2016/11/01 by Marco Di Francesco, Simone Fagioli, Di Francesco, Marco +5
Engineering · Social Sciences · #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Evacuation and Crowd Dynamics #FOS: Mathematics #Numerical Analysis (math.NA) #Traffic control and management #Transportation Planning and Optimization
paper · pdf · doi:10.48550/arxiv.1611.00319
openalex publication_date 2016/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We review our analytical and numerical results obtained on the microscopic Follow-The-Leader (FTL) many particle approximation of one-dimensional conservation laws. More precisely, we introduce deterministic particle schemes for the Hughes model for pedestrian movements and for two vehicular traffic models, that are the scalar Lighthill-Whitham-Richards model (LWR) and the 2×2 system Aw-Rascle-Zhang model (ARZ). Their approximation is performed by a set of ODEs, determining the motion of platoons of possible fractional vehicles or pedestrians seen as particles. Convergence results of the schemes in the many particle limit are stated. The numerical simulations suggest the consistency of the schemes.