A micro-macro numerical scheme for a self-organized hydrodynamics model enriched by a kinetic contribution
Year: 2026
Type: preprint
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.
Source: HAL
Institutions: Laboratoire de Mathématiques Jean Leray, Nantes Université
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214418251