IEM Mixing and Statistical Averaging

Table of Contents

• 1. IEM Mixing Update In Current Code
• 2. Required Dataflow For IEM
• 3. Statistics Pipeline (Postprocessor)
• 4. Averaging Terminology In PICurv
• 5. Related Pages
  • CFD Reader Guidance and Practical Use
    • What To Extract Before Changing A Case
    • Practical CFD Troubleshooting Pattern

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.

3. Statistics Pipeline (Postprocessor)

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.

5. Related Pages

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

CFD Reader Guidance and Practical Use

This page describes IEM Mixing and Statistical Averaging within the PICurv workflow. For CFD users, the most reliable reading strategy is to map the page content to a concrete run decision: what is configured, what runtime stage it influences, and which diagnostics should confirm expected behavior.

Treat this page as both a conceptual reference and a runbook. If you are debugging, pair the method/procedure described here with monitor output, generated runtime artifacts under runs/<run_id>/config, and the associated solver/post logs so numerical intent and implementation behavior stay aligned.

What To Extract Before Changing A Case

• Identify which YAML role or runtime stage this page governs.
• List the primary control knobs (tolerances, cadence, paths, selectors, or mode flags).
• Record expected success indicators (convergence trend, artifact presence, or stable derived metrics).
• Record failure signals that require rollback or parameter isolation.

Practical CFD Troubleshooting Pattern

1. Reproduce the issue on a tiny case or narrow timestep window.
2. Change one control at a time and keep all other roles/configs fixed.
3. Validate generated artifacts and logs after each change before scaling up.
4. If behavior remains inconsistent, compare against a known-good baseline example and re-check grid/BC consistency.