IEM Mixing and Statistical Averaging

Table of Contents

• 1. IEM Mixing Update In Current Code
• 2. Required Dataflow For IEM
• 4. Averaging Terminology In PICurv

PICurv currently couples a particle scalar micromixing model (IEM-style) with separate statistics/averaging utilities in solver and post-processing stages.

1. IEM Mixing Update In Current Code

For Psi, UpdateParticleField uses:

\[ \frac{d\Psi}{dt} = -\Omega(\Psi-\langle\Psi\rangle), \qquad \Omega = C_{IEM}\,\frac{\Gamma_{eff}}{\Delta^2}, \qquad \Delta^2\approx V^{2/3}. \]

Closed-form update implemented in code:

\[ \Psi^{n+1}=\langle\Psi\rangle + (\Psi^n-\langle\Psi\rangle)e^{-\Omega\Delta t}. \]

Code touchpoints:

• particle kernel: UpdateParticleField
• per-field particle loop: UpdateFieldForAllParticles
• stage wrapper: UpdateAllParticleFields

2. Required Dataflow For IEM

IEM update requires:

• per-particle diffusivity from swarm fields,
• host-cell IDs for indexing,
• Eulerian mean field (user->lPsi) and Jacobian (user->lAj) for volume scaling.

This means scatter/interpolation order matters: stale Eulerian means produce stale IEM forcing.

5. Statistics Pipeline

Current primary reduction kernel:

• ComputeParticleMSD

Implemented MSD physics includes:

\[ D = \frac{1}{Re\,Sc}, \qquad r_{theory} = \sqrt{6Dt}, \]

with global MPI reductions and CSV output per statistics call.

4. Averaging Terminology In PICurv

"Averaging" appears in multiple contexts:

• particle->grid count-normalized scatter,
• solver-side optional field averaging toggles,
• postprocessing global statistical reductions.

Treat these as distinct workflows with different configuration points.

1. Reference Scales

• Trilinear Interpolation and Particle-Grid Projection
• Particle Model and Coupling Overview
• Configuration Reference: Postprocessor YAML