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A Deterministic Particle Approximation for Non-linear Conservation Laws

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Theory, Numerics and Applications of Hyperbolic Problems I (HYP 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 236))

Abstract

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 \(2\times 2\) 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.

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Author information

Authors and Affiliations

  1. DISIM, Università degli Studi dell’Aquila, via Vetoio 1 (Coppito), 67100, L’Aquila, Italy

    Marco Di Francesco & Simone Fagioli

  2. Instytut Matematyki, Uniwersytet Marii Curie-Skłodowskiej, pl. Marii Curie-Skłodowskiej 1, 20-031, Lublin, Poland

    Massimiliano D. Rosini

  3. Dipartimento di Matematica ed Informatica, Università di Catania, viale Andrea Doria 6, 95125, Catania, Italy

    Giovanni Russo

Authors
  1. Marco Di Francesco
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  2. Simone Fagioli
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  3. Massimiliano D. Rosini
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  4. Giovanni Russo
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Corresponding author

Correspondence to Massimiliano D. Rosini .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Würzburg University, Würzburg, Germany

    Christian Klingenberg

  2. Department of Mathematics, RWTH Aachen University, Aachen, Germany

    Michael Westdickenberg

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Di Francesco, M., Fagioli, S., Rosini, M.D., Russo, G. (2018). A Deterministic Particle Approximation for Non-linear Conservation Laws. In: Klingenberg, C., Westdickenberg, M. (eds) Theory, Numerics and Applications of Hyperbolic Problems I. HYP 2016. Springer Proceedings in Mathematics & Statistics, vol 236. Springer, Cham. https://doi.org/10.1007/978-3-319-91545-6_37

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