Traffic and Pedestrian Follow-the-Leader Models with Reaction Time to First Order Convection-Diffusion Flow Models

In this work, we derive first order continuum traffic flow models from a microscopic delayed follow-the-leader model. Those are applicable in the context of vehicular traffic flow as well as pedestrian traffic flow. The microscopic model is based on an optimal velocity function and a reaction time parameter. The corresponding macroscopic formulations in Eulerian or Lagrangian coordinates result...

Derivation of Continuum Traffic Flow Models from Microscopic Follow-the-Leader Models

In this paper we establish a connection between a microscopic follow-the-leader model based on ordinary differential equations and a semidiscretization of a macroscopic continuum model based on a conservation law. Naturally, it also turns out that the natural discretization of the conservation law in Lagrangian coordinates is equivalent to a straightforward time discretization of the microscopi...

Exponential Asymptotics and Convection - Diffusion - Reaction Models

Reaction-diffusion models describing a two-lane traffic flow

A unidirectional two-lane road is approximated by a set of two parallel closed one-dimensional chains. Two types of cars, i.e., slow and fast ones are considered in the system. Based on the Nagel-Schreckenberg model of traffic flow [K. Nagel and M. Schreckenberg, J. Phys. 2, 2221 (1992)], a set of reaction-diffusion processes is introduced to simulate the behavior of the cars. Fast cars can pas...

SUPG reduced order models for convection-dominated convection-diffusion-reaction equations

This paper presents a Streamline-Upwind Petrov–Galerkin (SUPG) reduced order model (ROM) based on Proper Orthogonal Decomposition (POD). This ROM is investigated theoretically and numerically for convection-dominated convectiondi usion-reaction equations. The SUPG finite element method was used on realistic meshes for computing the snapshots, leading to some noise in the POD data. Numerical ana...