Hydrodynamic singular regimes in 1 + 1 kinetic models and spectral numerical methods

1 Numerical Methods for Delay Models in

Particle, Kinetic, and Hydrodynamic Models of Swarming

We review the state-of-the-art in the modelling of the aggregation and collective behavior of interacting agents of similar size and body type, typically called swarming. Starting with individual-based models based on “particle”-like assumptions, we connect to hydrodynamic/macroscopic descriptions of collective motion via kinetic theory. We emphasize the role of the kinetic viewpoint in the mod...

Kinetic and hydrodynamic models of chemotactic aggregation

We derive general kinetic and hydrodynamic models of chemotactic aggregation that describe certain features of the morphogenesis of biological colonies (like bacteria, amoebae, endothelial cells or social insects). Starting from a stochastic model defined in terms of N coupled Langevin equations, we derive a nonlinear mean field Fokker-Planck equation governing the evolution of the distribution...

A hybrid method for hydrodynamic-kinetic flow - Part II - Coupling of hydrodynamic and kinetic models

In this work we present a non stationary domain decomposition algorithm for multiscale hydrodynamic-kinetic problems, in which the Knudsen number may span from equilibrium to highly rarefied regimes. Our approach is characterized by using the full Boltzmann equation for the kinetic regime, the Compressible Euler equations for equilibrium, with a buffer zone in which the BGK-ES equation is used ...

Spectral Element Method Part 1 : Numerical

SPECTRAL ELEMENT METHOD PART 1: NUMERICAL ALGORITHMS Aimé Fournier, Joseph Tribbia National Center for Atmospheri Resear h Boulder CO 80307-3000 USA fournier u ar.edu Mark A. Taylor Albuquerque NM 87108 USA www.s d.u ar.edu/ ss/staff/taylor ABSTRACT It is well known that the fast and a urate solution of the partial di erential equations (PDEs) governing geophysi al uid dynami s presents a great...