Orateur
Description
From the Vicsek model, describing at the individual scale the motion of particles that tend to align with each others, a kinetic equation of Fokker-Planck type can be written. Works of Degond, Frouvelle, Motsch and Navoret investigate the large-scale ("hydrodynamic") limit, leading to the SOH model, and propose numerical scheme to approach its solution.
In this talk, I will first present a shock-preserving numerical scheme for the 1D SOH model. In our approach, the SOH model is composed of 2 equations: for the density and the velocity angle unknowns. We will then discuss a micro-macro model which aims to add a kinetic contribution to the SOH model. Here is the difficulty: the collisional operator of the kinetic model only admits a one-dimensional set of collisional invariants. This let us recover the macro equation on the density but not the equation on the velocity angle. To get this one, we have to consider "generalized" collision invariants. The obtained micro-macro model is well adapted to the development of asymptotic preserving scheme.
This work has been done with Marie Compain and Christophe Berthon.