arXiv subjects

Stéphane Popinet

Publications and source records attributed to Stéphane Popinet.

At least 19 recordsLinked to original sources

arXiv2026

A Three-dimensional Edge-Based Interface Tracking (EBIT) Method for Multiphase-flow Simulations

The Edge-Based Interface Tracking (EBIT) method is a novel Front-Tracking method in which the markers are located on grid edges, and their connectivity is implicitly represented by a color vertex field. This localized representation simplifies topology changes and allows for automatic parallelization. In this work, we propose a simplified extension of EBIT to three dimensions (3D). The directional split scheme used for interface advection in the two-dimensional (2D) version is generalized to 3D by decomposing each 3D directional advection step into 2D advection problems on the two corresponding cube faces. The same dimension-reduction strategy is applied to connectivity representation, allowing the main 2D algorithms and data structures to be reused and thereby reducing the algorithmic and implementation complexity. For coupling with the Navier--Stokes equations, volume fractions are reconstructed from the EBIT markers and color vertex field using the Front2VOF geometric method. The resulting volume fractions are then used to compute the fluid properties and surface-tension forces with the Height-Function method. The 3D EBIT method has been implemented in the free Basilisk framework, with the documented source code available in the online repository. The method is verified against five benchmark cases: translation with uniform velocity, 3D deformation test, oscillating drop, rising bubble, and bubble merging. The results show good agreement with reference solutions and with the Volume-of-Fluid (VOF) method implemented in Basilisk, demonstrating the effectiveness of the simplified extension. In addition, the 3D EBIT method exhibits excellent weak scalability, highlighting its potential advantage over traditional front-tracking methods for large-scale parallel computations.

physics.flu-dyn↗

arXiv2026

Applying contact angles based on a continuously moving contact line in 2D VOF simulations

A height-function-based numerical approach is developed for enforcing contact angles on flat and curved solid surfaces within two-dimensional volume-of-fluid simulations. This method incorporates the contact line position into the curvature estimation in the contact line cell, where the interface normal is constrained to the prescribed angle to ensure smooth contact line motion. On flat solid surfaces, the proposed model achieves higher accuracy than the conventional vertical height-function method for enforcing very small and very large contact angles. Moreover, it extends naturally to curved solid surfaces represented by the embedded boundary method, enabling the imposition of arbitrary contact angles without inducing significant spurious currents near the contact line. Numerical validations confirm the accuracy and robustness of the proposed method, demonstrating its applicability to multiphase flows involving complex wall geometries and contact-line dynamics.

physics.flu-dyn↗

arXiv2025

A consistent treatment of dynamic contact angles in the sharp-interface framework with the generalized Navier boundary condition

In this work, we revisit the Generalized Navier Boundary condition (GNBC) introduced by Qian et al.\ in the sharp interface Volume-of-Fluid context. We replace the singular uncompensated Young stress by a smooth function with a characteristic width $\varepsilon > 0$ that is understood as a physical parameter of the model. Therefore, we call the model the ``Contact Region GNBC'' (CR-GNBC). We show that the model is consistent with the fundamental kinematics of the contact angle transport described by Fricke, Köhne and Bothe. We implement the model in the geometrical Volume-of-Fluid solver Basilisk using a ``free angle'' approach. This means that the dynamic contact angle is not prescribed but reconstructed from the interface geometry and subsequently applied as an input parameter to compute the uncompensated Young stress. We couple this approach to the two-phase Navier Stokes solver and study the withdrawing tape problem with a receding contact line. It is shown that the model allows for grid-independent solutions and leads to a full regularization of the singularity at the moving contact line, which is in accordance with the thin-film equation subject to this boundary condition. In particular, it is shown that the curvature at the moving contact line is finite and mesh converging. As predicted by the fundamental kinematics, the parallel shear stress component vanishes at the moving contact line for quasi-stationary states (i.e. for $\dotθ_d=0$) and the dynamic contact angle is determined by a balance between the uncompensated Young stress and an effective contact line friction. Furthermore, a non-linear generalization of the model is proposed, which aims at reproducing the Molecular Kinetic Theory of Blake and Haynes for quasi-stationary states.

physics.flu-dyn↗

arXiv2025

Size Amplification of Jet Drops due to Insoluble Surfactants

Surface bubbles in the environment or engineering configurations, such as the ocean-atmosphere interface, sparkling wine, or during volcanic eruptions typically live on contaminated surfaces. A particularly common type of contamination is surface active agents (surfactants). We consider the effect of insoluble surfactant on jet drop formation by bubble bursting. Contrary to the observed trend that surfactants decrease the ejected drop radius for bubbles with precursor capillary waves, we find that surfactants increase the ejected drop radius for bubbles without precursor capillary waves - a regime characteristic of small bubbles. Consequently, the results have fundamental implications for understanding aerosol distributions in contaminated conditions. We find that the trend reversal is due to the effect of Marangoni stresses on the focusing of the collapsing cavity. We demonstrate quantitative agreement on the jet velocity and drop size between laboratory experiments and numerical simulations by using the measured surface tension dependence on surfactant concentration as the equation of state for the simulations. *Jun Eshima and Tristan Aurégan contributed equally to this work.

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arXiv2025

Growth rate and energy dissipation in wind-forced breaking waves

We investigate the energy growth and dissipation of wind-forced breaking waves at high wind speed using direct numerical simulations of the coupled air-water Navier-Stokes equations. A turbulent wind boundary layer drives the growth of a pre-existing narrowband wave field until it breaks, transferring energy into the water column. Under sustained wind forcing, the wave field resumes growth. We separately analyze energy transfers during wave growth and breaking-induced dissipation. Energy transfers are dominated by pressure input during growth and turbulent dissipation during breaking. Wind input during growth is balanced with dissipation during breaking over an entire growing-breaking cycle. The wave growth rate scales with $(u_\ast/c)^2$, modulated by the wave steepness due to sheltering, and the energy dissipation follows the inertial scaling with wave slope at breaking, confirming the universality of the process. Following breaking, near-surface vertical turbulence dissipation profiles scale as $z^{-1}$, with their magnitude controlled by the breaking-induced dissipation.

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arXiv2025

Turbulence and energy dissipation from wave breaking

Wave breaking is a critical process in the upper ocean: an energy sink for the surface wave field and a source for turbulence in the ocean surface boundary layer. We apply a novel multi-layer numerical solver resolving upper-ocean dynamics over scales from O(50cm) to O(1km), including a broad-banded wave field and wave breaking. The present numerical study isolates the effect of wave breaking and allows us to study the surface layer in wave-influenced and wave-breaking-dominated regimes. Following our previous work showing wave breaking statistics in agreement with field observations, we extend the analysis to underwater breaking-induced turbulence and related dissipation (in freely decaying conditions). We observe a rich field of vorticity resulting from the turbulence generation by breaking waves. We discuss the vertical profiles of dissipation rate which are compared with field observations, and propose an empirical universal shape function. Good agreement is found, further demonstrating that wave breaking can dominate turbulence generation in the near-surface layer. We examine the dissipation from different angles: the global dissipation of the wave field computed from the decaying wave field, the spectral dissipation from the fifth moment of breaking front distribution, and a turbulence dissipation estimated from the underwater strain rate tensor. Finally, we consider how these different estimates can be understood as part of a coherent framework.

physics.flu-dyn↗

arXiv2025

The atomizing pulsed jet

Direct Numerical Simulations of the injection of a pulsed round liquid jet in a stagnant gas are performed in a series of runs of geometrically progressing resolution. The Reynolds and Weber numbers and the density ratio are sufficiently large for reaching a complex high-speed atomization regime but not so large so that the small length scales of the flow are impossible to resolve, except for very small liquid-sheet thickness. The Weber number based on grid size is then small, an indication that the simulations are very well resolved. Computations are performed using octree adaptive mesh refinement with a finite volume method and height-function computation of curvature, down to a specified minimum grid size $Δ$. Qualitative analysis of the flow and its topology reveals a complex structure of ligaments, sheets, droplets and bubbles that evolve and interact through impacts, ligament breakup, sheet rupture and engulfment of air bubbles in the liquid. A rich gallery of images of entangled structures is produced. Most processes occurring in this type of atomization are reproduced in detail, except at the instant of thin sheet perforation or breakup. We analyze droplet statistics, showing that as the grid resolution is increased, the small-scale part of the distribution does not converge, and contains a large number of droplets close in order of magnitude to the minimum grid size with a significant peak at $d = 3Δ$. This non-convergence arises from the numerical sheet breakup effect, in which the interface becomes rough just before it breaks. The rough appearance of the interface is associated to a high-wavenumber oscillation of the curvature. To recover convergence, we apply the controlled "manifold death" numerical procedure, in which thin sheets are detected, and then pierced by fiat before they reach a set critical thickness $h_c$.

physics.flu-dyn↗

arXiv2024

Momentum fluxes in wind-forced breaking waves

We investigate the momentum fluxes between a turbulent air boundary layer and a growing-breaking wave field by solving the air-water two-phase Navier-Stokes equations through direct numerical simulations (DNS). A fully-developed turbulent airflow drives the growth of a narrowbanded wave field, whose amplitude increases until reaching breaking conditions. The breaking events result in a loss of wave energy, transferred to the water column, followed by renewed growth under wind forcing. We revisit the momentum flux analysis in a high-wind speed regime, characterized by the ratio of the friction velocity to wave speed $u_\ast/c$ in the range $[0.3-0.9]$, through the lens of growing-breaking cycles. The total momentum flux across the interface is dominated by pressure, which increases with $u_\ast/c$ during growth and reduces sharply during breaking. Drag reduction during breaking is linked to airflow separation, a sudden acceleration of the flow, an upward shift of the mean streamwise velocity profile, and a reduction in Reynolds shear stress. We characterize the reduction of pressure stress and flow acceleration through an aerodynamic drag coefficient by splitting the analysis between growing and breaking stages, treating them as separate sub-processes. While drag increases with $u_\ast/c$ during growth, it drops during breaking. Averaging over both stages leads to a saturation of the drag coefficient at high $u_\ast/c$, comparable to what is observed at high wind speeds in laboratory and field conditions. Our analysis suggests this saturation is controlled by breaking dynamics.

physics.flu-dyn↗

arXiv2024

An Edge-based Interface Tracking (EBIT) Method for Multiphase-flows Simulation with Surface Tension

We present a novel Front-Tracking method, the Edge-Based Interface Tracking (EBIT) method for multiphase flow simulations. In the EBIT method, the markers are located on the grid edges and the interface can be reconstructed without storing the connectivity of the markers. This feature makes the process of marker addition or removal easier than in the traditional Front-Tracking method. The EBIT method also allows almost automatic parallelization due to the lack of explicit connectivity. In a previous journal article we have presented the kinematic part of the EBIT method, that includes the algorithms for piecewise linear reconstruction and advection of the interface. Here, we complete the presentation of the EBIT method and combine the kinematic algorithm with a Navier--Stokes solver. A circle fit is now implemented to improve the accuracy of mass conservation in the reconstruction phase. Furthermore, to identify the reference phase and to distinguish ambiguous topological configurations, we introduce a new feature: the Color Vertex. For the coupling with the Navier--Stokes equations, we first calculate volume fractions from the position of the markers and the Color Vertex, then viscosity and density fields from the computed volume fractions and finally surface tension stresses with the Height-Function method. In addition, an automatic topology change algorithm is implemented into the EBIT method, making it possible the simulation of more complex flows. The two-dimensional version of the EBIT method has been implemented in the free Basilisk platform, and validated with seven standard test cases: stagnation flow, translation with uniform velocity, single vortex, Zalesak's disk, capillary wave, Rayleigh-Taylor instability and rising bubble. The results are compared with those obtained with the Volume-of-Fluid (VOF) method already implemented in Basilisk.

physics.flu-dyn↗

arXiv2024

Buoyancy driven motion of non-coalescing inertial drops: microstructure modeling with nearest particle statistics

In this study, we analyze the various arrangements that droplets can form within dispersed buoyant emulsions, which we refer to as the study of microstructure. To this end, we have developed a novel algorithm that effectively prevents numerical coalescence between drops while maintaining a reasonable computational cost. This algorithm is integrated into the Volume of Fluid (VoF) method and implemented using the open-source code http://basilisk.fr. Subsequently, we perform Direct Numerical Simulations (DNS) of statistically steady state mono-disperse buoyant emulsion over a broad range of dimensionless parameters, including the particle volume fraction ($ϕ$), the Galileo number ($Ga$) and the viscosity ratio ($λ$). We make use of nearest particle statistics to quantify the microstructure properties. As predicted by Zhang et al. (2023), it is demonstrated that the second moment of the nearest particle pair distribution can effectively quantify microstructural features such as particle clusters and layers. Specifically, the findings are: (1) In moderately inertial flows ($Ga = 10$), droplets form isotropic clusters. In high inertial regimes ($Ga = 100$), non-isotropic clusters, such as horizontal layers, are more likely to form. (3) The viscosity ratio plays a significant role in determining the microstructure, with droplets that are less viscous or equally viscous as the surrounding fluid tending to form layers preferentially. Overall, our study provides a quantitative measure of the microstructure in terms of $Ga$, $ϕ$ and $λ$.

physics.flu-dyn↗

arXiv2024

A coupled VOF/embedded boundary method to model two-phase flows on arbitrary solid surfaces

We present an hybrid VOF/embedded boundary method allowing to model two-phase flows in presence of solids with arbitrary shapes. The method relies on the coupling of existing methods: a geometric Volume of fluid (VOF) method to tackle the two-phase flow and an embedded boundary method to sharply resolve arbitrary solid geometries. Coupling these approaches consistently is not trivial and we present in detail a quad/octree spatial discretization for solving the corresponding partial differential equations. Modelling contact angle dynamics is a complex physical and numerical problem. We present a Navier-slip boundary condition compatible with the present cut cell method, validated through a Taylor-Couette test case. To impose the boundary condition when the fluid-fluid interface intersects a solid surface, a geometrical contact angle approach is developed. Our method is validated for several test cases including the spreading of a droplet on a cylinder, and the equilibrium shape of a droplet on a flat or tilted plane in 2D and 3D. The temporal evolution and convergence of the droplet spreading on a flat plane is also discussed for the moving contact line given the boundary condition (Dirichlet or Navier) used. The ability of our numerical methodology to resolve contact line statics and dynamics for different solid geometries is thus demonstrated.

physics.flu-dyn↗

arXiv2023

Bags mediated film atomization in a cough machine

We combine experiments and numerical computations to examine underlying fluid mechanical processes associated with bioaerosol generation during violent respiratory manoeuvres, such as coughing or sneezing. Analogous experiments performed in a cough machine -- consisting of a strong shearing airflow over a thin liquid film, allow us to illustrate the changes in film topology as it disintegrates into small droplets. We identify that aerosol generation during the shearing of the liquid film is mediated by the formation of inflated bag-like structures. The breakup of these bags is triggered by the appearance of retracting holes that puncture the bag surface. Consequently, the cascade from inflated bags to droplets is primarily controlled by the dynamics and stability of liquid rims bounding these retracting holes. We also reveal the stabilizing role of fluid viscosity that eventually leads to the generation of smaller droplets.

physics.flu-dyn↗

arXiv2022

Revisiting wind wave growth with fully-coupled direct numerical simulations

We investigate wind wave growth by direct numerical simulations solving for the two phase Navier-Stokes equations. We consider ratio of the wave speed $c$ to wind friction velocity $u_*$ from $c/u_*=$ 2 to 8, i.e. in the slow to intermediate wave regime; and initial wave steepness $ak$ from 0.1 to 0.3; the two being varied independently. The turbulent wind and the travelling, nearly monochromatic waves are fully coupled without any subgrid scale models. The novel fully-coupled approach captures the simultaneous evolution of the wave amplitude and shape, together with the underwater boundary layer (drift current), up to wave breaking. The wave energy growth computed from the time-dependent rms surface elevation is in quantitative agreement with that computed from the extracted surface pressure distribution, which confirms the leading role of the pressure forcing for finite amplitude gravity waves. The phase shift and the amplitude of the principal mode of surface pressure distribution are systematically reported, to provide direct evidence for possible wind wave growth theories. For the momentum and energy fluxes, we find that the wave form drag force is not a strong function of wave age but closely related to wave steepness. The time evolution of the rms steepness and the wave form drag suggests that there is an effect of the history of wind wave coupling. The normalised wave growth rate we obtain agrees with previous experimental and numerical studies. We make an effort to clarify various commonly-adopted underlying assumptions, and to reconcile the scattering of the data between different previous theoretical, numerical, and experimental results, as we revisit this longstanding problem with new numerical evidence.

physics.flu-dyn↗

arXiv2022

Breaking wave field statistics with a multilayer model

The statistics of breaking wave fields is characterised within a novel multi-layer framework, which generalises the single-layer Saint-Venant system into a multi-layer and non-hydrostatic formulation of the Navier-Stokes equations. We simulate an ensemble of phase-resolved surface wave fields in physical space, where strong non-linearities including wave breaking are modelled, without surface overturning. We extract the kinematics of wave breaking by identifying breaking fronts and their speed, for freely evolving wave fields initialised with typical wind wave spectra. The $Λ(c)$ distribution, defined as the length of breaking fronts (per unit area) moving with speed $c$ to $c+dc$ following Phillips 1985, is reported for a broad range of conditions. We recover the $Λ(c) \propto c^{-6}$ scaling without any explicit wind forcing for steep enough wave fields. A scaling of $Λ(c)$ based solely on the mean square slope and peak wave phase speed is shown to describe the modelled breaking distributions well. The modelled breaking distributions are found to be in good agreement with field measurements and the proposed scaling is consistent with previous empirical formulations. The present work paves the way for simulations of the turbulent upper ocean directly coupled with realistic breaking waves dynamics, including Langmuir turbulence, and other sub-mesoscale processes.

physics.flu-dyn↗

arXiv2022

High-resolution direct simulation of deep water breaking waves: transition to turbulence, bubbles and droplet production

[Abridged]We present high-resolution three-dimensional direct numerical simulations of breaking waves solving the two-phase Navier-Stokes equations. We investigate the role of the Reynolds and Bond numbers on the energy, bubble and droplet statistics of strong plunging breakers, and explore the asymptotic regimes at high Reynolds and Bond numbers to be compared with laboratory breaking waves. Energetically, the breaking wave transitions from laminar to three-dimensional turbulent flow on a timescale that depends on the turbulent Reynolds number up to a limiting value of $Re_λ\sim 100$, consistent with the mixing transition observed in other canonical turbulent flows. We characterize the role of capillary effects on the impacting jet and ingested main cavity shape and subsequent fragmentation process. We confirm two regimes in the bubble size distribution, separated by the Hinze scale $r_H$. We extend the buoyant-energetic scaling of Deike et al. (2016) to account for the cavity shape and its scale separation from the Hinze scale. We show resolved bubbles up to one order of magnitude below the Hinze scale and observe a good collapse of the numerical data compared to laboratory breaking waves (Deane and Stokes 2002). We resolve droplet statistics at high Bond number and our data show good agreement with recent experiments (Erinin et al., 2009) in various statistics. We discuss velocity distributions for the droplets, finding ejection velocities up to four times the phase speed of the wave, which are produced during the most intense splashing events of the breaking process.

physics.flu-dyn↗

arXiv2020

Direct Numerical Simulation of bubble-induced turbulence at high Reynolds numbers

We report on a investigation of turbulent bubbly flows. Bubbles of a size larger than the dissipative scale, cannot be treated as point-wise inclusions, and generate important hydrodynamic fields in the carrier fluid when in motion. Furthermore, when the volume fraction of bubbles is large enough, the bubble motion may induce a collective agitation due to hydrodynamic interactions which display some turbulent-like features. We tackle this complex phenomenon numerically, performing direct numerical simulations (DNS) with a Volume-of-fluid (VOF) method. In the first part of the work, we perform both 2D and 3D tests in order to determine appropriate numerical and physical parameters. We then carry out a highly-resolved simulation of a 3D bubble column, with a configuration and physical parameters similar to those used in laboratory experiments. This is the largest simulation attempted for such a configuration and is possible only thanks to adaptive grid refinement. Results are compared both with experiments and previous coarse-mesh numerical simulations. In particular, the one-point Probability Density Function (PDF) of the liquid velocity fluctuations is in good quantitative agreement with experiments, notably in the vertical direction, although more extreme events are sampled in the present configuration. The spectra of the liquid kinetic energy show a clear $k^{-3}$ scaling. The mechanisms underlying the energy transfer and notably the possible presence of a cascade are unveiled by a local scale-by-scale analysis in the physical space. The comparison with previous simulations indicate to what extent simulations not fully resolved may yet give correct results, from a statistical point of view.

physics.flu-dyn↗

arXiv2020

Dynamic wetting failure in curtain coating by the Volume-of-Fluid method

In this paper we investigate dynamic wetting in the curtain coating configuration. The two-phase Navier-Stokes equations are solved by a Volume-of-Fluid method on an adaptive Cartesian mesh. We introduce the Navier boundary condition to regularize the solution at the triple point and remove the implicit numerical slip induced by the cell-centered interface advection. We use a constant contact angle to describe the dynamic contact line. The resolution of the governing equations allows us to predict the substrate velocity at which wetting failure occurs. The model predictions are compared with prior computations and experimental observations.

physics.flu-dyn↗

arXiv2020

Short-term oscillation and falling dynamics for a water drop dripping in quiescent air

The short-term transient falling dynamics of a dripping water drop in quiescent air has been investigated through both simulation and experiment. The focus is on the short term behavior and the time range considered covers about eight dominant second-mode oscillations of the drop after it is formed. Due to the small fluid inertia the growth of the drop is quasi-static and is well captured by the static pendant drop theory. Nevertheless, the pinching dynamics and the resulting post-formation state of the drop trigger a nonlinear oscillation when the drop falls. The initial shape of the drop when it is just formed is decomposed into spherical harmonic modes. The pinching dynamics such as interface overturning introduces small-scale variation on the drop contour, which in turn contributes to the finite amplitudes of the higher-order modes. Furthermore, the initial kinetic energy when the droplet is just formed is as important as the initial surface energy contained in the drop shape, and is found to amplify the initial oscillation amplitude and to induce a phase shift in the oscillation of all the modes. By incorporating both the initial surface and kinetic energy, the linear model for a free drop oscillation yields very good predictions for the second and third modes. The mode amplitude spectra show both the primary frequencies that are consistent with the Lamb's theory and the secondary frequencies arising from different modes due to nonlinear inter-mode coupling. The complex transient flow inside and outside the drop is induced by the interaction between the falling motion and the nonlinear oscillation. The streamlines indicate that the internal flow is substantially different from the Hill vortex for a falling drop without oscillation. The temporal evolutions of both the internal flow and the wake morphology follow the dominant second oscillation mode.

physics.flu-dyn↗