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arxiv: 2604.14938 · v1 · submitted 2026-04-16 · ⚛️ physics.comp-ph · physics.flu-dyn

Recognition: unknown

Sharp-interface VOF method for phase-change simulations on unstructured meshes

Bojan Ni\v{c}eno, Jan Kren, Yohei Sato

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Pith reviewed 2026-05-10 08:35 UTC · model grok-4.3

classification ⚛️ physics.comp-ph physics.flu-dyn
keywords meshesphase-changeunstructuredbubblemethodpolyhedralanalyticalframework
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The pith

A sharp-interface VOF method for phase-change simulations on unstructured meshes computes evaporation rates from local temperature gradients at geometrically reconstructed interfaces and validates against analytical solutions on Stefan, Sucking, and Scriven problems.

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

Simulating how liquids turn into vapor or vice versa is key for engineering like power plants and cooling systems. Most accurate models use simple box-shaped grids, but real equipment has irregular shapes. This work builds a method that works on flexible, unstructured meshes made of many-sided cells. It tracks the boundary between liquid and gas using volume-of-fluid and then rebuilds a sharp version of that boundary geometrically. The speed of phase change is found by measuring temperature differences right at this rebuilt boundary. Tests on simple one-dimensional freezing and sucking problems plus a three-dimensional growing bubble match known exact answers. The method also avoids artificial stretching patterns that appear on regular grids. A quick check on turbulent boiling flow gives results that line up with earlier studies.

Core claim

We present a phase-change simulation method for unstructured meshes that combines the algebraic Volume-of-Fluid (VOF) technique with geometric interface reconstruction... Phase-change rates are computed from local temperature gradients evaluated at the reconstructed interface, without empirical closure models, using a reconstruction procedure that operates on arbitrary polyhedral cells.

Load-bearing premise

The reconstruction procedure that operates on arbitrary polyhedral cells accurately captures the interface geometry sufficiently for reliable local temperature gradient evaluation without introducing significant numerical artifacts or requiring empirical closures.

Figures

Figures reproduced from arXiv: 2604.14938 by Bojan Ni\v{c}eno, Jan Kren, Yohei Sato.

Figure 1
Figure 1. Figure 1: Non-orthogonal correction methods at face [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Interface-modified gradient stencil on a polyhedral mesh. For the highlighted cell [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Schematic of the one-dimensional Stefan and Sucking problems. The red curve shows the temperature profile [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: One-dimensional evaporation benchmarks: interface position and relative error for (a, b) the Stefan problem [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Sucking problem: instantaneous (a) temperature and (b) velocity profiles at [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Scriven problem at t = 0.63 ms: temperature field and mesh cross-sections through the bubble centre for (a) the structured hexahedral (1253 ) and (b) the polyhedral mesh. The solid black line shows the numerical interface (α = 0.5). Insets magnify the interface region, showing the thermal boundary layer resolved by approximately 4–6 cells in the radial direction. The full computational domain is a cube wit… view at source ↗
Figure 7
Figure 7. Figure 7: Scriven problem: temperature contours and velocity vectors on a cross-section through the bubble centre at [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Scriven problem: mass transfer rate m˙ on the z = 0 cross-section at three time instants, for (a–c) the structured 1253 mesh and (d–f) the polyhedral 1253 mesh. The mass transfer is localised at the interface and shows near-uniform angular distribution on both mesh types, despite the gradient anisotropy on the structured mesh. 3.2.2 Mesh convergence [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Scriven problem: (a) bubble radius growth on the [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Scriven bubble growth: sensitivity analysis. Normalised bubble radius [PITH_FULL_IMAGE:figures/full_fig_p022_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Scriven problem: temperature gradient magnitude [PITH_FULL_IMAGE:figures/full_fig_p023_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Polar distribution of temperature gradient magnitude [PITH_FULL_IMAGE:figures/full_fig_p024_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Illustration of the interface-modified gradient stencil on a structured mesh at three angular positions relative [PITH_FULL_IMAGE:figures/full_fig_p025_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Synthetic analysis of gradient stencil anisotropy: polar plots of the ratio [PITH_FULL_IMAGE:figures/full_fig_p025_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Computational mesh for the annular flow simulation: (a) perspective view of the 45 [PITH_FULL_IMAGE:figures/full_fig_p027_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Schematic of wave-modulated evaporation in upward co-current annular flow. The liquid film (blue) coats [PITH_FULL_IMAGE:figures/full_fig_p029_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Instantaneous snapshot on a sliced plane of the annular flow simulation: (a) phase distribution showing the [PITH_FULL_IMAGE:figures/full_fig_p030_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Hovmöller diagram of the interface perturbation [PITH_FULL_IMAGE:figures/full_fig_p031_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Quantitative analysis of wave-modulated mass transfer: (a) scatter plot of film thickness versus normalised [PITH_FULL_IMAGE:figures/full_fig_p032_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: One-dimensional schematic of the gradient stencil for a cell [PITH_FULL_IMAGE:figures/full_fig_p040_20.png] view at source ↗
read the original abstract

Unstructured meshes are among the most versatile approaches for capturing non-canonical geometries in fluid dynamics simulations. Despite this, most high-fidelity first-principles phase-change models are developed and applied on structured meshes. We present a phase-change simulation method for unstructured meshes that combines the algebraic Volume-of-Fluid (VOF) technique with geometric interface reconstruction, implemented in an in-house open-source CFD code. Phase-change rates are computed from local temperature gradients evaluated at the reconstructed interface, without empirical closure models, using a reconstruction procedure that operates on arbitrary polyhedral cells. Because the method relies on the standard finite-volume framework, it can be integrated into other cell-centred codes supporting unstructured meshes. The approach is validated against the one-dimensional Stefan and Sucking problems and the three-dimensional Scriven bubble growth on both hexahedral and polyhedral meshes, showing good agreement with analytical solutions in all three cases. A detailed analysis of the Scriven problem reveals that the interface-modified least-squares gradient stencil on Cartesian meshes overestimates the interfacial temperature gradient, producing a persistent overshoot of the analytical bubble radius and a coherent four-fold anisotropy that elongates the bubble along grid diagonals. On polyhedral meshes, the irregular face orientations eliminate both effects, yielding isotropic growth and monotonic convergence. Finally, we demonstrate the framework on turbulent upward co-current annular boiling flow, where early transient results are qualitatively consistent with a previous LES study and experimental observations of wave-modulated evaporation.

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

2 major / 2 minor

Summary. The manuscript presents a sharp-interface VOF method for phase-change simulations on unstructured meshes. It combines algebraic VOF with geometric interface reconstruction on arbitrary polyhedral cells to compute phase-change rates directly from local temperature gradients at the reconstructed interface, without empirical closures. The approach is implemented in an open-source finite-volume CFD code and validated against analytical solutions for the 1D Stefan problem, Sucking problem, and 3D Scriven bubble growth on both hexahedral and polyhedral meshes. A detailed analysis shows Cartesian-mesh artifacts (persistent radius overshoot and four-fold anisotropy) that are eliminated on irregular polyhedral meshes, with an additional demonstration on turbulent annular boiling flow.

Significance. If the central claims hold, the work is significant because it extends first-principles phase-change modeling to unstructured meshes, which are required for complex engineering geometries. The explicit documentation of Cartesian-mesh artifacts and their removal via polyhedral face orientations supplies a concrete, falsifiable insight into gradient evaluation near interfaces. The open-source implementation within the standard finite-volume framework and the parameter-free formulation (no fitted closures) are strengths that support reproducibility and broader adoption in boiling/condensation simulations.

major comments (2)
  1. [Validation section (Scriven problem)] Validation (Scriven bubble analysis): the claim that polyhedral meshes yield 'isotropic growth and monotonic convergence' is load-bearing for the central assertion that the reconstruction furnishes reliable gradients on arbitrary cells. However, the manuscript reports only qualitative agreement and visual elimination of anisotropy; quantitative error norms (e.g., L2 or L∞ deviation of bubble radius from the analytical Scriven solution, or sphericity measures) versus mesh resolution are not provided for the polyhedral cases, leaving the monotonicity claim partially unverified.
  2. [Numerical method] Numerical method (interface reconstruction and gradient evaluation): the reconstruction procedure that 'operates on arbitrary polyhedral cells' and the 'interface-modified least-squares gradient stencil' are the core technical contributions. The text describes the stencil's effect on Cartesian meshes but does not supply the explicit algorithmic steps, weighting, or stencil modification equations for general polyhedra, which are needed to confirm that the four-fold anisotropy is eliminated by geometry rather than by mesh-specific tuning.
minor comments (2)
  1. [Abstract] The abstract states that early transient results for annular boiling are 'qualitatively consistent' with prior LES and experiments; adding the specific non-dimensional time or physical time at which the comparison is made would clarify the scope of the demonstration.
  2. [Figures] Figure captions for the Scriven bubble results should explicitly state the mesh types (hexahedral vs. polyhedral) and resolutions used in each panel to allow direct cross-reference with the convergence discussion.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment and constructive comments. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Validation section (Scriven problem)] Validation (Scriven bubble analysis): the claim that polyhedral meshes yield 'isotropic growth and monotonic convergence' is load-bearing for the central assertion that the reconstruction furnishes reliable gradients on arbitrary cells. However, the manuscript reports only qualitative agreement and visual elimination of anisotropy; quantitative error norms (e.g., L2 or L∞ deviation of bubble radius from the analytical Scriven solution, or sphericity measures) versus mesh resolution are not provided for the polyhedral cases, leaving the monotonicity claim partially unverified.

    Authors: We agree that quantitative error norms would strengthen the validation. In the revised manuscript we will add L2 and L∞ norms of the bubble-radius deviation from the analytical Scriven solution together with sphericity measures, plotted versus mesh resolution for both hexahedral and polyhedral meshes. These data will quantitatively confirm isotropic growth and monotonic convergence on the polyhedral cases. revision: yes

  2. Referee: [Numerical method] Numerical method (interface reconstruction and gradient evaluation): the reconstruction procedure that 'operates on arbitrary polyhedral cells' and the 'interface-modified least-squares gradient stencil' are the core technical contributions. The text describes the stencil's effect on Cartesian meshes but does not supply the explicit algorithmic steps, weighting, or stencil modification equations for general polyhedra, which are needed to confirm that the four-fold anisotropy is eliminated by geometry rather than by mesh-specific tuning.

    Authors: The algorithmic description appears in Section 3. To make the procedure fully reproducible for arbitrary polyhedra we will expand the revised text with the explicit reconstruction steps on general polyhedral cells, the weighting scheme used in the least-squares gradient, and the precise stencil modification based on the reconstructed interface plane. This will demonstrate that the elimination of four-fold anisotropy follows directly from the irregular face orientations rather than any mesh-specific tuning. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper describes a numerical method that combines algebraic VOF with geometric interface reconstruction on arbitrary polyhedral cells within the standard finite-volume framework, then computes phase-change rates directly from reconstructed-interface temperature gradients. All load-bearing steps are explicit geometric and discretization procedures whose outputs are validated against independent analytical solutions (1D Stefan, Sucking, 3D Scriven) on both hexahedral and polyhedral meshes; the reported convergence, isotropy, and artifact removal are direct numerical outcomes rather than re-statements of fitted inputs or self-citations. No equation reduces to its own definition, no parameter fitted to a subset is relabeled a prediction, and no uniqueness theorem or ansatz is imported via self-citation. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based solely on abstract; no explicit free parameters or new entities are introduced. The approach rests on standard CFD assumptions.

axioms (2)
  • standard math Standard finite-volume discretization and gradient reconstruction assumptions hold for unstructured polyhedral meshes.
    The method relies on the standard finite-volume framework as stated in the abstract.
  • domain assumption Geometric interface reconstruction on arbitrary polyhedral cells yields sufficiently accurate interface normals and areas for temperature gradient evaluation.
    Central to computing phase-change rates without empirical models.

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