Godunov scheme and sampling technique for computing phase transitions in traffic flow modeling
type: Item
instance of: scholarly article
title: Godunov scheme and sampling technique for computing phase transitions in traffic flow modeling
zbMATH Open document ID: 1171.35429
DOI: 10.4171/IFB/186
author: Ch. Chalons
author: Paola Goatin
published in: Interfaces and Free Boundaries
publication date: 2008-08-13T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_abstract.php
review text: The authors propose a new version of the Godunov scheme for the numerical approximation of solutions of a continuous traffic flow model. The phenomenon of phase transitions between a free flow (described by a scalar conservation law) and a congested flow (described by a \(2\times 2\) system) is taken into account. From an analytical point of view the mathematical model is well posed for all initial data with bounded total variation. The proposed numerical model is based on a modified averaging strategy and a sampling procedure. The mesh cells are modified following the phase boundaries and as such the projection involves only values belonging to the same phase. In order to come back to the original cells, the projection step is completed with a Glimm-type sampling technique. The accuracy of the scheme is extended to second order, in space and time, which is \(L^1\)-stable in time, using a MUSCL technique and a second order Runge-Kutta method. The validity and convergence of the method is demonstrated by several numerical tests.
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 90B20
Mathematics Subject Classification ID: 35A35
zbMATH DE Number: 5311226
zbMATH Keywords: Hyperbolic Conservation Laws
zbMATH Keywords: continuous traffic models
zbMATH Keywords: phase transitions
zbMATH Keywords: Godunov scheme
zbMATH Keywords: sampling
MaRDI profile type: Publication
OpenAlex ID: W1985570727
description: scientific article; zbMATH DE number 5311226