**Powerpoint(
2000) version:**

talk1.ppt

Particle methods for rarefied gas and two-phase flows (plan) 1. Introduction

2. The Boltzmann equation

The particle acceleration

The drag force

The collision kernel

3. Scales of the problem

4. The Lagrangian approach: general algorithm of particle methods

Collision process in the homogeneous case

5. The Eulerian approach

6.1 Effects on particles of the fluid turbulence with RANS models (Case 1: Lagrangian approach)

A theoretical result on a Gossmann Ioannides type model

6.1 Effects on particles of the fluid turbulence with RANS models (Case 2: Eulerian approach)

6.2 Effects on particles of the fluid turbulence with LES models

7. Effects of particles on the fluid turbulence

Diagram of turbulence modulation

8. Justification of the particle self diffusion in a simple case