A weighted essentially non-oscillatory numerical scheme for a multi-class Lighthill–Whitham–Richards traffic flow model

Zhang, Mengping; Shu, Chi‐Wang; Wong, G. C. K.; Wong, S. C.

doi:10.1016/s0021-9991(03)00344-9

Cited by 82 publications

(86 citation statements)

References 17 publications

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“…[10]. Such models have been proposed for example in [3,4,27,28,26] and in [10]. The latter publication introduces a source-destination model based on the LWR equation for a road network and analyzes its mathematical properties [10].…”

Section: Introductionmentioning

confidence: 99%

Multi-class traffic models on road networks

Herty

Kirchner²,

Moutari³

2006

Communications in Mathematical Sciences

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Section: Introductionmentioning

confidence: 99%

Multi-class traffic models on road networks

Herty

Kirchner²,

Moutari³

2006

Communications in Mathematical Sciences

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“…In numerical simulations, many efforts were done for MCLWR model, Zhang et al [3] applied the weighted essentially non-oscillatory(WENO) scheme to the MCLWR model with heterogeneous drivers, and Chen et al [4] adopted the fourth relax scheme, and Ngoduy and Liu [5] use the first order HLLE(Harten-van Leer-Lax and Einfeldt) scheme and so on.…”

Section: Introductionmentioning

confidence: 99%

An improved WENO-Z scheme for a multi-class Lighthill-Whitham-Richards traffic flow model

Luo¹,

Tang²

2016

Proceedings of the 2016 International Forum on Energy, Environment and Sustainable Development

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Abstract. In this paper, we mainly propose a new semi-discrete central-upwind scheme to solve a MCLWR model based on fifth order improved WENO-Z reconstruction and semi-discrete central-upwind numerical fluxes. By introducing the new WENO-Z reconstruction, the order of accuracy of the schemes is improved, and preserve essential non-oscillatory property. The main advantage of this procedure is that the capacity of much better resolution at the smooth parts of the solution, while keeping the same numerical stability of the original WENO-Z at shocks and discontinuities. This property must be contrasted with classical upwind WENO schemes. The time integration we adopt is the third order TVD Runge-Kutta scheme. The effectiveness of our method is demonstrated in several numerical examples.

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“…System (5) has been extensively studied both in the mathematical and traffic flow literatures, e.g. (Wong and Wong, 2002;Zhang et al, 2003;2006;Herty et al, 2008;Jin, 2012). Such a system is well-posed if it is hyperbolic (Leveque, 1992).…”

Section: Introducing a New Modeling Framework With Multiple Macroscopmentioning

confidence: 99%

Macroscopic traffic dynamics with heterogeneous route patterns

Leclercq

Parzani

Knoop

et al. 2015

Transportation Research Part C: Emerging Technologies

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This paper investigates at an aggregated (macroscopic) scale the effects of route patterns on a road network. Four main variables are considered: the production, the mean speed, the outflow and the mean travel distance. First, a simple network with heterogeneous travel distances between origins and destinations is studied by simulation. It appears that the mean travel distance is not only very sensitive to the changes in the origin-destination (OD) matrix but also to the internal traffic conditions within the network. When this distance is assumed constant as usual in the literature, significant errors may appear when estimating the outflow at the network perimeter. The OD matrix also modifies the shape of the macroscopic fundamental diagram (MFD) to a lesser extend. Second, a new modelling framework is proposed to account for multiple macroscopic routes within reservoirs (spatial aggregates of road network) in the context of MFD simulation. In contrast to existing works, partial accumulations are defined per route and traffic waves are tracked at this level. This leads to a better representation of wave propagation between the reservoir frontiers. A Godunov scheme is combined to a HLL Riemann approximate solver in order to derive the model numerical solutions. The accuracy of the resulting scheme is assessed for several simple cases. The new framework is similar to some multiclass models that have been elaborated in the context of link traffic dynamics.

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A weighted essentially non-oscillatory numerical scheme for a multi-class Lighthill–Whitham–Richards traffic flow model

Cited by 82 publications

References 17 publications

Multi-class traffic models on road networks

Multi-class traffic models on road networks

An improved WENO-Z scheme for a multi-class Lighthill-Whitham-Richards traffic flow model

Macroscopic traffic dynamics with heterogeneous route patterns

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