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Lagrangian-antidiffusive remap schemes for non-local multi-class traffic flow models

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Abstract

This paper focuses on the numerical approximation of the solutions of a class of non-local systems in one space dimension, arising in traffic modeling. We propose alternative simple schemes by splitting the non-local conservation laws into two different equations, namely the Lagrangian and the remap steps. We provide some properties and estimates recovered by approximating the problem with the Lagrangian-antidiffusive remap (L-AR) scheme, and we prove the convergence to weak solutions in the scalar case. Finally, we show some numerical simulations illustrating the efficiency of the L-AR schemes in comparison with classical first- and second-order numerical schemes.

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Acknowledgements

This research was supported by the Inria Associated Team Efficient numerical schemes for non-local transport phenomena (NOLOCO; 2018-2020). LMV is supported by CONICYT-Chile through FONDECYT project 1181511 and by project AFB170001 of the PIA Program: Concurso Apoyo a Centros Científicos y Tecnológicos de Excelencia con Financiamiento Basal.

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Authors and Affiliations

  1. Inria Sophia Antipolis-Méditerranée, Université Côte d’Azur, Inria, CNRS, LJAD, 2004 route des Lucioles, BP 93, 06902, Sophia Antipolis Cedex, France

    Felisia Angela Chiarello & Paola Goatin

  2. GIMNAP-Departamento de Matemáticas, Universidad del Bío-Bío, Casilla 5-C, Concepción, Chile

    Luis Miguel Villada

  3. CI2MA, Universidad de Concepción, Casilla 160-C, Concepción, Chile

    Luis Miguel Villada

Authors
  1. Felisia Angela Chiarello
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  2. Paola Goatin
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  3. Luis Miguel Villada
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Correspondence to Felisia Angela Chiarello.

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Communicated by Antonio José Silva Neto.

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Chiarello, F.A., Goatin, P. & Villada, L.M. Lagrangian-antidiffusive remap schemes for non-local multi-class traffic flow models. Comp. Appl. Math. 39, 60 (2020). https://doi.org/10.1007/s40314-020-1097-9

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  • DOI: https://doi.org/10.1007/s40314-020-1097-9

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