Resolution robustness of vortex shedding in Lattice Boltzmann cylinder flow: a scaling study for reduced-cost simulation.

Key Finding

Vortex shedding frequency in 2D cylinder flow at Re = 100 is remarkably robust under spatial coarsening. The Strouhal number is preserved within 2.5% across a 9× grid reduction (320,000 → 35,511 cells), yielding 37× wall time speedup. Mean drag coefficient remains within the literature range at all resolutions.

What This Means

The dominant wake physics behaves as a resolution-robust coherent mode: the vortex shedding frequency is set by global geometry and Reynolds number, not by fine-scale boundary layer resolution. This has implications for:

• Reduced-order modelling: coarsened simulations preserve dominant flow physics
• Adaptive mesh strategies: resolution can be targeted where force accuracy matters, not where frequency is already captured
• Sub-grid model design: models should target force amplitude recovery rather than frequency recovery, since frequency is already preserved by large-scale dynamics

Motivation

This work is part of the Kinetic-Pressure Ballooning Model (KPBM) framework, which proposes that vortex shedding can be understood as a geometric instability at the interface between fast and slow fluid regions. The scaling study establishes the DNS baseline against which KPBM's sub-grid enhancement can be rigorously evaluated.

The KPBM target (red diamond in panel d) is: 37× speedup with recovered DNS-level accuracy — matching the coarse grid's speed while recovering the fine grid's precision through nodal stability checks at high-shear interfaces.

Related Work

• Parks Node Ejection Protocol (PNEP) — geometric diagnostic for gravitational few-body dynamics
• Parks ISW Morphology — morphology-dependent ISW signal in Planck CMB data

All three projects share a common principle: sparse geometric sampling at privileged moments preserves dominant physics at reduced computational cost.

Repository Structure

├── README.md
├── Parks_KPBM_scaling.pdf       # Paper
├── Parks_KPBM_scaling.tex       # LaTeX source
├── fig_scaling_tradeoff.png     # Main figure
├── make_figure.py               # Figure generation script
├── figures/
│   └── fig_scaling_tradeoff.png
├── results/
│   └── scaling_results.json     # Machine-readable results
├── solvers/
│   └── validated_lbm.py         # D2Q9 LBM solver
├── ci/
│   ├── golden_harness.py        # CI validation pipeline
│   └── reference_values.json    # Benchmark values
└── LICENSE

Reproducing the Results

Requirements

pip install numpy scipy matplotlib

Quick run (Colab-friendly)

from solvers.validated_lbm import run_case

# Fine grid (DNS baseline)
r100 = run_case(800, 400, Re=100, U_inf=0.04, N_steps=25000, label="DNS")

# Coarse 2x
r100_c2 = run_case(400, 200, Re=100, U_inf=0.04, N_steps=12500, label="2x")

# Coarse 3x
r100_c3 = run_case(267, 133, Re=100, U_inf=0.04, N_steps=8333, label="3x")

CI validation

cd ci/
python golden_harness.py

Results Summary

Benchmark: 2D Cylinder, Re = 100, D2Q9 LBM
Geometry: Frozen (20:10 aspect, 10% blockage)
Dynamic similarity: Re as only control parameter

DNS:      St = 0.1333,  Cd = 1.279,  320,000 cells,  2958s
2x coarse: St = 0.1333,  Cd = 1.325,   80,000 cells,   296s  (10x faster)
3x coarse: St = 0.1300,  Cd = 1.302,   35,511 cells,    81s  (37x faster)

Key: Frequency preserved, force amplitude degrades moderately.

Limitations

• Absolute St (0.133) is 18.7% below literature (0.164) due to 10% blockage ratio
• Internal consistency across resolutions is excellent
• 2D only; 3D vortex stretching not addressed
• Re = 100 only; higher Re and turbulent transition not tested

Author

Alika M. Parks — Independent Researcher, Kalaheo, HI, USA — alikamp@gmail.com

License

MIT