Particle Methods
Particles for multiphysics simulations
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 evolution of th trajectories and the evolution of the properties carried by the particles.
Lagrangian descriptions of discrete and continuum systems
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 a continuum, these properties can be macroscopic, e.g. density, momentum, vorticity,... for a discrete system, such as atoms, we will consider mass, velocity and electric charge.
Lagrangian descriptions of discrete and continuum systems
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 a continuum, these properties can be macroscopic, e.g. density, momentum, vorticity,... for a discrete system, such as atoms, we will consider mass, velocity and electric charge.
Molecular Dynamics of water and Carbon Nanotubes 
Particle Laden Flow Simulations Using Particles

Continuum systems, particle methods and computational challenges
We study Lagrangian, multiresolution, particle methods for the simulation of continuous systems with an empahsis on fluid mechanics applications. Particle methods, such as Smoothed Particle Hydrodynamics (SPH) and Vortex Methods (VM) enjoy the inherent robustness and adaptivity of Lagrangian methods. At the same time though, uncontrolled particle distortion leads to degraded accuracy and the computation of of spatial differential operators on the particles is highly inefficient. For these reasons, we develop hybrid particlemesh methodologies which periodically reinitialize the particle positions through high order, moment conserving interpolation and use the mesh for efficient computations of differential operators.
Remeshed particle methods: lost adaptivity?
Our hybrid particlemesh approach also allows consistent formulations for adaptivity, such as multiresolution analysis. We have developed the ParticleWavelet Method, a variant which combines the versatility and efficiency of gridbased Wavelet collocation methods while retaining the virtues of a particle method.
We study Lagrangian, multiresolution, particle methods for the simulation of continuous systems with an empahsis on fluid mechanics applications. Particle methods, such as Smoothed Particle Hydrodynamics (SPH) and Vortex Methods (VM) enjoy the inherent robustness and adaptivity of Lagrangian methods. At the same time though, uncontrolled particle distortion leads to degraded accuracy and the computation of of spatial differential operators on the particles is highly inefficient. For these reasons, we develop hybrid particlemesh methodologies which periodically reinitialize the particle positions through high order, moment conserving interpolation and use the mesh for efficient computations of differential operators.
Remeshed particle methods: lost adaptivity?
Our hybrid particlemesh approach also allows consistent formulations for adaptivity, such as multiresolution analysis. We have developed the ParticleWavelet Method, a variant which combines the versatility and efficiency of gridbased Wavelet collocation methods while retaining the virtues of a particle method.
left: Principle of wavelet based adaptation in 2D: after the data is compressed on a regular grid, particles are created with appropriate core sizes. middle and right: ParticleWavelet method as extended to the simulation of transport problems on implicit geometries: the particles adapt to small scales in both the function and the geometry on which it is defined.
Discrete particle methods : challenges and lessons from continuum simulations
We develop molecular dynamics (MD) for the simulation of flows at the atomistic scale and Dissipative Particle Dynamics (DPD) methods for the simulations of flows at mesoscopic scales. In these simualtions we employ Fast Poisson solvers that have been developed for related continuum simulations. Additional challenges involve simulations for nonperiodic boundaries and the coupling of atomisticcontinuum simulations. We develop a systematic framework for the simulation of hybrid atomisticcontinuum systems. The underlying idea is to use each method for a particular part of the domain depending on the flow physics that is being simulated. Applications involve : flows in nanodevices and flows of biological interest such as those in small arteries and in biosensors
We develop molecular dynamics (MD) for the simulation of flows at the atomistic scale and Dissipative Particle Dynamics (DPD) methods for the simulations of flows at mesoscopic scales. In these simualtions we employ Fast Poisson solvers that have been developed for related continuum simulations. Additional challenges involve simulations for nonperiodic boundaries and the coupling of atomisticcontinuum simulations. We develop a systematic framework for the simulation of hybrid atomisticcontinuum systems. The underlying idea is to use each method for a particular part of the domain depending on the flow physics that is being simulated. Applications involve : flows in nanodevices and flows of biological interest such as those in small arteries and in biosensors
People: Philippe Chatelain, Michael Bergdorf, Jens Honore Walther, Diego Rossinelli, Evangelos Kotsalis, Alvaro Foletti
Collaborators: Anthony Leonard (Caltech), GeorgesHenri Cottet (Grenoble), Richard Jaffe (NASA Ames)
Funding: ETHZ, Swiss National Science Foundation
Student Projects:
Selected Publications:
 P. Koumoutsakos, Multiscale flow simulations using particles, Annual Review Fluid Mechanics, 37, 45787, 2005 (Abstract) (pdf)
 M. Bergdorf, G.H. Cottet, P. Koumoutsakos, Multilevel adaptive particle methods for convectiondiffusion equations, Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 4(1), 328357, 2005 (Abstract) (pdf)
 I.F. Sbalzarini, J.H. Walther, M. Bergdorf, S.E. Hieber, E.M. Kotsalis, P. Koumoutsakos. PPM  A highly efficient parallel particlemesh library for the simulation of continuum systems. J. Computational Physics, 215:566588, 2006 (Abstract) (pdf)
 Chatelain P., Cottet G.H., Koumoutsakos P., Particle Mesh Hydrodynamics for Astrophysics Simulations, Int. J. Modern Physics C, 18, 4, 610618, 2007 (Abstract) (pdf)
 Altenhoff A., Walther J.H., Koumoutsakos P., A Stochastic Boundary Forcing for Dissipative Particle Dynamics, J. Computational Physics, 225, 11251136, 2007 (Abstract) (pdf)