In this paper, we review recent developments on the derivation and properties of macroscopic models of collective motion and self-organization. The starting point is a model of self-propelled particles interacting with its neighbors through alignment. We successively derive a mean-field model and its hydrodynamic limit. The resulting macroscopic model is the Self-Organized Hydrodynamics (SOH). We review the available existence results and known properties of the SOH model and discuss it in view...
We build a non-dissipative second order algorithm for the approximate resolution of the
one-dimensional Euler system of compressible gas dynamics with two components. The
considered model was proposed in [1]. The algorithm is based on [8] which deals with a
non-dissipative first order resolution in Lagrange-remap formalism. In the present paper
we describe, in the same framework, an algorithm that is second order accurate in time and
space, and that...
In this work, we consider the computation of the boundary conditions for the linearized
Euler–Poisson derived from the BGK kinetic model in the small mean free path regime.
Boundary layers are generated from the fact that the incoming kinetic flux might be far
from the thermodynamical equilibrium. In [2], the authors propose a method to compute
numerically the boundary conditions in the hydrodynamic limit relying on an analysis of
the boundary layers....
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