Well-posedness and finite volume approximations of the LWR traffic flow model with non-local velocity

Paola Goatin; Sheila  Scialanga; Paola Goatin; Sheila  Scialanga

doi:10.3934/nhm.2016.11.107

Networks and Heterogeneous Media

2016, Volume 11, Issue 1: 107-121. doi: 10.3934/nhm.2016.11.107

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Well-posedness and finite volume approximations of the LWR traffic flow model with non-local velocity

Paola Goatin ^{1
,},
Sheila Scialanga ^{2
,}

1.
INRIA Sophia Antipolis - Méditerranée, EPI OPALE, 2004, route des Lucioles - BP 93, 06902 Sophia Antipolis Cedex
2.
Inria Sophia Antipolis - Méditerranée, 2004, route des Lucioles - BP 93, 06902 Sophia Antipolis Cedex

Received: 01 April 2015 Revised: 01 October 2015
Primary: 35L65; Secondary: 65M12, 90B20.

We consider an extension of the traffic flow model proposed by Lighthill, Whitham and Richards, in which the mean velocity depends on a weighted mean of the downstream traffic density. We prove well-posedness and a regularity result for entropy weak solutions of the corresponding Cauchy problem, and use a finite volume central scheme to compute approximate solutions. We perform numerical tests to illustrate the theoretical results and to investigate the limit as the convolution kernel tends to a Dirac delta function.
- Scalar conservation laws,
- non-local flux,
- macroscopic traffic flow models,
- finite volume schemes
Citation: Paola Goatin, Sheila Scialanga. Well-posedness and finite volume approximations of the LWR traffic flow model with non-local velocity[J]. Networks and Heterogeneous Media, 2016, 11(1): 107-121. doi: 10.3934/nhm.2016.11.107

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Abstract

We consider an extension of the traffic flow model proposed by Lighthill, Whitham and Richards, in which the mean velocity depends on a weighted mean of the downstream traffic density. We prove well-posedness and a regularity result for entropy weak solutions of the corresponding Cauchy problem, and use a finite volume central scheme to compute approximate solutions. We perform numerical tests to illustrate the theoretical results and to investigate the limit as the convolution kernel tends to a Dirac delta function.

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