A nonlocal Lagrangian traffic flow model and the zero-filter limit
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866917560731041792 |
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| author | Coclite, Giuseppe M. Karlsen, Kenneth H. Risebro, Nils Henrik |
| author_facet | Coclite, Giuseppe M. Karlsen, Kenneth H. Risebro, Nils Henrik |
| contents | In this study, we start from a Follow-the-Leaders model for traffic flow that is based on a weighted harmonic mean (in Lagrangian coordinates) of the downstream car density. This results in a nonlocal Lagrangian partial differential equation (PDE) model for traffic flow. We demonstrate the well-posedness of the Lagrangian model in the $L^1$ sense. Additionally, we rigorously show that our model coincides with the Lagrangian formulation of the local LWR model in the ``zero-filter'' (nonlocal-to-local) limit. We present numerical simulations of the new model. One significant advantage of the proposed model is that it allows for simple proofs of (i) estimates that do not depend on the ``filter size'' and (ii) the dissipation of an arbitrary convex entropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_03889 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A nonlocal Lagrangian traffic flow model and the zero-filter limit Coclite, Giuseppe M. Karlsen, Kenneth H. Risebro, Nils Henrik Analysis of PDEs 35L65, 65M12, 90B20 In this study, we start from a Follow-the-Leaders model for traffic flow that is based on a weighted harmonic mean (in Lagrangian coordinates) of the downstream car density. This results in a nonlocal Lagrangian partial differential equation (PDE) model for traffic flow. We demonstrate the well-posedness of the Lagrangian model in the $L^1$ sense. Additionally, we rigorously show that our model coincides with the Lagrangian formulation of the local LWR model in the ``zero-filter'' (nonlocal-to-local) limit. We present numerical simulations of the new model. One significant advantage of the proposed model is that it allows for simple proofs of (i) estimates that do not depend on the ``filter size'' and (ii) the dissipation of an arbitrary convex entropy. |
| title | A nonlocal Lagrangian traffic flow model and the zero-filter limit |
| topic | Analysis of PDEs 35L65, 65M12, 90B20 |
| url | https://arxiv.org/abs/2302.03889 |