A review on attractive–repulsive hydrodynamics for consensus in collective behavior

José A. Carrillo, Young Pil Choi, Sergio P. Perez

Research output: Chapter in Book/Report/Conference proceedingChapter

53 Citations (Scopus)


This survey summarizes and illustrates the main qualitative properties of hydrodynamics models for collective behavior. These models include a velocity consensus term together with attractive–repulsive potentials leading to non-trivial flock profiles. The connection between the underlying particle systems and the swarming hydrodynamic equations is performed through kinetic theory modeling arguments. We focus on Lagrangian schemes for the hydrodynamic systems showing the different qualitative behaviors of the systems and its capability of keeping properties of the original particle models. We illustrate the known results concerning large-time profiles and blowup in finite time of the hydrodynamic systems to validate the numerical scheme. We finally explore the unknown situations making use of the numerical scheme showcasing a number of conjectures based on the numerical results.

Original languageEnglish
Title of host publicationModeling and Simulation in Science, Engineering and Technology
PublisherSpringer Basel
Number of pages40
Publication statusPublished - 2017

Publication series

NameModeling and Simulation in Science, Engineering and Technology
ISSN (Print)2164-3679
ISSN (Electronic)2164-3725

Bibliographical note

Funding Information:
Acknowledgements J. A. C. was partially supported by the Royal Society via a Wolfson Research Merit Award. J. A. C. and Y. -P. C. were partially supported by EPSRC grant EP/K008404/1. Y. -P. C. was supported by the ERC-Stating grant HDSPCONTR “High-Dimensional Sparse Optimal Control”. S. P. P. was partially supported by a Erasmus+ scholarship.

Publisher Copyright:
© Springer International Publishing AG 2017.

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Engineering(all)
  • Fluid Flow and Transfer Processes
  • Computational Mathematics


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