Annu. Rev. Fluid Mech. 2005. 37:457–87 doi: 10.1146/annurev.fluid.37.061903.175753 Copyright c  2005 by Annual Reviews. All rights reserved MULTISCALE FLOW SIMULATIONS USING PARTICLES Petros Koumoutsakos Computational Science and Engineering Laboratory, Swiss Federal Institute of Technology, Zurich, CH-8001, Switzerland; email: petros@inf.ethz.ch Key Words vortex methods, smooth particle hydrodynamics, molecular dynamics, continuum-molecular simulations, domain decomposition ■ Abstract Flow simulations are one of the archetypal multiscale problems. Sim- ulations of turbulent and unsteady separated flows have to resolve a multitude of interacting scales, whereas molecular phenomena determine the structure of shocks and the validity of the no-slip boundary condition. Particle simulations of continuum and molecular phenomena can be formulated by following the motion of interacting particles that carry the physical properties of the flow. In this article we review La- grangian, multiresolution, particle methods such as vortex methods and smooth particle hydrodynamics for the simulation of continuous flows and molecular dynamics for the simulation of flows at the atomistic scale. We review hybrid molecular-continuum sim- ulations with an emphasis on the computational aspects of the problem. We identify the common computational characteristics of particle methods and discuss their properties that enable the formulation of a systematic framework for multiscale flow simulations. 1. INTRODUCTION The simulation of the motion of interacting particles is a deceivingly simple, yet powerful and natural, method for exploring physical systems as diverse as planetary dark matter and proteins, unsteady separated flows, and plasmas. Particles can be viewed as objects carrying a physical property of a system, that is being simulated through the solution of Ordinary Differential Equations (ODEs) that determine the trajectories and the evolution of the properties carried by the particles. Particle methods amount to the solution of a system of ODEs: d x p dt = u p (x p , t ) = N  q =1 K (x p , x q ; ω p , ω q ) (1) d ω p dt = N  q =1 F(x p , x q ; ω p , ω q ), (2) 0066-4189/05/0115-0457$14.00 457 Annu. Rev. Fluid Mech. 2005.37:457-487. Downloaded from arjournals.annualreviews.org by Institute of Mechanics - Chinese Academy of Sciences on 01/17/07. For personal use only.