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arxiv: 2604.13407 · v1 · submitted 2026-04-15 · ⚛️ physics.flu-dyn · physics.comp-ph

Improved third-order scheme in pseudopotential lattice Boltzmann model for multiphase flows

Rongzong Huang , Jiayi Huang , Qing Li This is my paper

Pith reviewed 2026-05-10 13:00 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn physics.comp-ph
keywords lattice Boltzmann methodpseudopotential modelmultiphase flowsspurious velocitythird-order schemePoiseuille flowinterface oscillations
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The pith

An improved third-order scheme suppresses spurious velocity oscillations near phase interfaces in pseudopotential lattice Boltzmann multiphase flow simulations.

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

The paper carries out a discrete-level analysis of two-phase Poiseuille flow using the pseudopotential lattice Boltzmann model. It derives the finite-difference velocity equation for both grid-aligned and grid-oblique interfaces to locate the specific terms that generate spurious velocity oscillations. From this analysis the authors construct an improved third-order scheme that removes those terms. The new scheme introduces no extra conceptual or computational cost and reverts exactly to the original scheme when the flow is static. Validation runs on Poiseuille flow, annular shear flow with curved interfaces, and falling droplets confirm that oscillations are reduced and that drag forces and droplet trajectories become more accurate.

Core claim

The lattice Boltzmann equation with a third-order scheme provides a unified framework for the pseudopotential model; discrete analysis of the resulting velocity equation shows that particular finite-difference terms produce spurious oscillations at interfaces, and a targeted modification of the scheme eliminates those terms while preserving the original behavior under static conditions.

What carries the argument

The finite-difference velocity equation obtained for grid-aligned and grid-oblique cases, which isolates the oscillation-producing terms and directly motivates the improved third-order scheme.

If this is right

  • Spurious velocity oscillations are suppressed in two-phase Poiseuille flow for both aligned and oblique grids.
  • The same suppression occurs in annular shear flow even when the phase interface is curved.
  • Falling-droplet simulations yield drag forces without systematic overestimation and produce consistent falling patterns.
  • Reliable multiphase results require the improved scheme to avoid artifacts caused by interface oscillations.

Where Pith is reading between the lines

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

  • The same discrete-analysis route could be used to locate and correct similar hidden errors in other lattice Boltzmann schemes.
  • The approach may allow more trustworthy simulations of industrial flows that involve droplets, bubbles, or emulsions.
  • Extension to three-dimensional or highly deformable interfaces would likely require repeating the grid-aligned and oblique velocity-equation derivation.

Load-bearing premise

The finite-difference velocity equation derived for grid-aligned and grid-oblique cases correctly identifies the terms responsible for spurious velocity oscillations.

What would settle it

If two-phase Poiseuille flow simulations performed with the improved scheme still display large spurious velocity oscillations near the interface, the claim that the scheme suppresses them would be falsified.

Figures

Figures reproduced from arXiv: 2604.13407 by Jiayi Huang, Qing Li, Rongzong Huang.

Figure 1
Figure 1. Figure 1: Schematics of LB simulations of two-phase Poiseuille flow with the lattice node, lattice grid, and coordinate system [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Schematics of two-phase Poiseuille flow driven by a constant force [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Velocity profiles of two-phase Poiseuille flow obtained from the LB equation with the original third-order scheme for [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Velocity profiles of two-phase Poiseuille flow obtained from the LB equation with the improved third-order scheme for [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of coexistence curves obtained from LB simulations of two-phase Poiseuille flow in the grid-oblique case [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Schematic of two-phase annular shear flow driven by an angular force [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Velocity profiles of two-phase annular shear flow obtained from the LB equation with the original third-order scheme. [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Velocity profiles of two-phase annular shear flow obtained from the LB equation with the improved third-order [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Schematic of a droplet falling in an infinite vertical channel under gravitational acceleration [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Snapshots of the falling droplet and the corresponding velocity field in the quasi-steady state obtained from the LB [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Temporal variations of the vertical velocity of the mass center of the falling droplet, obtained from the LB equation [PITH_FULL_IMAGE:figures/full_fig_p021_11.png] view at source ↗
read the original abstract

The lattice Boltzmann (LB) equation with a third-order scheme can be regarded as a unified and self-consistent framework of the pseudopotential LB model for multiphase flows. In this work, we theoretically analyze pseudopotential LB simulations of two-phase Poiseuille flow at the discrete level. The finite-difference velocity equation is derived for both grid-aligned and grid-oblique cases. The terms responsible for spurious velocity oscillations near the phase interface are identified. Based on this discrete-level analysis, an improved third-order scheme is proposed to suppress spurious velocity oscillations. This scheme does not introduce any additional conceptual or computational complexity compared with the original one and reduces to the original scheme under static conditions. Numerical simulations of two-phase Poiseuille flow validate the present theoretical analysis and demonstrate the effectiveness of the improved scheme. Then, annular shear flow with a curved phase interface is considered to show that spurious velocity oscillations can also be effectively suppressed by the improved scheme in cases with such interfaces. Finally, the falling of a droplet in a vertical channel is simulated, and the results show that spurious velocity oscillations can lead to an overestimation of the drag force and distinct falling patterns. These results highlight the necessity of using the improved third-order scheme to suppress spurious oscillations and obtain reliable results.

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 paper theoretically analyzes the pseudopotential lattice Boltzmann model for two-phase Poiseuille flow at the discrete level by deriving the finite-difference velocity equation for grid-aligned and grid-oblique cases. It identifies terms causing spurious velocity oscillations near the phase interface and proposes an improved third-order scheme to suppress them. This scheme maintains the same complexity as the original and reduces to it under static conditions. The analysis is validated numerically for Poiseuille flow, and the scheme's effectiveness is demonstrated for annular shear flow with curved interfaces and falling droplet simulations, where it reduces oscillations and improves drag force estimates.

Significance. Should the improved scheme reliably suppress spurious velocities in a variety of multiphase flow scenarios, it would offer a straightforward enhancement to existing pseudopotential LB models, leading to more accurate and reliable simulations of interfacial flows without additional computational overhead. The discrete derivation provides insight into the origin of these artifacts.

major comments (1)
  1. [Theoretical analysis and numerical validations] The finite-difference velocity equation is derived specifically for two-phase Poiseuille flow (grid-aligned and grid-oblique cases). For the annular shear flow and falling-droplet cases, which involve curved interfaces, the paper relies solely on numerical evidence without a corresponding derivation of the velocity equation. This raises the question of whether the identified error terms are the dominant ones in curved-interface geometries, and whether the modification could affect other discrete properties such as force balance.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comments and the opportunity to clarify the scope of our discrete analysis. We address the major comment point by point below.

read point-by-point responses

  1. Referee: The finite-difference velocity equation is derived specifically for two-phase Poiseuille flow (grid-aligned and grid-oblique cases). For the annular shear flow and falling-droplet cases, which involve curved interfaces, the paper relies solely on numerical evidence without a corresponding derivation of the velocity equation. This raises the question of whether the identified error terms are the dominant ones in curved-interface geometries, and whether the modification could affect other discrete properties such as force balance.

    Authors: We acknowledge that the exact derivation of the finite-difference velocity equation is performed only for the Poiseuille flow configuration, which permits a closed-form discrete analysis with planar interfaces. The spurious terms we identify arise from truncation errors in the local finite-difference stencils used to evaluate the velocity and the pseudopotential force; these stencils operate pointwise and do not depend on the global geometry or curvature of the interface. Consequently, the same error terms are present near curved interfaces. The numerical results for annular shear flow and the falling droplet demonstrate that the improved scheme suppresses the oscillations in these geometries as well, indicating that the identified terms remain dominant. With respect to force balance, the improved scheme is constructed to be identical to the original scheme whenever the velocity field is zero; therefore the discrete equilibrium force balance is preserved exactly. We have added a clarifying paragraph in the revised manuscript (Section 4.2) that explains the local character of the discretization errors and the preservation of static force balance. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation proceeds from discrete LB equations to scheme modification

full rationale

The paper derives the finite-difference velocity equation directly from the pseudopotential LB model for grid-aligned and grid-oblique Poiseuille flow, identifies the oscillation-causing terms at the discrete level, and proposes the improved third-order scheme to target those terms. The scheme is stated to reduce to the original under static conditions as a consistency property, and effectiveness is checked via independent numerical simulations on Poiseuille, annular shear, and falling-droplet cases. No self-definitional loops, fitted inputs renamed as predictions, or load-bearing self-citations appear in the derivation chain; the analysis is self-contained against the model's own discrete equations and external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard assumptions of the lattice Boltzmann framework and discrete finite-difference expansions without introducing new entities or fitted parameters.

axioms (1)
  • domain assumption The lattice Boltzmann equation with a third-order scheme can be regarded as a unified and self-consistent framework of the pseudopotential LB model for multiphase flows.
    This is the foundational premise stated at the start of the abstract.

pith-pipeline@v0.9.0 · 5527 in / 1106 out tokens · 51525 ms · 2026-05-10T13:00:17.136588+00:00 · methodology

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Reference graph

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