Introduction to Particle Tracing Modeling

Particle tracing provides a Lagrangian description of a problem by solving ordinary differential equations using Newton’s law of motion. The trajectories of individual particles are always solved for in the time domain. Newton’s law of motion requires specification of the particle mass and all forces acting on the particle. The forces acting on particles may due to external fields which can be specified directly or computed using a different physics interface, often using the Finite Element Method (FEM).

For each particle, a second-order ordinary differential equation is solved for each component of the position vector. This means that three ordinary differential equations are solved for each particle in 3D and two in 2D. A first-order formulation of Newton’s law of motion is also available, in which coupled first-order ordinary differential equations are solved for the components of the particle position and velocity. The Mathematical Particle Tracing interface also includes a Hamiltonian formulation that solves coupled first-order ordinary differential equations for the particle position and generalized momentum.

At each time step taken by the solver, the forces acting on each particle are queried from the external fields at the current particle position. If particle-particle interaction forces are included in the model then they are added to the total force. The particle position is then updated and the process repeats until the specified end time for the simulation is reached. During each time step, the particles may interact with boundaries in the geometry, or they may be subjected to other phenomena that can discontinuously change the particle velocity.

Because the Particle Tracing Module uses a very general formulation for computing particle trajectories, the particle tracing interfaces can be used to model charged particle motion in electromagnetic fields, large scale planetary and galactic movement, and particle motion in laminar, turbulent, and multiphase fluid systems.