Particle Tracing Module

Particle Tracing Module

• Released with version 4.2a in October 2011

• Add-on to COMSOL Multiphysics

• Combines with any COMSOL Multiphysics Module

Particle Tracing

• Particle tracing can be used as an alternative to

the finite element method for solving real world

physics problems

• Advantages:

– No numerical instabilities which occur in the finite element

method due to high Peclet numbers

– Much simpler mathematics involved in formulating the

problem

– Solves a different class of problems which COMSOL

currently can’t handle

Ion cyclotron motion

Key Applications

• AC/DC – Mass spectrometry

– Beam physics and ion optics

• Fluid Flow – Fluid flow visualization

– Sprays

– Separation and filtration

• RF – Ray tracing for smoothly graded materials (limited

ray tracing)

• Plasma – Ion energy distribution function

• Acoustics – Acoustic streaming

• Mathematics – Classical mechanics

Ion energy distribution function

Particle trajectories in a static mixer

Key Features

• Particle tracing is now available as a physics interface

which means: – The powerful solvers used to solve finite element based problems in

COMSOL can be utilized

– Hundreds of thousands of particles can be modeled comfortably

– Parametric sweep machinery can be used

– Boundary conditions can be applied to the particles

– Solution is stored in the model rather than computed during

postprocessing

– Implicit timestepping

– Particle/field interaction is supported

– Predefined forces are available as features in the model tree

– Hamiltonian formulation allows ray tracing to be modeled

– New postprocessing tools

Luneburg lens

Quadrupole mass spectrometer

Magnetic lens

Physics Interfaces

• There are three physics interfaces included with the

Particle Tracing Module

• Mathematical Particle Tracing – Specify the equations of motion using Massless, Newtonian,

Lagrangian or Hamiltonian formulations

– Complete freedom over the equations solved allows, for example,

ray tracing to be modeled

• Charged Particle Tracing – Model ion and electron trajectories in electric and magnetic fields

– Easy to define electric, magnetic and collisional forces

• Particle Tracing for Fluid Flow – Model microscopic and macroscopic particles in a fluid

– Includes drag, gravitational, dielectrophoretic, acoustophoretic and

many other forces

Charged Particle Tracing

• Use this to model ion and electron trajectories in

electric and magnetic fields

• Predefined forces

• Typically the fields are pre-computed from one of

the AC/DC interfaces

• Particle-field interactions

Particle Tracing for Fluid Flow

• Use this to model motion of microscopic

particles in a fluid

• Predefined forces

• Typically the velocity field is pre-computed

using one of the interfaces in the CFD or

Microfluidics modules

• Fluid-particle interactions

Formulation Equation of motion Charged Particle in a Magnetic Field

Lagrangian

Hamiltonian

Newtonian

Massless N/A

Mathematical Particle Tracing

• Complete freedom over the equations solved for each particle

– Analogous to the PDE modes offered in COMSOL Multiphysics

• Many different ways of solving the same problem, for example:

Boundary conditions - Freeze

• Freeze (default)

– Particles stick to the wall when they strike it

– The velocity of the particles at the moment of impact with the wall is frozen for

all subsequent timesteps.

– This is useful to recover the velocity and energy distribution function of particles

when they strike the wall

– Used to compute the ion energy distribution function in plasma models

Boundary conditions - Bounce

• Bounce

– Particles can bounce off walls (specular reflection) for the Newtonian,

Lagrangian and Hamiltonian formulations

– This option is not available for Massless particle tracing

– Momentum is conserved exactly

– Useful in fluid based applications and on symmetry axis

Boundary conditions

Stick

Disappear Bounce

Freeze (default)

Release of Particles

• Mesh Based

– Set the refinement factor. The higher the refinement factor, the more particles

are released.

• Set the density of particles proportional to an expression

– The expression can be a function of parameters and variables. Setting this to

one will give a uniform distribution.

• Uniform distribution on boundaries

– Gives an exact uniform distribution of particles on flat surfaces.

• Grid based particle release

– Enter a grid of coordinates for the initial positions of the particles.

Mesh Based Particle Release

Refinement factor =

1

Refinement factor =

2

Density Based Particle Release

Expression = 1 Expression = 1/(x2+y2)

Grid Based Particle Release

Release uniformly from -0.4 to 0.4 Graded grid

Uniform Particle Release

Uniform release on a boundary Uniform release on a boundary in 3D

Postprocessing Features

• Particle trajectory plots

• Poincare sections & maps

• Phase portraits

• Point and click on particles interactively

• Animations

• Histograms

• Transmission probabilities Phase portrait

Poincare map for a Rossler attractor

Advanced Features

• Particle-field interaction

• Add auxiliary dependent variables to

compute particle mass, temperature, spin

etc

• Integrate auxiliary dependent variables with

respect to time or along the particle

trajectory

• Reflect particles off walls (specular

reflection)

• User defined forces

Particle field interaction

Integrated shear rate

along particle trajectories

Summary

• Flexible particle tracing tool for all types of

physics

• Addresses many of the problems reported

by our user base with the current particle

tracing functionality

• Advanced modeling tools

• Massless, Newtonian, Lagrangian and

Hamiltonian formulations

Mixing in a static mixer

END