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arxiv: 2606.02467 · v1 · pith:XSM6OXNKnew · submitted 2026-06-01 · ⚛️ physics.flu-dyn

Sharp-interface Simulations of Energetic Multiphase Flows with Large Density and Viscosity Ratios

Tzu-Yao Huang , Nicolas Valle , Artur K. Lidtke , Kelli Hendrickson , Gabriel D. Weymouth This is my paper

Pith reviewed 2026-06-28 12:32 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords sharp-interface methodsmultiphase flowsdensity ratiomomentum conservationnumerical stabilityviscosity limiterwave breakingCMOM transport
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The pith

SynDRoM synchronizes momentum fluxes to remove spurious velocities in high-density-ratio sharp-interface flows.

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

The paper addresses the challenge of simulating energetic multiphase flows with large density and viscosity ratios, such as wave breaking, where standard velocity-based methods lose robustness. It builds on the Consistent Mass-Momentum transport framework, which enforces momentum conservation and semi-discrete energy conservation, but creates momentum shocks when paired with sharp interfaces. To fix this, the work introduces Synchronized Donor-Region of Momentum fluxes that enforces monotonicity on the transported velocity field. A separate viscosity limiter based on bounded kinetic viscosity is added to prevent instabilities at the interface. Tests on scalar transport, shear instability, and a breaking wave case show the combined schemes remove oscillations while keeping physical behavior intact.

Core claim

The Synchronized Donor-Region of Momentum fluxes (SynDRoM) replaces conventional shock-capturing by synchronizing donor regions to enforce monotonicity of the advected velocity field; this eliminates spurious velocity oscillations in CMOM-based sharp-interface simulations of large density ratio flows without loss of physical fidelity, as shown in scalar transport and interfacial shear instability cases, while a bounded kinetic viscosity limiter removes additional instabilities from improper interface viscosity estimates.

What carries the argument

SynDRoM, which synchronizes the donor regions for momentum fluxes to enforce monotonicity of the transported velocity field.

If this is right

  • Spurious velocity oscillations are eliminated in scalar transport and interfacial shear instability test cases.
  • Numerical instabilities from improper viscosity estimation near the interface are addressed at finite time steps.
  • The combined schemes enable assessment of performance on breaking wave simulations.
  • Momentum conservation and semi-discrete energy conservation from the underlying CMOM framework are retained.

Where Pith is reading between the lines

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

  • The monotonicity approach could be tested on other discontinuous transport problems such as compressible multiphase flows.
  • Further checks in fully three-dimensional air-entrainment cases would show whether the limiter scales without new artifacts.
  • The same donor-region synchronization idea might stabilize other sharp-interface conservation laws beyond momentum.

Load-bearing premise

The monotonicity enforcement in SynDRoM and the viscosity limiter preserve physical fidelity and do not introduce new artifacts when applied to complex three-dimensional breaking wave simulations.

What would settle it

A breaking wave simulation that still shows persistent spurious velocity oscillations or clear deviation from expected physical interface motion after applying SynDRoM and the viscosity limiter.

Figures

Figures reproduced from arXiv: 2606.02467 by Artur K. Lidtke, Gabriel D. Weymouth, Kelli Hendrickson, Nicolas Valle, Tzu-Yao Huang.

Figure 1
Figure 1. Figure 1: Interface shape and vorticity field of the 2D dam break example at 𝑡 √︁ 𝑔/𝐻 = 0.6. Teal blue hatches show the water region. Flow field irregularities of velocity and original CMOM formulations indicated and zoomed in with purple oval insets. Flow field of SynDRoM is also enlarged with green oval for comparison purpose. (𝑁𝑥, 𝑁𝑦) = (96, 96) [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Temporal evolution of energy and its compo￾nents of the dam break case. of dam break after a few time steps, with velocity pointing downwards. The simplified governing equations reduce to 𝜕𝑡 𝜌+𝜕𝑗Ψ = 0, 𝜕𝑡 𝑞+𝜕𝑗Ψ𝑣 = 0, where Ψ = 𝜌𝑈 is the horizontal mass flux and 𝑞 = 𝜌𝑣 is the vertical momentum. Simulation results are summarized in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Variable arrangement on a 2D staggered cell complex. The background black cell represents the col￾located grid, while the green and purple cells correspond to the horizontal and vertical staggered cells, respectively. We follow Patankar’s compass notation for cell and face naming. Pressure 𝑝 and density 𝜌 are stored in collocated cells, while the velocities 𝑢𝑖 and isometric-averaged den￾sities 𝜌𝑢𝑖 resides … view at source ↗
Figure 4
Figure 4. Figure 4: Quasi-one-dimensional high density droplet (teal blue shade) transport. The high vertical shear present at the rear interface of the droplet (grid cell P) and is transported by 𝑈. After one time step Δ𝑡, the horizontal velocity transfer all but no more than the remaining high density fluid in P to E – the volume fraction inside the central satisfies 𝛼 = 𝑈Δ𝑡/Δ𝑥. The new vertical velocity of the central cell… view at source ↗
Figure 5
Figure 5. Figure 5: One-dimensional periodic droplet advection of density ratio 𝜆𝜌 = 10−3 . Initial vertical velocity (gray line) has a (inverse) top-hat profile with a little overlap with the droplet (teal blue shade); the field is convected using forward Euler and superbee interpolation. Result and comparison are present after one convection period (𝑡𝑈/𝐿 = 1). 𝑁𝑥 = 32, CFL = 𝑈Δ𝑡/Δ𝑥 = 0.05. The shades of CMOM variants show t… view at source ↗
Figure 6
Figure 6. Figure 6: Mass-flux-based donor region concept in SynDRoM with linear density distribution assumption, example using horizontal mass flux with focus on cell P. Panel (a) shows the density distribution and mass flux and (b) those for velocity and momentum. Center of mass are labeled with vertical mustard line, and the level of original velocity is signified with horizontal mustard line in (b). Lines pivoting around t… view at source ↗
Figure 7
Figure 7. Figure 7: All is similar to [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Directionally-split mass update of a droplet’s side tangentially passing through a collocated cell. The figures are presented in visual order. The solid line represents the true motion path while the dash lines signify the auxiliary path from directional split algorithm. The 𝑥 sweep (b) is performed first and then the 𝑦 one (c). Bold red outlines around the arrows show the influenced mass fluxes. (a) 𝑡𝑈/𝐿 … view at source ↗
Figure 9
Figure 9. Figure 9: Evolution of thick shear layer Kelvin-Helmholtz instability on the interface, contoured by non-dimensional vorticity. The black line is the interface. Teal blue hatches signify the water parts. Green arrows show the initial horizontal velocity profile. (𝑁𝑥, 𝑁𝑦) = (96, 192). 𝑡𝑈/𝐿 = 3.8 in panel (d) is approximately when the maximum kinetic energy drain happens [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Temporal evolution of perturbations of inter￾face amplitude and maximum vertical velocity in Kelvin￾Helmholtz instability, where the dashed line denotes the theoretical prediction. The interface amplitude is filtered by Fourier transform such that it only contains the largest wavelength, i.e. horizontal domain size [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Time derivatives of total kinetic energy of Kelvin-Helmholtz test case with zero line indicated [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Change of the horizontal momentum of the Kelvin-Helmholtz case. The vertical momentum is not shown as the slip boundary condition is imposed on the top and bottom boundaries. A finite-thickness shear layer is imposed in the dense phase. The horizontal velocity transitions smoothly from (1, 0)𝑈 to (−1, 0)𝑈, as indicated by the green arrows in Figure 9a, creating a velocity deflection near the inter￾face th… view at source ↗
Figure 13
Figure 13. Figure 13: Locations at which viscosity is evaluated in a staggered-grid configuration. The hollow star de￾notes the collocated-cell vertex (edge in 3D), used for cross-difference terms, while the solid star denotes the collocated-cell center, used for inline-difference terms. collocated-cell centers (solid stars) for inline-difference terms. While the viscosity at cell centers is directly avail￾able, the vertex val… view at source ↗
Figure 14
Figure 14. Figure 14: Gravity-driven stratified Poiseuille flow–case setup and simulation results. UnboundAri: arithmetic averaging without bounded treatment; Harmonic: harmonic mean following Tryggvason et al. (2011); BoundAri: arithmetic averaging with bounded treatment. The horizontal line marks the interface. The dark red box indicates the onset of divergence for UnboundAri. (𝑁𝑥, 𝑁𝑦) = (16, 1). Only the cross-difference te… view at source ↗
Figure 15
Figure 15. Figure 15: Evolution of a diagonal sine standing wave with inviscid condition. The free surface is shown and colored by velocity magnitude. Instants corresponding to peaks or troughs of kinetic and potential energy are presented. 𝑁𝑥 = 𝑁𝑦 = 𝑁𝑧 = 256. parts. The presence of viscosity continuously moderates the flow field, degrading the strength of the most violent events and inhibiting the transition toward turbulence… view at source ↗
Figure 16
Figure 16. Figure 16: Mechanical energy evolution and its temporal derivatives. The zero level of the energy derivative is indicated by a gray dashed line. The color family of black (resp. blue) represents inviscid (resp. viscous) solution [PITH_FULL_IMAGE:figures/full_fig_p014_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Relative change of horizontal momentum for the wave-breaker case. Vertical momentum is omitted due to slip boundary conditions at the top and bottom. The color family of black (resp. blue) represents inviscid (resp. viscous) solution. variants of Consistent Mass-Momentum (CMOM) meth￾ods violate the Total Variation Diminishing (TVD) condi￾tion near emptying interface cells, a deficiency that inher￾ently th… view at source ↗
Figure 18
Figure 18. Figure 18: Grid-convergence of mechanical energy and its temporal derivative in inviscid simulation. The temporal derivative is window-averaged for clarity. the mass donor region, eliminating the need for interpola￾tion from collocated to staggered mass (Le Chenadec and Pitsch, 2013), but at the expense of more sophisticated velocity-pressure decoupling, such as Santos et al. (2025). The current methods also demonst… view at source ↗
read the original abstract

Flows with high density ratios, such as wave breaking and air entrainment in maritime applications, remain challenging to simulate due to their energetic and strongly nonlinear nature. In such regimes, maintaining numerical robustness is difficult when using the commonly adopted velocity-based formulation. The Consistent Mass-Momentum (CMOM) transport framework improves numerical robustness by enforcing fundamental physical properties, most notably momentum conservation and semi-discrete energy-conserving. However, CMOM replaces the advection of a continuous velocity field with that of a discontinuous momentum field. When combined with sharp interface methods, this leads to severe momentum shocks, for which conventional shock-capturing schemes are ineffective. To reconcile physical fidelity with numerical robustness, this work proposes a Synchronized Donor-Region of Momentum fluxes (SynDRoM) that enforces monotonicity of the transported velocity field. The resulting algorithm effectively eliminates spurious velocity oscillations without sacrificing physical fidelity, as demonstrated through scalar transport and interfacial shear instability test cases. Beyond difficulties from large density ratio, improper estimation of viscosity in the vicinity of the interface can introduce numerical instabilities at finite time steps, thereby undermining overall robustness. To address this issue, a viscosity limiter based on the bounded kinetic viscosity concept is introduced and validated using a gravity-driven plane shear flow. Finally, a breaking wave simulation is performed to assess the combined performance of the proposed physics-preserving numerical schemes for multiphase flows.

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 paper introduces the Synchronized Donor-Region of Momentum fluxes (SynDRoM) scheme to enforce monotonicity on the velocity field within the Consistent Mass-Momentum (CMOM) framework for sharp-interface multiphase simulations at large density/viscosity ratios. It also proposes a bounded-kinetic-viscosity limiter to stabilize interface viscosity estimates. These are tested on scalar transport, 2-D interfacial shear instability, gravity-driven plane shear flow, and a 3-D breaking-wave case, with the central claim that spurious velocity oscillations are eliminated while physical fidelity is preserved.

Significance. If the quantitative support for fidelity preservation holds, the methods would offer a practical route to stable, momentum-conserving simulations of energetic flows such as wave breaking and air entrainment, where standard velocity-based and shock-capturing approaches fail. The targeted fixes for momentum shocks and interface viscosity are directly relevant to maritime and multiphase CFD applications.

major comments (2)
  1. [breaking-wave simulation subsection] Breaking-wave simulation subsection: the claim that SynDRoM and the viscosity limiter preserve physical fidelity in complex 3-D cases rests solely on a qualitative description of the simulation having been 'performed to assess combined performance.' No quantitative diagnostics (kinetic-energy spectra, air-entrainment volume fractions, wave-height decay rates, or comparison against experimental or reference data) are reported, leaving the central fidelity assertion unsupported for the most demanding test.
  2. [scalar transport and interfacial shear instability sections] Scalar-transport and interfacial-shear-instability sections: while the abstract states that these cases demonstrate elimination of spurious oscillations 'without sacrificing physical fidelity,' the provided description supplies no error norms, convergence rates, or direct comparison against analytic or high-resolution reference solutions that would quantify any alteration introduced by the monotonicity constraint.
minor comments (2)
  1. [Introduction] The abstract and introduction use 'semi-discrete energy-conserving' without an explicit statement of the discrete energy identity being preserved; a short derivation or reference to the precise CMOM energy statement would clarify the property being retained.
  2. [SynDRoM description] Notation for the donor-region fluxes in SynDRoM is introduced without an accompanying schematic or explicit stencil diagram, making the synchronization step difficult to reconstruct from the text alone.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback identifying the need for stronger quantitative support of the physical-fidelity claims. We respond to each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [breaking-wave simulation subsection] Breaking-wave simulation subsection: the claim that SynDRoM and the viscosity limiter preserve physical fidelity in complex 3-D cases rests solely on a qualitative description of the simulation having been 'performed to assess combined performance.' No quantitative diagnostics (kinetic-energy spectra, air-entrainment volume fractions, wave-height decay rates, or comparison against experimental or reference data) are reported, leaving the central fidelity assertion unsupported for the most demanding test.

    Authors: We acknowledge that the breaking-wave subsection currently offers only a qualitative assessment. In the revised manuscript we will add quantitative diagnostics such as kinetic-energy spectra, air-entrainment volume fractions, and wave-height decay rates, together with comparisons to available experimental or reference data, to substantiate the fidelity claim for this demanding case. revision: yes

  2. Referee: [scalar transport and interfacial shear instability sections] Scalar-transport and interfacial-shear-instability sections: while the abstract states that these cases demonstrate elimination of spurious oscillations 'without sacrificing physical fidelity,' the provided description supplies no error norms, convergence rates, or direct comparison against analytic or high-resolution reference solutions that would quantify any alteration introduced by the monotonicity constraint.

    Authors: The current sections demonstrate oscillation removal through direct visual comparison with expected physical behavior. To quantify any effect of the monotonicity constraint, the revised manuscript will include error norms, convergence rates, and comparisons against analytic or high-resolution reference solutions for both test cases. revision: yes

Circularity Check

0 steps flagged

No circularity: independent algorithmic proposals validated on external test cases

full rationale

The paper introduces SynDRoM for monotonicity enforcement and a bounded kinetic viscosity limiter as new components within the CMOM framework. These are validated on scalar transport, interfacial shear instability, gravity-driven shear flow, and a breaking wave case, with claims of preserved physical fidelity resting on those external demonstrations rather than any self-referential definitions, fitted inputs renamed as predictions, or load-bearing self-citations that reduce the central result to its inputs by construction. No equations or steps in the provided text exhibit the enumerated circular patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work relies on standard fluid dynamics conservation principles and domain assumptions about numerical stability in multiphase flows. No free parameters, new physical entities, or ad-hoc axioms beyond conventional CFD are explicitly introduced in the abstract.

axioms (2)
  • standard math Standard conservation laws for mass and momentum hold in the fluid system.
    The CMOM framework and SynDRoM build directly on enforcing these properties.
  • domain assumption The chosen test cases sufficiently represent the challenges of energetic real-world flows.
    Validation of the new schemes depends on scalar transport, shear instability, and breaking wave cases.

pith-pipeline@v0.9.1-grok · 5792 in / 1273 out tokens · 32509 ms · 2026-06-28T12:32:52.093160+00:00 · methodology

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Reference graph

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