A conservative scheme for non-classical solutions to a strongly coupled PDE-ODE problem
type: Item
instance of: scholarly article
title: A conservative scheme for non-classical solutions to a strongly coupled PDE-ODE problem
zbMATH Open document ID: 1404.65110
DOI: 10.4171/IFB/392
author: Ch. Chalons
author: M. L. Delle Monache
author: Paola Goatin
published in: Interfaces and Free Boundaries
publication date: 2018-03-23T00:00:00Z
review text: Summary: We consider a strongly coupled PDE-ODE system modeling the influence of a slow and large vehicle on road traffic. The model consists of a scalar conservation law describing the main traffic evolution and an ODE accounting for the trajectory of the slower vehicle that depends on the downstream traffic density. The moving constraint is operated by an inequality on the flux, which accounts for the bottleneck created on the road by the presence of the slower vehicle. We introduce a conservative scheme for the constrained hyperbolic PDE and we use a tracking algorithm for the ODE. We perform numerical tests and compute numerically the order of convergence.
Mathematics Subject Classification ID: 65M08
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 90B20
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65L05
zbMATH DE Number: 6852567
zbMATH Keywords: scalar conservation laws with local moving constraints
zbMATH Keywords: traffic flow modeling
zbMATH Keywords: PDE-ODE coupling
zbMATH Keywords: conservative finite volume schemes
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/ifb/392
OpenAlex ID: W2233442915
Recommended article: Conerservative and Nonconservative Schemes for the Solution of the Nonlinear Schrödinger Equation
Recommended article: Compact and efficient conservative schemes for coupled nonlinear <scp>S</scp>chrödinger equations
Recommended article: Decoupled conservative schemes for computing dynamics of the strongly coupled nonlinear Schrödinger system
Recommended article: Numerical analysis of a new conservative scheme for the coupled nonlinear Schrödinger equations
Recommended article: High-order conservative schemes for the nonlinear Schrödinger equation in the semiclassical limit
Recommended article: Conservative compact difference schemes for the coupled nonlinear schrödinger system
Recommended article: A linearly implicit conservative scheme for the coupled nonlinear Schrödinger equation
Recommended article: Q3054596
Recommended article: New conservative difference schemes for a coupled nonlinear Schrödinger system
Recommended article: Convergent and conservative schemes for nonclassical solutions based on kinetic relations. I
description: scientific article; zbMATH DE number 6852567