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arxiv: 2509.23820 · v3 · submitted 2025-09-28 · ⚛️ physics.flu-dyn

Exploring the Applicability of the Lattice-Boltzmann Method for Two-Dimensional Turbulence Simulation

Raquel Dapena-Garc\'ia , Vicente P\'erez-Mu\~nuzuri This is my paper

Pith reviewed 2026-05-18 12:50 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords Lattice-Boltzmann methodtwo-dimensional turbulencevon Karman vortex streetrigid disksfluid dynamics simulationmesoscopic hydrodynamicsturbulent flow
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The pith

A custom Lattice-Boltzmann solver produces accurate results for two-dimensional turbulent flow around rigid disks by generating von Karman vortex streets.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper tests whether a custom Lattice-Boltzmann implementation can handle the challenges of two-dimensional turbulence. The authors place randomly located rigid disks in a flow field and examine the vortex streets that form in their wakes. A sympathetic reader would care because traditional methods struggle with turbulent regimes, and a mesoscopic lattice approach might offer a simpler route to reliable simulations. If the results hold, the method becomes a viable option for modeling flows with obstacles without extensive extra corrections for turbulence.

Core claim

The authors develop and apply a Lattice-Boltzmann solver to a two-dimensional turbulent flow containing randomly located rigid disks. The simulation generates the characteristic von Karman vortex street in the wake of these obstacles, which the authors present as evidence that the solver accurately captures the turbulent flow behavior.

What carries the argument

The Lattice-Boltzmann method, a mesoscopic approach that evolves particle distribution functions on a discrete lattice to recover the macroscopic Navier-Stokes equations for both laminar and turbulent flows.

If this is right

  • The solver can be used to study wake dynamics and turbulence in domains filled with multiple rigid obstacles.
  • Making the implementation available as supplementary material enables direct reproduction and extension by other researchers.
  • The approach handles the extra difficulties of turbulent flows that go beyond standard laminar cases.
  • Initial validation through pattern recognition can guide further development of the method for more demanding flow conditions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same qualitative validation strategy could be applied to test the method with different obstacle densities or Reynolds numbers.
  • If the 2D results prove robust, the implementation might be adapted to explore simplified models of real-world flows such as flow past arrays of cylinders.
  • Adding built-in quantitative diagnostics in future versions would make the accuracy claims easier to verify independently.

Load-bearing premise

That visual or qualitative agreement with expected von Karman vortex street patterns is sufficient to establish overall accuracy of the turbulent simulation without quantitative error metrics or comparison to established benchmarks.

What would settle it

A side-by-side quantitative comparison of velocity fields, energy spectra, or drag coefficients between the Lattice-Boltzmann results and those from a standard Navier-Stokes solver on the same random-disk setup that shows large systematic differences.

Figures

Figures reproduced from arXiv: 2509.23820 by Raquel Dapena-Garc\'ia, Vicente P\'erez-Mu\~nuzuri.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic of the D2Q9 velocity set. A fictitious particle located at the central node can move in eight possible [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Representation of the simulation setup. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Instantaneous visualization of a 2D flow passing through an array of disks for different disks sizes and Reynolds number: [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Spatio-temporal kinetic energy and enstrophy mean values as a function of the disk radius for several number of disks. [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Power spectral density (PSD) for the kinetic energy and enstrophy (left panel), and scaling exponents [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Spatio-temporal kinetic energy and enstrophy mean values as a function of the Reynolds number for various numbers [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
read the original abstract

The Lattice-Boltzmann method is a mesoscopic approach for solving hydrodynamic problems involving both laminar and turbulent fluids. Although the suitability for the former cases is supported by a myriad of studies, turbulent flows always give rise to additional challenges that need to be addressed properly. In this paper, we estimate the accuracy of the simulation results obtained via a custom implementation of a Lattice-Boltzmann solver for a two-dimensional turbulent flow. To this end, a two-dimensional flow field filled with randomly located rigid disks was simulated, and the von Karman vortex street generated after the wake of such obstacles was studied. To ensure reproducibility, the implementation underlying these results is provided as supplementary material.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript presents a custom Lattice-Boltzmann solver for two-dimensional turbulent flows. It estimates the accuracy of results by simulating flow past randomly located rigid disks and examining the von Karman vortex street formed in their wakes. The implementation is supplied as supplementary material to support reproducibility.

Significance. If the accuracy claim were supported by quantitative validation, the work would provide a reproducible LBM tool for 2D turbulence studies; the open supplementary code is a clear strength that aids verification.

major comments (1)
  1. [Abstract] Abstract: the accuracy estimate for the two-dimensional turbulent flow simulation is asserted via observation of the von Karman vortex street after randomly placed rigid disks. Vortex-street formation occurs in laminar-to-transitional regimes and does not test the inverse energy cascade, enstrophy cascade, or dissipation scaling that define 2D turbulence; no quantitative diagnostics (energy spectra, structure functions, or DNS/experiment comparisons at matched Re) are described.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive feedback on our manuscript. We address the major comment in detail below and indicate the changes we will make in revision.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the accuracy estimate for the two-dimensional turbulent flow simulation is asserted via observation of the von Karman vortex street after randomly placed rigid disks. Vortex-street formation occurs in laminar-to-transitional regimes and does not test the inverse energy cascade, enstrophy cascade, or dissipation scaling that define 2D turbulence; no quantitative diagnostics (energy spectra, structure functions, or DNS/experiment comparisons at matched Re) are described.

    Authors: We agree that the observation of von Karman vortex streets provides only a qualitative check and is primarily associated with laminar-to-transitional wake dynamics rather than the defining cascades and scaling of two-dimensional turbulence. The multi-disk configuration was chosen to create interacting wakes in a complex geometry at Reynolds numbers where turbulent features emerge, but we acknowledge that this does not constitute a rigorous test of inverse energy cascade, enstrophy cascade, or dissipation scaling. In the revised manuscript we will add quantitative diagnostics, specifically kinetic energy spectra and structure functions, together with comparisons to theoretical expectations or reference data at matched Reynolds numbers. These additions will be incorporated into both the abstract and the main text. revision: yes

Circularity Check

0 steps flagged

No circularity in derivation or validation chain

full rationale

The paper presents a numerical simulation study using a custom LBM solver for 2D flow past randomly placed rigid disks, with accuracy estimated via observation of von Karman vortex streets. No mathematical derivation chain, equations, or fitted parameters are described that would reduce the accuracy claim to a self-defined quantity or input by construction. No self-citations, uniqueness theorems, or ansatzes are invoked in a load-bearing way. The central claim rests on the simulation output itself rather than any circular reduction, making the work self-contained against external benchmarks even if the chosen validation (qualitative visualization) is limited in scope.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; the work relies on standard Lattice-Boltzmann assumptions for fluid dynamics.

pith-pipeline@v0.9.0 · 5652 in / 943 out tokens · 27926 ms · 2026-05-18T12:50:26.831032+00:00 · methodology

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Reference graph

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