2024/05/31 by Niklas Kolbe, Kolbe, Niklas
Mathematics · Physics and Astronomy · #35L65 #90B10 #90B20 #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Physics of Superconductivity and Magnetism #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2405.21005
openalex publication_date 2024/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A new coupling rule for the Lighthill-Whitham-Richards model at merging junctions is introduced that imposes the preservation of the ratio between inflow from a given road to the total inflow into the junction. This rule is considered both in the context of the original traffic flow model and a relaxation setting giving rise to two different Riemann solvers that are discussed for merging 2-to-1 junctions. Numerical experiments are shown suggesting that the relaxation based Riemann solver is capable of suitable predictions of both, free-flow and congestion scenarios without relying on flow maximization.