Influence of a slow moving vehicle on traffic: Well-posedness and approximation for a mildly nonlocal model
| Autor: | Abraham Sylla |
|---|---|
| Přispěvatelé: | Sylla, Abraham, Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Conservation law Finite volume method Applied Mathematics Scalar (mathematics) General Engineering Macroscopic model Ode [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA] 01 natural sciences Computer Science Applications 010101 applied mathematics finite volume scheme Applied mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] 0101 mathematics [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP] Moving vehicle non-local point constraint Road traffic Scalar conservation law Well posedness [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] Mathematics |
| Popis: | In this paper, we propose a macroscopic model that describes the influence of a slow moving large vehicle on road traffic. The model consists of a scalar conservation law with a non-local constraint on the flux. The constraint level depends on the trajectory of the slower vehicle which is given by an ODE depending on the downstream traffic density. After proving well-posedness, we first build a finite volume scheme and prove its convergence, and then investigate numerically this model by performing a series of tests. In particular, the link with the limit local problem of [M.L. Delle Monache and P. Goatin, J. Differ. Equ. 257(11), 4015-4029 (2014)] is explored numerically. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|