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PreprintCC BY-NC-ND 4.0HAL

A micro-macro numerical scheme for a self-organized hydrodynamics model enriched by a kinetic contribution

  • Marie Compain
  • Christophe Berthon
  • Anaïs Crestetto
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Abstract

The present work investigates the continuous individual based Couzin-Vicsek model, the associated kinetic model and its macroscopic derivation, called the Self-Organized Hydrodynamics (SOH) model.They describe self-organized motions, which emerge in nature as insect swarms or bird flocks for instance. In particular, the SOH model takes into account only motions where all individuals are part of the equilibrium. Here, according to a micro-macro decomposition, we enrich the model with a kinetic contribution of the deviation from equilibrium. First of all, a micro-macro model is derived. We then design an asymptotic preserving numerical scheme for this model, where the equilibrium variables are discretized thanks to a finite volume method, while the kinetic deviation is approximated with a particle method. Finally, some test cases are computed, and the micro-macro scheme is validated in different asymptotic regimes.

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Cite

BibTeXRIS
BibTeX
@misc{compain2026micromacro,
  title = {{A micro-macro numerical scheme for a self-organized hydrodynamics model enriched by a kinetic contribution}},
  author = {Marie Compain and Christophe Berthon and Anaïs Crestetto},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  url = {https://hal.science/hal-05760398v1},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - A micro-macro numerical scheme for a self-organized hydrodynamics model enriched by a kinetic contribution
AU  - Marie Compain
AU  - Christophe Berthon
AU  - Anaïs Crestetto
PY  - 2026
DA  - 2026/09/23
PB  - HAL
UR  - https://hal.science/hal-05760398v1
AB  - The present work investigates the continuous individual based Couzin-Vicsek model, the associated kinetic model and its macroscopic derivation, called the Self-Organized Hydrodynamics (SOH) model.They describe self-organized motions, which emerge in nature as insect swarms or bird flocks for instance. In particular, the SOH model takes into account only motions where all individuals are part of the equilibrium. Here, according to a micro-macro decomposition, we enrich the model with a kinetic contribution of the deviation from equilibrium. First of all, a micro-macro model is derived. We then design an asymptotic preserving numerical scheme for this model, where the equilibrium variables are discretized thanks to a finite volume method, while the kinetic deviation is approximated with a particle method. Finally, some test cases are computed, and the micro-macro scheme is validated in different asymptotic regimes.
ER  -