Particle Tracing Module

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1 Particle Tracing Module

2 Particle Tracing Module Released with version 4.2a in October 2011 Add-on to COMSOL Multiphysics Combines with any COMSOL Multiphysics Module

3

4 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

5 Key Applications Particle trajectories in a static mixer AC/DC Mass spectrometry Beam physics and ion optics Fluid Flow RF Fluid flow visualization Sprays Separation and filtration Ray tracing for smoothly graded materials (limited ray tracing) Plasma Ion energy distribution function Acoustics Acoustic streaming Mathematics Classical mechanics Ion energy distribution function

6 Key Features Luneburg lens 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 Magnetic lens Quadrupole mass spectrometer

7 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

8 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

9 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

10 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: Formulation Equation of motion Charged Particle in a Magnetic Field Lagrangian Hamiltonian Newtonian Massless N/A

11 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

12 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

13 Boundary conditions Freeze (default) Stick Disappear Bounce

14 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.

15 Mesh Based Particle Release Refinement factor = 1 Refinement factor = 2

16 Density Based Particle Release Expression = 1 Expression = 1/(x 2 +y 2 )

17 Grid Based Particle Release Release uniformly from -0.4 to 0.4 Graded grid

18 Uniform Particle Release Uniform release on a boundary Uniform release on a boundary in 3D

19 Postprocessing Features Particle trajectory plots Poincare sections & maps Phase portraits Point and click on particles interactively Animations Histograms Transmission probabilities Poincare map for a Rossler attractor Phase portrait

20 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

21 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

22 END

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