High-resolution central-upwind scheme for second-order macroscopic traffic flow models

Traffic flow models are important tools for traffic management applications such as traffic incident detection and traffic control. In this paper, we propose a novel numerical approximation method for second-order macroscopic traffic flow models. The method is based on the semi-discrete central-upwind numerical flux and high-order reconstructions for spatial discretizations. We then apply the designed high-resolution schemes to three representative types of second-order traffic flow models and perform a variety of numerical experiments to validate the proposed methods. The simulation results illustrate the effectiveness, simplicity and universality of the central-upwind scheme as numerical approximation method for macroscopic traffic flow models

Fully adaptive multiresolution schemes for strongly degenerate parabolic equations with discontinuous flux

A fully adaptive finite volume multiresolution scheme for one-dimensional strongly degenerate parabolic equations with discontinuous flux is presented. The numerical scheme is based on a finite volume discretization using the Engquist--Osher approximation for the flux and explicit time--stepping. An adaptivemultiresolution scheme with cell averages is then used to speed up CPU time and meet memory requirements. A particular feature of our scheme is the storage of the multiresolution representation of the solution in a dynamic graded tree, for the sake of data compression and to facilitate navigation. Applications to traffic flow with driver reaction and a clarifier--thickener model illustrate the efficiency of this method

Coupling traffic models on networks and urban dispersion models for simulating sustainable mobility strategies

AbstractThe aim of the present paper is to investigate the viability of macroscopic traffic models for modeling and testing different traffic scenarios, in order to define the impact on air quality of different strategies for the reduction of traffic emissions. To this aim, we complement a well assessed traffic model on networks (Garavello and Piccoli (2006) [1]) with a strategy for estimating data needed from the model and we couple it with the urban dispersion model Sirane (Soulhac (2000) [2])

Coupling traffic models on networks and urban dispersion models for simulating sustainable mobility strategies

The aim of the present paper is to investigate the viability of macroscopic traffic models for modeling and testing different traffic scenarios, in order to define the impact on air quality of different strategies for the reduction of traffic emissions. To this aim, we complement a well assessed traffic model on networks (Garavello, Piccoli, 2006) with a strategy for estimating data needed from the model and we couple it with the urban dispersion model Sirane (Soulhac, 2000)

Hyperbolic Balance Laws: modeling, analysis, and numerics (hybrid meeting)

This workshop brought together leading experts, as well as the most promising young researchers, working on nonlinear hyperbolic balance laws. The meeting focused on addressing new cutting-edge research in modeling, analysis, and numerics. Particular topics included ill-/well-posedness, randomness and multiscale modeling, flows in a moving domain, free boundary problems, games and control

Differential Models, Numerical Simulations and Applications

This Special Issue includes 12 high-quality articles containing original research findings in the fields of differential and integro-differential models, numerical methods and efficient algorithms for parameter estimation in inverse problems, with applications to biology, biomedicine, land degradation, traffic flows problems, and manufacturing systems

Contribution à l'étude du trafic routier sur réseaux à l'aide des équations d'Hamilton-Jacobi

This work focuses on modeling and simulation of traffic flows on a network. Modeling road traffic on a homogeneous section takes its roots in the middle of XXth century and it has generated a substantial literature since then. However, taking into account discontinuities of the network such as junctions, has attracted the attention of the scientific circle more recently. However, these discontinuities are the major sources of traffic congestion, recurring or not, that basically degrades the level of service of road infrastructure. This work therefore aims to provide a unique perspective on this issue, while focusing on scale problems and more precisely on microscopic-macroscopic passage in existing models. The first part of this thesis is devoted to the relationship between microscopic car-following models and macroscopic continuous flow models. The asymptotic passage is based on a homogenization technique for Hamilton-Jacobi equations. In a second part, we focus on the modeling and simulation of vehicular traffic flow through a junction. The considered macroscopic model is built on Hamilton-Jacobi equations as well. Finally, the third part focuses on finding analytical or semi-analytical solutions, through representation formulas aiming to solve Hamilton-Jacobi equations under adequate assumptions. In this thesis, we are also interested in a generic class of second order macroscopic traffic flow models, the so-called GSOM modelsCe travail porte sur la modélisation et la simulation du trafic routier sur un réseau. Modéliser le trafic sur une section homogène (c'est-à-dire sans entrée, ni sortie) trouve ses racines au milieu du XXème siècle et a généré une importante littérature depuis. Cependant, la prise en compte des discontinuités des réseaux comme les jonctions, n'a attiré l'attention du cercle scientifique que bien plus récemment. Pourtant, ces discontinuités sont les sources majeures des congestions, récurrentes ou non, qui dégradent la qualité de service des infrastructures. Ce travail se propose donc d'apporter un éclairage particulier sur cette question, tout en s'intéressant aux problèmes d'échelle et plus particulièrement au passage microscopique-macroscopique dans les modèles existants. La première partie de cette thèse est consacrée au lien existant entre les modèles de poursuite microscopiques et les modèles d'écoulement macroscopiques. Le passage asymptotique est assuré par une technique d'homogénéisation pour les équations d'Hamilton-Jacobi. Dans une deuxième partie, nous nous intéressons à la modélisation et à la simulation des flux de véhicules au travers d'une jonction. Le modèle macroscopique considéré est bâti autour des équations d'Hamilton-Jacobi. La troisième partie enfin, se concentre sur la recherche de solutions analytiques ou semi-analytiques, grâce à l'utilisation de formules de représentation permettant de résoudre les équations d'Hamilton-Jacobi sous de bonnes hypothèses. Nous nous intéressons également dans cette thèse, à la classe générique des modèles macroscopiques de trafic de second ordre, dits modèles GSO

Nonclassical solutions of hyperbolic conservation laws.

M. Sc. University of KwaZulu-Natal, Pietermaritzburg 2015.This dissertation studies the nonclassical shock waves which appears as limits of certain type diffusive-dispersive regularisation to hyperbolic of conservation laws. Such shocks occur very often when the ux function lacks the convexity especially when the initial conditions for Riemann problem belong to different region of convexity. They have negative entropy dissipation. They do not verify the classical Oleinik entropy criterion. The cubic function is taken as a ux function. The existence and uniqueness of such shock waves are studied. They are constructed as limits of traveling-wave solutions for diffusive-dispersive regularisation. A kinetic relation is introduced to choose a unique nonclassical solution to the Riemann problem. The numerical simulations are investigated using a transport-equilibrium scheme to enable computing the nonclassical solution at the discrete level of kinetic function. The method is composed of an equilibrium step containing the kinetic relation at any nonclassical shock and a transport step advancing the discontinuity with time