Pith. sign in

REVIEW 3 major objections 5 minor 59 references

CLIP: A CUDA-Accelerated Lattice Boltzmann Framework for Interfacial Phenomena with Application to Liquid Jet Simulations

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read GPU lattice Boltzmann solver reproduces liquid jet breakup and sets drip-to-jet transition at Weber 2.2.

desk verdict A solid CUDA phase-field LBM benchmark suite, but We_cr ≈ 2.2 is a two-simulation bracket under idealized jet conditions and should not be treated as a sharp result yet. read the letter →

arxiv 2505.12205 v1 pith:4LFHROUL submitted 2025-05-18 physics.flu-dyn physics.comp-ph

Mehdi Shadkhah , Mohammad Taeibi Rahni , Azadeh Kebriaee , Mohammad Reza Salimi This is my paper · ORCID
classification physics.flu-dynphysics.comp-ph PACS 47.55.df47.55.nb47.11.-j
keywords latticeBoltzmannmethodphase-fieldmodelAllen-Cahnequationweightedmulti-relaxationtimeCUDAGPUaccelerationliquidjetbreakupdrippingandjettingregimes
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper presents a CUDA-accelerated, phase-field lattice Boltzmann framework, named CLIP, for simulating two-phase flows with large density and viscosity contrasts, and claims that it quantitatively reproduces the breakup of a liquid jet in air. The authors validate the solver on five benchmark problems: capillary wave decay, a stationary drop obeying Laplace's law, two-phase Poiseuille flow, a circular interface in shear flow, and Rayleigh-Taylor instability. They then simulate a water jet at a density ratio of 814 with physical properties matched to a published experiment, and find that the dripping-to-jetting transition occurs at a critical Weber number of about $2.2$, inside the range $2<\mathrm{We}<3$ reported by that experiment. Simulated breakup lengths and droplet sizes follow the same trends as the measurements across both regimes. If the claim holds, a desktop-computable solver can connect interface physics to an engineering-scale regime boundary without a computing cluster.

What carries the argument

The load-bearing machinery is a pair of lattice Boltzmann equations on a D3Q19 lattice, which has nineteen discrete velocities. One distribution function set solves the incompressible Navier-Stokes equations with surface tension written through a chemical-potential force; the other solves the conservative Allen-Cahn equation for the phase-field variable $\phi$, which marks the liquid and gas and defines the diffuse interface. Stability at density ratio $814$ comes from the weighted multi-relaxation-time (WMRT) collision operator, a variant of MRT that relaxes weighted, orthogonalized moments rather than simple velocity-space populations. Speed comes from mapping collision, streaming, boundary, and macro-variable steps onto the GPU's parallel memory layout, so one iteration over sixteen million or more lattice nodes runs in fractions of a second. The jet application adds three boundary choices: a uniform velocity inlet, free-slip side walls, and a convective outlet, all intended to keep the domain free of artificial disturbances so that capillary physics alone drives breakup.

What would settle it

Run the same water-air jet setup at Weber numbers just below and above 2.2 while adding a controlled inlet perturbation amplitude (for example, 1 percent of the jet velocity at a few Rayleigh frequencies) and observe whether the dripping-to-jetting transition shifts noticeably; a large shift would falsify the paper's claim that the transition is an intrinsic property of the capillary jet under the stated conditions.

Watch

Extended reading notes

Core claim

The core discovery the authors argue for is that the combination of the conservative Allen-Cahn interface-tracking equation, the weighted multi-relaxation-time (WMRT) collision operator, and GPU parallelism makes a phase-field lattice Boltzmann model stable and accurate enough to act as a predictive tool for liquid jet breakup. Concretely, their D3Q19 simulation of a water jet in air at $\mathrm{Oh}=4.4\times10^{-3}$ and density ratio $814$ places the transition from dripping to jetting at a Weber number of approximately $2.2$, while the matching experiment places it between $2$ and $3$. The same simulations reproduce the observed increase of breakup length with Weber number in both regimes and the decrease of mean droplet size across the transition, including coalescence events in the jetting regime. On the paper's terms, this means the model captures the force balance that governs jet breakup and locates the regime boundary more tightly than the experiment alone did.

Load-bearing premise

The jet simulations assume an idealized setup: a uniform velocity at the nozzle inlet, free-slip side walls, and a convective outlet with no artificial disturbances, and the claim that $\mathrm{We}_{\mathrm{cr}}\approx 2.2$ depends on these conditions being physically representative of the experiment.

Editorial extensions

If this is right

  • The dripping-to-jetting transition in a water-air system at $\mathrm{Oh}=4.4\times10^{-3}$ is pinned to $\mathrm{We}\approx 2.2$, which is a sharper bound than the experiment's $2<\mathrm{We}<3$ range.
  • A solver built on a desktop GPU can perform three-dimensional, high-density-ratio, high-viscosity-ratio multiphase simulations that previously required a high-performance computing cluster.
  • The validated benchmarks establish a baseline accuracy for the phase-field WMRT approach: capillary wave decay, Laplace's law, two-phase Poiseuille flow (about second-order convergence), shear-deformed interface recovery, and Rayleigh-Taylor spike and bubble evolution.
  • Because the phase-field formulation keeps the interface diffuse but locally tracked, the approach can be extended to other low-Weber-number interfacial processes such as drop formation on demand or microfluidic droplet generation.
  • The reported speedups, about 48 times for a two-dimensional case and 86 times for a three-dimensional case on a modest desktop GPU, indicate that parameter sweeps over dimensionless groups are now practical on standard hardware.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If $\mathrm{We}_{\mathrm{cr}}\approx 2.2$ is robust, it offers a clean calibration point for other diffuse-interface and volume-of-fluid methods at the same Ohnesorge number; discrepancies would indicate sensitivity to the interface model or boundary treatment rather than to unresolved turbulence.
  • The paper's jet setup uses an idealized, uniform inlet with no imposed perturbations; the transition value may shift if realistic velocity fluctuations or nozzle geometry are introduced, and a systematic sweep of inlet perturbation amplitude would reveal how much of the result is a property of the ideal capillary jet.
  • The same CUDA-based framework could be used to produce a detailed Ohnesorge-Reynolds regime diagram for a wider range of liquid-gas pairs, and the critical-Weber line could be tested against the classical Ohnesorge correlation, which is an extension the paper does not explicitly compute.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The manuscript introduces CLIP, a CUDA-accelerated phase-field lattice Boltzmann framework for immiscible two-phase flows with high density and viscosity contrasts. The method uses a conservative Allen-Cahn interface equation, a weighted multi-relaxation-time (WMRT) collision operator, and D3Q19/D2Q9 lattices. The paper validates the solver against capillary wave decay, Laplace-law stationary drops, two-phase Poiseuille flow, shear-driven interface deformation, and 2D/3D Rayleigh-Taylor instability, reporting close agreement with analytical solutions and prior numerical data. The framework is then applied to a water-air liquid jet in conditions matched to the experiment of Suñol and González-Cinca (2015), and the authors report breakup lengths and droplet sizes in agreement with the experiment and claim a dripping-to-jetting transition at a critical Weber number Wecr ≈ 2.2.

Significance. If the claims hold, this is a useful contribution: the paper supplies an open-source GPU-accelerated solver, documents the CUDA implementation, and demonstrates the model on several nontrivial benchmarks, including density ratios of 1000 and 3D Rayleigh-Taylor evolution. The benchmark evidence is credible and reasonably complete: Laplace-law errors are below about 1%, the two-phase Poiseuille flow shows roughly second-order convergence, and the Rayleigh-Taylor positions track published data. The novelty is primarily in the integration and GPU implementation rather than in a new constitutive model. The main scientific claim beyond the benchmarks is the jet transition value Wecr ≈ 2.2, which is a falsifiable, physically meaningful output; however, as discussed in the major comments, the support for this specific value is currently too thin, so the paper needs revision before the central jet claim can be accepted.

major comments (3)
  1. [§6.3, Fig. 22] The claimed critical Weber number Wecr ≈ 2.2 is inferred from exactly two bracketing simulations: We = 2.17 is classified as dripping and We = 2.27 as jetting. No grid-refinement study is reported for the jet simulations. Given the stated domain of 120 × 120 × 300 (or 400) lattice nodes and the domain size 6Dj × 6Dj × 20Dj, the jet diameter is resolved by only about 20 lattice units, which is marginal for resolving the thin neck and the growth of capillary perturbations. A resolution study on the two bracketing cases (e.g., doubling the lattice resolution while holding dimensionless parameters fixed) is needed to establish that the dripping/jetting classification and the inferred transition value do not shift with resolution. The manuscript's own caveat in §6.3 that the boundary 'may not be sharply defined and could vary depending on specific conditions' underscores that this point is load-bearing.
  2. [§6.1, boundary conditions] The jet simulations use a uniform velocity profile at the inlet, free-slip side walls, and a convective outlet, with the text explicitly stating 'no artificial disturbances'. Liquid jet breakup is highly sensitive to inlet velocity profile, nozzle geometry, and the amplitude of disturbances; a perfectly uniform inlet removes the naturally occurring perturbation spectrum that triggers capillary instability in experiments. The manuscript does not test whether the idealized inlet profile reproduces the nozzle conditions of Ref. [53], nor does it report a perturbation-sensitivity study. Because the dripping/jetting boundary is identified by the behavior of these two simulations, the authors should either add simulations with a controlled inlet perturbation (e.g., small sinusoidal or broadband disturbances of amplitude 0.1–1% of uj) or provide evidence that the uniform inlet gives the same transition as a developed profile. Without this, the claimed Wecr ≈ 2.2 could be an artifact of the idealized setup even if all validation benchmarks are correct.
  3. [§6.2, Fig. 21] The manuscript states that the jet breakup length and droplet size results 'align well' and show 'excellent agreement' with the experiment, but no quantitative error metric is reported. The experimental points in Fig. 21 appear without error bars or a stated measurement uncertainty, and the numerical data in Fig. 21b show noticeable scatter in the jetting regime. The authors should report a quantitative comparison (e.g., mean or maximum relative deviation for Lb/Dj and de/Dj) and comment on the scatter, including the role of coalescence events that are mentioned in the text. A quantitative error statement is needed to substantiate the abstract's claim that the results 'closely match experimental observations.'
minor comments (5)
  1. [Algorithm 3, lines 26–28] The pseudocode for velocity update reads 'ux← f[index][ex[i]]' and similarly for uy and uz, which is not a valid moment summation; it should presumably be something like 'ux ← ux + f[index][i] * ex[i]' (and analogously for y and z). Please correct the pseudocode.
  2. [Table 1] The entries in Table 1 are ambiguous (e.g., 'Color-fluid 10 3 > 104 > 104 > 1'), and the column alignment is not clear. Please reformat the table so that each dimensionless number has an explicit value or range, and add a note explaining the provenance of these reported capabilities.
  3. [Eq. (7)] In Eq. (7), the term 'γ 1− 4(ϕ−ϕ0)2 ξ n' is missing parentheses; it should read γ (1 − 4(φ − φ0)^2 / ξ) n, as in the subsequent conservative form in Eq. (8).
  4. [Table 6] Table 6 marks some cases with an asterisk and states that these are chosen to match the target experimental study, but not all compared cases are marked. Please clarify which cases are direct experimental matches and which are additional numerical cases used to map the regime diagram.
  5. [References] Reference [8] is listed with inconsistent volume/year information (volume 27, pages 821–834, year 2012 in the first occurrence and 2017 in the DOI line), and the author name 'Suñol' appears as 'Sunol' in figure captions and text. Please standardize these.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the model is benchmarked against external analytical and experimental data, the critical Weber number is a simulation output rather than a fitted input, and no load-bearing self-citation chain appears.

full rationale

The CLIP framework is assembled from externally published lattice Boltzmann components rather than from the authors' own prior results: the D3Q19 lattice and MRT/WMRT collision operators are tied to Refs. [40-42], the conservative Allen-Cahn interface-tracking scheme to Refs. [22,43], and the hydrodynamic formulation to standard LB references [34-38]. None of these is a self-citation of the present authors, and no uniqueness theorem or prior author-affiliated result is invoked to force the model choice. The validation section is self-contained against external benchmarks: capillary-wave decay is compared with the analytical Prosperetti solution (Eq. 41), the stationary drop test with Laplace's law (Eq. 44), two-phase Poiseuille flow with finite-difference solutions and a reported second-order convergence rate, the shear-flow interface test with the Rudman reference and a mass-conservation check, and Rayleigh-Taylor evolution with data from Refs. [19,21,23]. For the liquid-jet application, the authors set the Ohnesorge number and fluid properties to match the external experiment [53]; doing so is standard case selection, not fitting of the target outputs. The breakup lengths and drop sizes are then compared with those experimental measurements, and the critical Weber number is obtained as an output of bracketing simulations at We=2.17 (dripping) and We=2.27 (jetting). The experimental transition bracket 2<We<3 is broad, and refining it to Wecr≈2.2 is a predictive claim supported by the simulation results, not a quantity inserted into the model by construction. The paper's own caveat, that the dripping/jetting boundary 'may not be sharply defined and could vary depending on specific conditions' (Sec. 6.3), is an honest limitation about regime classification. The noted idealizations—uniform inlet velocity, free-slip side walls, convective outlet, and the absence of a reported grid-refinement or inlet-perturbation study for the jet—are legitimate correctness and robustness concerns, and the manuscript's 'GitHub page' placeholder is a completeness issue; neither constitutes circularity. No equation or fitted parameter in the paper reduces to the claimed prediction, and no self-referential derivation chain is present.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The model relies on standard LBM and phase-field assumptions from the cited literature. The only user-defined parameters are numerical discretization choices: interface thickness, mobility, and grid resolution. No new physical entities are introduced.

free parameters (3)
  • Interface thickness ξ = ξ = 4 or 5 in lattice units
    Controls the diffuse interface width in lattice units; set by hand for stability and accuracy in each test, not fitted to experimental data.
  • Mobility M and phase-field relaxation time τφ = M = 0.02 (capillary wave), 0.0002 (shear flow)
    Controls the interface relaxation speed; chosen to fix the Peclet number or maintain numerical stability; not measured from physical parameters.
  • Grid resolution and domain size = e.g., 120 x 120 x 300 for jet cases
    Numerical discretization choice; no resolution study is reported for the jet transition result.
assumptions (4)
  • domain assumption The LBM with the D3Q19 lattice and the MRT/WMRT collision operator recovers the incompressible Navier-Stokes equations and the conservative Allen-Cahn equation via Chapman-Enskog analysis (Section 3.2).
    Relies on standard LBM theory (refs. [34-36]); the specific WMRT transformation matrix in Appendix A.2 is not derived or independently validated.
  • domain assumption The phase-field model with a tanh interface profile and the chemical potential in Eqs. (10)-(12) produces the correct surface tension force (Korteweg stress) (Section 3.1).
    Adopted from prior literature (Jacqmin 2000; Jamet et al. 2002); no independent verification is provided in this paper.
  • ad hoc to paper The idealized jet setup: uniform inlet velocity, free-slip side walls, and convective outflow boundary, with no inlet perturbations, adequately represents the experimental jet of Ref. [53] (Section 6.1).
    Jet breakup is highly sensitive to inlet conditions and nozzle geometry; the paper gives no sensitivity analysis for the transition result.
  • domain assumption The interpolation of viscosity via Eq. (25) combined with the halfway bounce-back boundary treatment is sufficient for the high density and viscosity ratios used in the jet simulations, ρ* = 814 and μ* = 55 (Sections 3.2 and B.3).
    Standard practice in multiphase LBM, but no verification is provided for these specific conditions in the present study.

how reviews work

0 comments
Cite this review

Pith. "Pith review of CLIP: A CUDA-Accelerated Lattice Boltzmann Framework for Interfacial Phenomena with Application to Liquid Jet Simulations." pith.science (2026). https://pith.science/paper/4LFHROUL

@misc{pith2026250512205,
  author       = {Pith},
  title        = {Pith review of: CLIP: A CUDA-Accelerated Lattice Boltzmann Framework for Interfacial Phenomena with Application to Liquid Jet Simulations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4LFHROUL}},
  note         = {Machine review of arXiv:2505.12205}
}
read the original abstract

This work introduces CLIP, a CUDA-accelerated phase-field lattice Boltzmann framework for simulating immiscible two-phase flows with high density and viscosity ratios in both two- and three-dimensional domains. By leveraging GPU parallelism, the framework delivers substantial computational speedups, enabling large-scale simulations to be performed efficiently on standard desktop hardware without the need for high-performance computing clusters. It employs the Weighted Multi-Relaxation Time (WMRT) collision operator to enhance numerical stability and improve interface tracking under challenging multiphase conditions. The model is validated through a series of benchmark cases, including capillary wave dynamics, stationary drop tests, two-phase Poiseuille flow, shear-driven interface deformation, and Rayleigh-Taylor instability. It is further applied to simulate liquid jet breakup, capturing the transition from dripping to jetting regimes and identifying a critical Weber number of approximately 2.2. The results closely match experimental observations, offering detailed insights into breakup length, drop size distributions, and flow regime transitions. With its efficiency, accuracy, and scalability, the proposed framework serves as a powerful and accessible tool for investigating complex interfacial phenomena in multiphase flow physics.

Figures

Figures reproduced from arXiv: 2505.12205 by the authors.

Figure 1
Figure 1. (a) Ohnesorge diagram highlighting the transition between jet breakup regimes. (b) Visualization of jet breakup patterns as a function of Weber and outlet velocity, showcasing axisymmetric and non-axisymmetric behaviors. formation of small droplets [9]. The accuracy of such simulations is highly sensitive to mesh resolution, particularly in regions with strong droplet-vorticity coupling. In addition to conventional … view at source ↗
Figure 2
Figure 2. Three-dimensional 19-velocity (D3Q19) lattice. The diagram illustrates the discrete velocity vectors in the D3Q19 model, including the central rest velocity and velocities along the axes, face diagonals, and space diagonals. is relatively large in size, is accessible to all threads on the GPU as well as the host (CPU). However, global memory access is slower compared to other memory types. Threads within a block can… view at source ↗
Figure 3
Figure 3. CUDA device memory model (source from NVIDIA). 12 [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figures from the paper (20 more)
Figure 4
Figure 4. Figure 4: illustrates the procedural differences between sequential program execution on the CPU and the parallelized implementation on the GPU. Fig. 4a highlights how GPU-based par￾allel computing enables simultaneous processing of computational nodes for collision, streaming, …
Figure 5
Figure 5. Figure 5: Average execution time breakdown for one iteration on a 3D D3Q19 lattice arrangement: Execution times for lattice Boltzmann simulation procedures (Collision, Streaming, Boundary Condition, and Macroscopic Variables) across mesh sizes ranging from 2M to 64M lattice node…
Figure 6
Figure 6. Figure 6: Average execution time breakdown for one iteration on a 3D D3Q19 lattice arrangement: The figure illustrates the average execution times for various lattice Boltzmann simulation procedures (Collision, Streaming, Boundary Condition, and Macroscopic Variables) for a doma…
Figure 7
Figure 7. Figure 7: Schematic representation of the simulation setup for capillary wave dynamics. The initial sinusoidal perturbation is applied at the interface between two immiscible fluids with densities ρL (light fluid) and ρH (heavy fluid). The top and bottom boundaries are subjected…
Figure 8
Figure 8. Figure 8: Comparison of the normalized interface amplitude η ∗ as a function of normalized time t ∗ between the current LBM simulation and the analytical solution by Prosperetti (1981). Subfigure (a) corresponds to ν = 0.0005, while subfigure (b) corresponds to ν = 0.005. to the…
Figure 9
Figure 9. Figure 9: Validation of the LBM model using Laplace law tests and density profile analysis. (a) Laplace law tests for three surface tension coefficients (σ = 0.001, σ = 0.005, and σ = 0.010) show agreement between LBM results and theoretical predictions. (b) The density profile …
Figure 10
Figure 10. Figure 10: Schematic of the two-phase Poiseuille flow configuration: A periodic computational domain with density and viscosity stratification (ρH, µH in the upper half and ρL, µL in the lower half). The flow is driven by a body force g, with no-slip boundary conditions applied …
Figure 11
Figure 11. Figure 11: (a) Comparison between FDM solution (solid lines) and LBM-PF solution (symbols) for the normalized longitudinal velocity profile in two-phase Poiseuille flow with ρ ∗ = 10 and µ ∗ = 100. (b) Same as (a) but for ρ ∗ = 1000 and µ ∗ = 100. (c) Convergence study of two-ph…
Figure 12
Figure 12. Figure 12: Evolution of a circular interface in a shear flow at Pe = 600. The interface (ϕ = 0) is shown at five distinct time steps: T = 0, T = Tf /2, T = Tf , T = 3Tf /2, and T = 2Tf , illustrating the deformation and recovery process of the interface under shear flow. 5.5. Ra…
Figure 13
Figure 13. Figure 13: Time evolution of the normalized mass of the system for circular interface in a shear flow. 23 [PITH_FULL_IMAGE:figures/full_fig_p023_13.png]
Figure 14
Figure 14. Figure 14: Boundary conditions and initial setup for the Rayleigh-Taylor instability simulations in 2D and 3D. (a) shows the 2D setup with a solid wall at the top and bottom, and periodic boundaries horizontally. (b) illustrates the 3D domain with similar boundary conditions and…
Figure 15
Figure 15. Figure 15: Comparison of interface evolution in 2D Rayleigh-Taylor instability simulations for low- and high￾density ratios. 25 [PITH_FULL_IMAGE:figures/full_fig_p025_15.png]
Figure 16
Figure 16. Figure 16: Evolution of the interface pattern in the 3D Rayleigh-Taylor instability simulations. Time histories of the dimensionless positions in the 2D and 3D computational domains are presented in [PITH_FULL_IMAGE:figures/full_fig_p026_16.png]
Figure 17
Figure 17. Figure 17: Time evolution of the bubble front, saddle, and spike tip for Rayleigh-Taylor instability. 6.1. Setup The boundary conditions and computational domain play a crucial role in determining the accuracy and reliability of numerical studies for liquid jet breakup. The setu…
Figure 18
Figure 18. Figure 18: Liquid jet setup for numerical simulations. (a) The computational domain layout. (b) Boundary conditions, including a uniform velocity inlet, free-slip walls, and a convective outflow boundary. (c) Forces affecting jet breakup, including viscous drag, inertia, and sur…
Figure 19
Figure 19. Figure 19: Interface evolution of liquid jet breakup in the dripping regime. (a) W e = 0.44, Re = 151, F r = 2.60. (b) W e = 1.79, Re = 302, F r = 5.22. The computational domain is set to 120 × 120 × 300. In the dripping regime, drop formation occurs mainly at the tip of the noz…
Figure 20
Figure 20. Figure 20: Interface evolution of liquid jet breakup in the jetting regime. (a) W e = 3.52, Re = 423, F r = 7.31. (b) W e = 4.05, Re = 454, F r = 7.84. The computational domain is set to 120 × 120 × 400. In the jetting regime, Rayleigh waves dominate, causing the axisymmetric li…
Figure 21
Figure 21. Figure 21: Comparison of numerical and experimental results for liquid jet breakup. (a) Breakup length (Lb/Dj ) as a function of W e, showing increasing length with higher Weber numbers. (b) Droplet size (de/Dj ) decreases with increasing W e, highlighting the transition between…
Figure 22
Figure 22. Figure 22: Interface evolution of liquid jet breakup in the transition regime. (a) W e = 2.17, Re = 332, F r = 5.74. (b) W e = 2.27, Re = 340, F r = 5.87. The computational domain is set to 120 × 120 × 300. Increasing the Weber number leads to growing perturbations on the liquid…
Figure 23
Figure 23. Figure 23: Phase diagram of liquid jet breakup regimes as a function of Reynolds number (Re) and Ohnesorge number (Oh). The diagram highlights two distinct regimes: the dripping regime (red circles) and the jetting regime (black triangles). The boundary between these regimes is …

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

59 extracted references · 31 canonical work pages

  1. [53]

    Su˜ nol, R

    F. Su˜ nol, R. Gonz´ alez-Cinca, Liquid jet breakup and subsequent droplet dynamics under normal gravity and in microgravity conditions, Physics of Fluids 27 (2015) 077102. URL: http://aip.scitation.org/doi/10.1063/1.4927365. doi:10.1063/1.4927365

    work page doi:10.1063/1.4927365 2015

  2. [1]

    G. K. Batchelor, A. E. Gill, Analysis of the stability of axisymmetric jets, Journal of Fluid Mechanics 14 (1962) 529. URL: http://www.journals.cambridge.org/abstract_ S0022112062001421. doi:10.1017/S0022112062001421

    work page doi:10.1017/s0022112062001421 1962

  3. [2]

    Michalke, Survey on jet instability theory, Progress in Aerospace Sciences 21 (1984) 159–199

    A. Michalke, Survey on jet instability theory, Progress in Aerospace Sciences 21 (1984) 159–199. URL: https://linkinghub.elsevier.com/retrieve/pii/0376042184900058. doi:10.1016/0376-0421(84)90005-8

    arXiv 1984

  4. [3]

    P. J. Morris, Instability of elliptic jets, AIAA Journal 26 (1988) 172–178. URL: https: //arc.aiaa.org/doi/10.2514/3.9869. doi:10.2514/3.9869

    work page doi:10.2514/3.9869 1988

  5. [4]

    Rayleigh, On The Instability Of Jets, Proceedings of the London Mathemati- cal Society s1-10 (1878) 4–13

    L. Rayleigh, On The Instability Of Jets, Proceedings of the London Mathemati- cal Society s1-10 (1878) 4–13. URL: http://doi.wiley.com/10.1112/plms/s1-10.1.4. doi:10.1112/plms/s1-10.1.4

    doi:10.1112/plms/s1-10.1.4

  6. [5]

    Mayinger, Mixture Formation in Internal Combustion Engine, Heat, Mass Trans- fer, Springer Berlin Heidelberg, 2006

    F. Mayinger, Mixture Formation in Internal Combustion Engine, Heat, Mass Trans- fer, Springer Berlin Heidelberg, 2006. URL: http://link.springer.com/10.1007/ 3-540-30836-9. doi:10.1007/3-540-30836-9

    work page doi:10.1007/3-540-30836-9 2006

  7. [6]

    W. V. Ohnesorge, The formation of drops by nozzles and the breakup of liquid jets, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f¨ ur Angewandte Mathematik und Mechanik 16 (1936) 355–358. URL: https://onlinelibrary.wiley. com/doi/10.1002/zamm.19360160611. doi:10.1002/zamm.19360160611

    work page doi:10.1002/zamm.19360160611 1936

  8. [7]

    Bonhoeffer, A

    B. Bonhoeffer, A. Kwade, M. Juhnke, Impact of Formulation Properties and Pro- cess Parameters on the Dispensing and Depositioning of Drug Nanosuspensions Us- ing Micro-Valve Technology, Journal of Pharmaceutical Sciences 106 (2017) 1102–

    work page 2017

Show all 59 references
  1. [8]

    Rajendran, M

    S. Rajendran, M. A. Jog, R. M. Manglik, EXPERIMENTAL INVESTIGATION OF JET BREAKUP AT LOW WEBER NUMBER, Atomization and Sprays 27 (2012) 821–834. URL: http://www.dl.begellhouse.com/journals/6a7c7e10642258cc, 3d4684f46a8a5e93,436cb82a2bda8443.html. doi:10.1615/AtomizSpr.2017019424

    2012 doi

  2. [9]

    Fuster, A

    D. Fuster, A. Bagu´ e, T. Boeck, L. Le Moyne, A. Leboissetier, S. Popinet, P. Ray, R. Scardovelli, S. Zaleski, Simulation of primary atomization with an octree adaptive mesh refinement and VOF method, International Journal of Multiphase Flow 35 (2009) 550–565. URL: http://dx.d...

    2009 doi

  3. [10]

    C. Hirt, B. Nichols, Volume of fluid (vof) method for the dynamics of free boundaries, Journal of Computational Physics 39 (1981) 201–225

    1981

  4. [11]

    A. G. Lamorgese, D. Molin, R. Mauri, Phase field approach to multiphase flow modeling, Milan Journal of Mathematics 79 (2011) 597–642. 39

    2011

  5. [12]

    Lebas, T

    R. Lebas, T. Menard, P. A. Beau, A. Berlemont, F. X. Demoulin, Numerical simula- tion of primary break-up and atomization: DNS and modelling study, International Journal of Multiphase Flow 35 (2009) 247–260. URL: http://dx.doi.org/10.1016/j. ijmultiphaseflow.2008.11.005. doi:1...

    2009 doi

  6. [13]

    Shinjo, A

    J. Shinjo, A. Umemura, Surface instability and primary atomization character- istics of straight liquid jet sprays, International Journal of Multiphase Flow 37 (2011) 1294–1304. URL: http://dx.doi.org/10.1016/j.ijmultiphaseflow.2011. 08.002https://linkinghub.elsevier.com/retri...

    2011 doi

  7. [14]

    A. K. Gunstensen, D. H. Rothman, S. Zaleski, G. Zanetti, Lattice Boltzmann model of immiscible fluids, Physical Review A 43 (1991) 4320–4327. URL: https://link.aps.org/ doi/10.1103/PhysRevA.43.4320. doi:10.1103/PhysRevA.43.4320

    1991 doi

  8. [15]

    X. Shan, H. Chen, Lattice Boltzmann model for simulating flows with multiple phases and components, Physical Review E 47 (1993) 1815–1819. URL: https://link.aps.org/ doi/10.1103/PhysRevE.47.1815. doi:10.1103/PhysRevE.47.1815

    1993 doi

  9. [16]

    X. Shan, H. Chen, Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation, Physical Review E 49 (1994) 2941–2948. URL: https:// link.aps.org/doi/10.1103/PhysRevE.49.2941. doi:10.1103/PhysRevE.49.2941

    1994 doi

  10. [17]

    M. R. Swift, E. Orlandini, W. R. Osborn, J. M. Yeomans, Lattice Boltzmann simulations of liquid-gas and binary fluid systems, Physical Review E 54 (1996) 5041–5052. URL: https: //link.aps.org/doi/10.1103/PhysRevE.54.5041. doi:10.1103/PhysRevE.54.5041

    1996 doi

  11. [18]

    X. He, S. Chen, R. Zhang, A Lattice Boltzmann Scheme for Incompressible Multiphase Flow and Its Application in Simulation of Rayleigh–Taylor Instability, Journal of Computa- tional Physics 152 (1999) 642–663. URL:https://linkinghub.elsevier.com/retrieve/ pii/S0021999199962575....

    1999

  12. [19]

    Y. Q. Zu, S. He, Phase-field-based lattice Boltzmann model for incompressible binary fluid systems with density and viscosity contrasts, Physical Review E 87 (2013) 043301. URL: https://link.aps.org/doi/10.1103/PhysRevE.87.043301. doi:10.1103/PhysRevE.87.043301

    2013 doi

  13. [20]

    Falcucci, S

    G. Falcucci, S. Ubertini, C. Biscarini, S. D. Francesco, D. Chiappini, S. Palpacelli, A. D. Maio, S. Succi, Lattice Boltzmann Methods for Multiphase Flow Simula- tions across Scales, Communications in Computational Physics 9 (2011) 269–296. URL: https://www.cambridge.org/core/...

    2011

  14. [21]

    X. He, R. Zhang, S. Chen, G. D. Doolen, On the three-dimensional Rayleigh–Taylor instability, Physics of Fluids 11 (1999) 1143–1152. URL: http://aip.scitation.org/ doi/10.1063/1.869984. doi:10.1063/1.869984

    1999 doi

  15. [22]

    Chiu, Y.-T

    P.-H. Chiu, Y.-T. Lin, A conservative phase field method for solving incompress- ible two-phase flows, Journal of Computational Physics 230 (2011) 185–204. URL: 40 http://dx.doi.org/10.1016/j.jcp.2010.09.021https://linkinghub.elsevier. com/retrieve/pii/S0021999110005243. doi:1...

    2011 doi

  16. [23]

    F. Ren, B. Song, M. C. Sukop, H. Hu, Improved lattice Boltzmann modeling of binary flow based on the conservative Allen-Cahn equation, Physical Review E 94 (2016) 023311. URL: https://link.aps.org/doi/10.1103/PhysRevE.94.023311. doi:10.1103/PhysRevE.94.023311

    2016 doi

  17. [24]

    Fakhari, M

    A. Fakhari, M. Geier, D. Bolster, A simple phase-field model for interface tracking in three dimensions, Computers & Mathematics with Applications 78 (2019) 1154–1165. URL: http://dx.doi.org/10.1016/j.camwa.2016.08.021https:// linkinghub.elsevier.com/retrieve/pii/S089812211630...

    2019 doi

  18. [25]

    Zhang, Z

    A. Zhang, Z. Guo, Q. Wang, S. Xiong, Three-dimensional numerical simulation of bubble rising in viscous liquids: A conservative phase-field lattice-Boltzmann study, Physics of Fluids 31 (2019) 063106. URL: http://dx.doi.org/10.1063/1.5096390http://aip. scitation.org/doi/10.106...

    2019 doi

  19. [26]

    Y. Hu, D. Li, Q. He, Generalized conservative phase field model and its lattice Boltzmann scheme for multicomponent multiphase flows, International Journal of Multiphase Flow 132 (2020) 103432. URL: https://doi.org/10.1016/j.ijmultiphaseflow. 2020.103432https://linkinghub.else...

    2020

  20. [27]

    Januszewski, M

    M. Januszewski, M. Kostur, Sailfish: A flexible multi-GPU implementation of the lattice Boltzmann method, Computer Physics Communications 185 (2014) 2350–2368. URL: https://linkinghub.elsevier.com/retrieve/pii/S0010465514001520. doi: 10.1016/ j.cpc.2014.04.018. arXiv:1311.2404

    2014 arXiv

  21. [28]

    J. Latt, O. Malaspinas, D. Kontaxakis, A. Parmigiani, D. Lagrava, F. Brogi, M. B. Belgacem, Y. Thorimbert, S. Leclaire, S. Li, F. Marson, J. Lemus, C. Kotsalos, R. Conradin, C. Coreixas, R. Petkantchin, F. Raynaud, J. Beny, B. Chopard, Pala- bos: Parallel Lattice Boltzmann Sol...

    2021 doi

  22. [29]

    Y. Sun, C. Beckermann, Sharp interface tracking using the phase-field equa- tion, Journal of Computational Physics 220 (2007) 626–653. URL: https: //www.sciencedirect.com/science/article/pii/S0021999106002531. doi: https:// doi.org/10.1016/j.jcp.2006.05.025

    2007 doi

  23. [30]

    H. Ding, P. D. Spelt, C. Shu, Diffuse interface model for incompressible two-phase flows with large density ratios, Journal of Computational Physics 226 (2007) 2078–2095. URL: https://linkinghub.elsevier.com/retrieve/pii/S0021999107002793. doi: 10.1016/ j.jcp.2007.06.028. 41

    2007

  24. [31]

    Q. Li, K. H. Luo, Y. J. Gao, Y. L. He, Additional interfacial force in lat- tice Boltzmann models for incompressible multiphase flows, Physical Review E 85 (2012) 026704. URL: https://link.aps.org/doi/10.1103/PhysRevE.85.026704. doi:10.1103/PhysRevE.85.026704

    2012 doi

  25. [32]

    Jamet, D

    D. Jamet, D. Torres, J. U. Brackbill, On the theory and computation of surface tension: The elimination of parasitic currents through energy conservation in the second-gradient method, Journal of Computational Physics 182 (2002) 262–276. doi: 10.1006/jcph.2002. 7165

    2002 doi

  26. [33]

    JACQMIN, Contact-line dynamics of a diffuse fluid interface, Journal of Fluid Mechan- ics 402 (2000) 57–88

    D. JACQMIN, Contact-line dynamics of a diffuse fluid interface, Journal of Fluid Mechan- ics 402 (2000) 57–88. URL: https://www.cambridge.org/core/product/identifier/ S0022112099006874/type/journal_article. doi:10.1017/S0022112099006874

    2000 doi

  27. [34]

    M. C. Sukop, D. T. Thorne, Lattice boltzmann modeling: An introduction for geoscientists and engineers, Springer Berlin Heidelberg, 2006. URL: http://link.springer.com/10. 1007/978-3-540-27982-2 . doi:10.1007/978-3-540-27982-2

    2006 doi

  28. [35]

    Huang, M

    H. Huang, M. C. Sukop, X. Y. Lu, Multiphase Lattice Boltzmann Methods: Theory and Application, John Wiley & Sons, Ltd, 2015. URL: http://doi.wiley.com/10.1002/ 9781118971451. doi:10.1002/9781118971451

    2015 doi

  29. [36]

    Kr¨ uger, H

    T. Kr¨ uger, H. Kusumaatmaja, A. Kuzmin, O. Shardt, G. Silva, E. M. Viggen, The Lattice Boltzmann Method, volume 58 of Graduate Texts in Physics , Springer International Pub- lishing, 2017. URL: http://link.springer.com/10.1007/978-3-319-44649-3 . doi:10. 1007/978-3-319-44649-...

    2017 arXiv

  30. [37]

    Z. Guo, C. Zheng, B. Shi, Discrete lattice effects on the forcing term in the lattice Boltz- mann method, Physical Review E 65 (2002) 046308. URL: https://link.aps.org/doi/ 10.1103/PhysRevE.65.046308. doi:10.1103/PhysRevE.65.046308

    2002 doi

  31. [38]

    Fakhari, T

    A. Fakhari, T. Mitchell, C. Leonardi, D. Bolster, Improved locality of the phase-field lattice-Boltzmann model for immiscible fluids at high density ratios, Physical Review E 96 (2017) 053301. URL: https://link.aps.org/doi/10.1103/PhysRevE.96.053301. doi:10.1103/PhysRevE.96.053301

    2017 doi

  32. [39]

    P. L. Bhatnagar, E. P. Gross, M. Krook, A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems, Physical Re- view 94 (1954) 511–525. URL: https://link.aps.org/doi/10.1103/PhysRev.94.511. doi:10.1103/PhysRev.94.511

    1954 doi

  33. [40]

    Lallemand, L.-S

    P. Lallemand, L.-S. Luo, Theory of the lattice Boltzmann method: Disper- sion, dissipation, isotropy, Galilean invariance, and stability, Physical Review E 61 (2000) 6546–6562. URL: https://link.aps.org/doi/10.1103/PhysRevE.61.6546. doi:10.1103/PhysRevE.61.6546

    2000 doi

  34. [41]

    P. J. Dellar, Nonhydrodynamic modes and a priori construction of shallow water lattice Boltzmann equations, Physical Review E 65 (2002) 036309. URL: https://link.aps. org/doi/10.1103/PhysRevE.65.036309. doi:10.1103/PhysRevE.65.036309. 42

    2002 doi

  35. [42]

    Geier, M

    M. Geier, M. Sch¨ onherr, A. Pasquali, M. Krafczyk, The cumulant lattice Boltzmann equation in three dimensions: Theory and validation, Computers and Mathematics with Applications 70 (2015) 507–547. doi: 10.1016/j.camwa.2015.05.001

    2015 doi

  36. [43]

    Geier, A

    M. Geier, A. Fakhari, T. Lee, Conservative phase-field lattice Boltzmann model for inter- face tracking equation, Physical Review E 91 (2015) 063309. URL: https://link.aps. org/doi/10.1103/PhysRevE.91.063309. doi:10.1103/PhysRevE.91.063309

    2015 doi

  37. [44]

    Kumar, Isotropic finite-differences, Journal of Computational Physics 201 (2004) 109–

    A. Kumar, Isotropic finite-differences, Journal of Computational Physics 201 (2004) 109–

    2004

  38. [45]

    K. K. Mattila, L. A. Hegele J´ unior, P. C. Philippi, High-accuracy approximation of high- rank derivatives: Isotropic finite differences based on lattice-Boltzmann stencils, The Scientific World Journal 2014 (2014) 1–16. URL: http://www.hindawi.com/journals/ tswj/2014/142907/...

    2014 doi

  39. [46]

    C. Li, J. P. Y. Maa, H. Kang, Solving generalized lattice Boltzmann model for 3- D cavity flows using CUDA-GPU, Science China Physics, Mechanics and Astronomy 55 (2012) 1894–1904. URL: http://link.springer.com/10.1007/s11433-012-4856-9 . doi:10.1007/s11433-012-4856-9

    2012 doi

  40. [47]

    Prosperetti, Motion of two superposed viscous fluids, Physics of Fluids 24 (1981) 1217 – 1223

    A. Prosperetti, Motion of two superposed viscous fluids, Physics of Fluids 24 (1981) 1217 – 1223. URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-0019376759& doi=10.1063%2f1.863522&partnerID=40&md5=eb53d8f4f5117a9f1224ba3ed1d61239. doi:10.1063/1.863522, cited by: 149

    1981 doi

  41. [48]

    T. Reis, T. N. Phillips, Lattice Boltzmann model for simulating immiscible two-phase flows, Journal of Physics A: Mathematical and Theoretical 40 (2007) 4033–4053. URL: https://iopscience.iop.org/article/10.1088/1751-8113/40/14/018. doi: 10.1088/ 1751-8113/40/14/018

    2007 doi

  42. [49]

    Leclaire, M

    S. Leclaire, M. Reggio, J. Y. Tr´ epanier, Numerical evaluation of two recoloring operators for an immiscible two-phase flow lattice Boltzmann model, Applied Mathematical Mod- elling 36 (2012) 2237–2252. URL: https://linkinghub.elsevier.com/retrieve/pii/ S0307904X11005270. doi...

    2012 doi

  43. [50]

    A. J. Ladd, Numerical Simulations of Particulate Suspensions Via a Discretized Boltzmann Equation. Part 1. Theoretical Foundation, Journal of Fluid Mechanics 271 (1994) 285–309. URL: https://www.cambridge.org/core/product/identifier/S0022112094001771/ type/journal_article. doi...

    1994 doi

  44. [51]

    Rudman, VOLUME-TRACKING METHODS FOR INTERFACIAL FLOW CALCU- LATIONS, International Journal for Numerical Methods in Fluids 24 (1997) 671–691

    M. Rudman, VOLUME-TRACKING METHODS FOR INTERFACIAL FLOW CALCU- LATIONS, International Journal for Numerical Methods in Fluids 24 (1997) 671–691. URL: https://linkinghub.elsevier.com/retrieve/pii/0168822794900140https: //onlinelibrary.wiley.com/doi/10.1002/(SICI)1097-0363(19970...

    1997

  45. [52]

    Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Dover Books on Physics Series, Dover Publications, 1981

    S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Dover Books on Physics Series, Dover Publications, 1981. URL: https://books.google.de/books?id=oU%5C_ -6ikmidoC

    1981

  46. [54]

    A. J. Ladd, R. Verberg, Lattice-Boltzmann simulations of particle-fluid suspensions, Jour- nal of Statistical Physics 104 (2001) 1191–1251. doi: 10.1023/A:1010414013942

    2001 doi

  47. [55]

    Q. Lou, Z. Guo, B. Shi, Evaluation of outflow boundary conditions for two-phase lattice Boltzmann equation, Physical Review E 87 (2013) 063301. URL: https://link.aps.org/ doi/10.1103/PhysRevE.87.063301. doi:10.1103/PhysRevE.87.063301

    2013 doi

  48. [56]

    Yang, Lattice Boltzmann outflow treatments: Convective conditions and oth- ers, Computers & Mathematics with Applications 65 (2013) 160–171

    Z. Yang, Lattice Boltzmann outflow treatments: Convective conditions and oth- ers, Computers & Mathematics with Applications 65 (2013) 160–171. URL: http://dx.doi.org/10.1016/j.camwa.2012.11.012https://linkinghub.elsevier. com/retrieve/pii/S0898122112006736. doi:10.1016/j.camw...

    2013 doi

  49. [57]

    Orlanski, A simple boundary condition for unbounded hyperbolic flows, Journal of Computational Physics 21 (1976) 251–269

    I. Orlanski, A simple boundary condition for unbounded hyperbolic flows, Journal of Computational Physics 21 (1976) 251–269. URL: https://linkinghub.elsevier.com/ retrieve/pii/0021999176900231. doi:10.1016/0021-9991(76)90023-1. 44

    1976

  50. [118]

    doi:10.1016/j.jcp.2004.05.005

    URL: https://linkinghub.elsevier.com/retrieve/pii/S0021999104002037. doi:10.1016/j.jcp.2004.05.005

    2004 doi

  51. [1110]

    elsevier.com/retrieve/pii/S0022354916419453

    URL: http://dx.doi.org/10.1016/j.xphs.2016.12.019https://linkinghub. elsevier.com/retrieve/pii/S0022354916419453. doi:10.1016/j.xphs.2016.12.019

    2016 doi

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.