GitHub - alikamp/Parks-KPBM-Scaling: Resolution robustness of vortex shedding in Lattice Boltzmann cylinder flow: a scaling study for reduced-cost simulation.

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.

Method Cells Wall Time St St Error Cd Cd Error Speedup

DNS (fine) 320,000 2958s 0.1333 ref 1.279 ref 1.0×

Coarse 2× 80,000 296s 0.1333 0.0% 1.325 3.6% 10.0×

Coarse 3× 35,511 81s 0.1300 2.5% 1.302 1.8% 36.7×

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