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arxiv: 2605.20565 · v1 · pith:VVYF3FSMnew · submitted 2026-05-19 · ⚛️ physics.flu-dyn

Simulations of Particle-Laden Flows with Large Dispersed-Phase Size Disparities Using Highly Scalable Parallel Adaptive Methods

Linfeng Jiang , Enrico Calzavarini , Dominik Krug This is my paper

Pith reviewed 2026-05-21 05:58 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords multiphase flowsadaptive octree gridslattice Boltzmann methodimmersed boundary methodbubble-particle collisionsparticle-laden flowshydrodynamic interception
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The pith

A parallel adaptive octree framework couples lattice Boltzmann and immersed boundary methods to simulate flows with large particle size disparities.

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

The paper develops a computational framework for multiphase flows where objects like millimeter bubbles and micron particles differ greatly in scale. It combines the lattice Boltzmann method with the immersed boundary method on dynamically adaptive octree grids and adds a parallel host-cell searching algorithm to track many small Lagrangian particles efficiently across distributed grids. This setup resolves thin boundary layers around large objects without the expense of uniform fine grids over the entire domain. Validation on standard cases such as oscillating cylinders and sedimenting spheres confirms the method's accuracy before it is applied to bubble-particle collisions.

Core claim

The framework couples the lattice Boltzmann method with the immersed boundary method on a dynamically adaptive octree grid and introduces a parallel host-cell searching algorithm to track large numbers of small particles. In quiescent flow, this setup captures the hydrodynamic interception mechanism and reproduces the theoretical collision efficiency scaling law proportional to the square of the particle-to-bubble size ratio. The same framework is then used for fully resolved bubbles interacting with inertial point particles in homogeneous isotropic turbulence.

What carries the argument

The parallel host-cell searching algorithm on distributed adaptive octree grids, which tracks Lagrangian points representing small particles while coupling to the immersed boundary method for large finite-size objects.

Load-bearing premise

The parallel host-cell searching algorithm correctly and efficiently tracks Lagrangian points for small particles without significant numerical errors or load imbalances when coupled to the immersed boundary method for large objects.

What would settle it

A simulation of bubble-particle collisions in quiescent flow that fails to reproduce the collision efficiency scaling law proportional to the square of the particle-to-bubble size ratio would show that the hydrodynamic interception mechanism is not accurately captured.

Figures

Figures reproduced from arXiv: 2605.20565 by Dominik Krug, Enrico Calzavarini, Linfeng Jiang.

Figure 1
Figure 1. Figure 1: Schematic illustration of one collision-streaming loop on the coarse grid (level [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Flowchart of the recursive time-stepping algorithm for the coupled LBM-IBM solver on adaptive grids. The diagram illustrates how [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Illustration of the parallel adaptive grid configuration for the LBM-IBM simulation of flow past a cylinder. (a) Grid-level distribution [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Illustration of two types of parallel processes of Lagrangian points. Panels (a–c) show the redistribution of Lagrangian points across [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The speedup of the proposed algorithm for the Lagrangian data communication step compared with the communication step using [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of the primary and auxiliary grid structures. (a) Representation of the grid cells: The left side shows the LBM fluid [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Velocity profiles for three different phase angles (a) [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Temporal evolution of the drag coefficient ( [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Comparison of numerical results with the experimental data of ten Cate et al. [39] for sphere sedimentation. (a) Time evolution of [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: (a) Drag coefficient CD of the bubble as a function of Reynolds number Reb. The solid line represents the standard empirical correlation [44]. (b) Collision efficiency Ec versus particle-to-bubble radius ratio rp/rb for different Reb, demonstrating the square-law scaling. (c) The proportionality coefficient αc, extracted from the power-law fits Ec = αc(rp/rb) 2 , as a function of Reb. Open circles denote … view at source ↗
Figure 11
Figure 11. Figure 11: (a) Temporal evolution of the normalized turbulent kinetic energy comparing the adaptive grid simulation (with a moving refinement [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
read the original abstract

The numerical simulation of multiphase flows involving dispersed components with large scale disparities, such as the collisions between millimeter-sized bubbles and micron-sized mineral particles in flotation, poses a significant computational challenge. Accurately resolving the thin boundary layers of finite-size objects while tracking massive numbers of small particles within a large turbulent domain is often prohibitively expensive on uniform grids. To address this, we present a parallel scalable computational framework that couples the lattice Boltzmann method with the immersed boundary method on a dynamically adaptive octree grid. A key algorithm is developed for the efficient parallel host-cell searching, which significantly accelerates the tracking of Lagrangian points on distributed unstructured grids. The accuracy and robustness of the code are rigorously validated against canonical benchmarks, including the flow induced by an oscillating cylinder and the sedimentation of a sphere. The framework is applied to the multiscale problem of bubble-particle collisions. In quiescent flow, the simulations accurately capture the hydrodynamic interception mechanism, reproducing the theoretical collision efficiency scaling law proportional to the square of the particle-to-bubble size ratio. Furthermore, the framework is applied to the simulation of fully resolved bubbles interacting with inertial point particles in homogeneous isotropic turbulence.

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 / 1 minor

Summary. The manuscript presents a parallel scalable framework coupling the lattice Boltzmann method with the immersed boundary method on dynamically adaptive octree grids for multiphase flows with large dispersed-phase size disparities (e.g., millimeter bubbles and micron particles). A central algorithmic contribution is a parallel host-cell searching method to accelerate Lagrangian point tracking on distributed grids. The code is validated on canonical single-body problems (oscillating cylinder flow and sedimenting sphere) and then applied to bubble-particle collisions, where it is reported to reproduce the theoretical hydrodynamic interception scaling of collision efficiency proportional to the square of the particle-to-bubble size ratio in quiescent flow, together with fully resolved simulations in homogeneous isotropic turbulence.

Significance. If the accuracy claims hold, the work would provide a practical route to high-fidelity simulation of multiscale particle-laden flows that are currently limited by uniform-grid cost, with direct relevance to industrial processes such as flotation. The emphasis on distributed adaptive octrees and the new host-cell search algorithm addresses a genuine computational bottleneck; the reproduction of an independent theoretical scaling law is a positive indicator of fidelity when the supporting evidence is robust.

major comments (1)
  1. [Abstract and application to bubble-particle collisions] Abstract and bubble-particle collision results: the central claim that the simulations 'accurately capture the hydrodynamic interception mechanism' and reproduce the (r_p/r_b)^2 collision-efficiency scaling rests on the fidelity of Lagrangian trajectory integration near the immersed bubble surface. The only validations described are single-body benchmarks (oscillating cylinder, sedimenting sphere) that do not exercise the coupled IBM-Lagrangian system at the relevant scale disparity; no trajectory-error comparison against analytic Stokes flow around a sphere or grid-convergence study of computed efficiency versus r_p/r_b is reported. This leaves open the possibility that interpolation or load-balancing artifacts localized near the bubble could affect the distinction between colliding and non-colliding streamlines.
minor comments (1)
  1. [Abstract] The abstract states that accuracy is 'rigorously validated' yet provides no quantitative error norms, grid sizes, or figure references; adding these would improve clarity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive and detailed review. The comments highlight an important aspect of validation for the coupled IBM-Lagrangian system under large scale disparities. We address the point below and will incorporate additional evidence in the revised manuscript.

read point-by-point responses

  1. Referee: [Abstract and application to bubble-particle collisions] Abstract and bubble-particle collision results: the central claim that the simulations 'accurately capture the hydrodynamic interception mechanism' and reproduce the (r_p/r_b)^2 collision-efficiency scaling rests on the fidelity of Lagrangian trajectory integration near the immersed bubble surface. The only validations described are single-body benchmarks (oscillating cylinder, sedimenting sphere) that do not exercise the coupled IBM-Lagrangian system at the relevant scale disparity; no trajectory-error comparison against analytic Stokes flow around a sphere or grid-convergence study of computed efficiency versus r_p/r_b is reported. This leaves open the possibility that interpolation or load-balancing artifacts localized near the bubble could affect the distinction between colliding and non-colliding streamlines.

    Authors: We agree that direct validation of Lagrangian trajectory accuracy near the immersed surface at the relevant scale disparity would strengthen the central claim. The oscillating-cylinder and sedimenting-sphere benchmarks confirm the accuracy of the IBM-LBM coupling and adaptive-grid resolution for single-body flows, while the parallel host-cell search algorithm is specifically constructed to maintain consistent interpolation and load balance for Lagrangian points on distributed octree meshes. The reproduction of the exact theoretical (r_p/r_b)^2 scaling in quiescent flow provides supporting evidence that systematic artifacts are not present, because any consistent bias in near-surface trajectories would be expected to alter the scaling. Nevertheless, to address the referee’s concern explicitly, we will add two new elements to the revised manuscript: (i) a quantitative comparison of computed particle trajectories against the analytic Stokes flow solution around a sphere, reporting trajectory-error norms as a function of grid resolution, and (ii) a grid-convergence study of collision efficiency for several r_p/r_b ratios, demonstrating that the measured efficiencies converge to the theoretical values with refinement. These results will be presented in a dedicated subsection of the bubble-particle collision results. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central claims rest on independent benchmarks and external theory

full rationale

The paper develops a numerical method (LBM+IBM on adaptive octrees with new host-cell search) and validates it on external canonical cases (oscillating cylinder, sedimenting sphere). The key result is a simulation reproduction of the known analytic collision-efficiency scaling E ~ (r_p/r_b)^2 taken from independent hydrodynamic theory, not a derivation or fit performed inside the paper. No self-definitional equations, no parameters fitted to the target outputs then relabeled as predictions, and no load-bearing self-citations that close the argument on themselves. The derivation chain for the algorithm is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The framework rests on standard assumptions of the lattice Boltzmann and immersed boundary methods plus the correctness of the new parallel searching algorithm; no free parameters or new physical entities are introduced in the abstract.

axioms (2)
  • domain assumption Lattice Boltzmann method with immersed boundary coupling accurately resolves hydrodynamic interactions around finite-size objects at the resolved scales.
    Core modeling choice stated in the method description.
  • domain assumption Dynamically adaptive octree grids maintain sufficient resolution in boundary layers while remaining computationally tractable for large domains.
    Implicit in the choice of adaptive grid for multiscale problems.

pith-pipeline@v0.9.0 · 5742 in / 1457 out tokens · 39671 ms · 2026-05-21T05:58:29.322796+00:00 · methodology

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