Stéphane Popinet

• PhD
• Directeur de recherche at French National Centre for Scientific Research

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 numeric...

Accurate numerical modeling of surface tension has been a challenging aspect of multiphase flow simulations. The integral formulation for modeling surface tension forces is known to be consistent and conservative, and to be a natural choice for the simulation of flows driven by surface tension gradients along the interface. This formulation was int...

Fragmentation of a fluid body into droplets underlies many contamination and disease transmission processes where pathogens are transported in a liquid phase. An important class of such processes involves formation of a fluid ligament and its destabilization into droplets. Inertial detachment (Gilet & Bourouiba, J. R. Soc. Interface , vol. 12, 2015...

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 $\varepsilon$ that is understood as a physical parameter of the model. Therefore, we call the model th...

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 condi...

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...

Improved numerical methods are needed to understand the effect of surfactants in interfacial fluid mechanics, with various applications including thin films, inkjet printing, and ocean-atmosphere interactions. We provide a three-dimensional coupled volume of fluid (VoF) and phase field numerical approach to simulate the effects of insoluble surfact...

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...

Numerical methods for the simulation of cavitation processes have been developed for more than 50 years. The rich variety of physical phenomena triggered by the collapse of a bubble has several applications in medicine and environmental science but requires the development of sophisticated numerical methods able to capture the presence of sharp int...

Granular flows occur in various contexts, including laboratory experiments, industrial processes, and natural geophysical flows. To investigate their dynamics, different kinds of physically based models have been developed. These models can be characterized by the length scale at which dynamic processes are described. Discrete models use a microsco...

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 t...

The statistics of breaking wave fields are 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 nonlinearities, includi...

We combine experiments and numerical computations to examine underlying fluid mechanical processes associated with bioaerosol generation during violent respiratory maneuvers, 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 cha...

We perform direct numerical simulations of a gas bubble dissolving in a surrounding liquid. The bubble volume is reduced due to dissolution of the gas, with the numerical implementation of an immersed boundary method, coupling the gas diffusion and the Navier–Stokes equations. The methods are validated against planar and spherical geometries’ analy...

In this paper, we introduce a novel way to represent the interface for two-phase flows with phase change. We combine a level-set method with a Cartesian embedded boundary method and take advantage of both. This is part of an effort to obtain a numerical strategy relying on Cartesian grids allowing the simulation of complex boundaries with possible...

This paper is associated with a poster winner of a 2021 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2021.GFM.P0005.

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 includin...

We investigate wind wave growth by direct numerical simulations solving for the two-phase Navier–Stokes equations. We consider the ratio of the wave speed $c$ to the 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. Th...

A well-known drawback of the Volume-Of-Fluid (VOF) method is that the breakup of thin liquid films or filaments is mainly caused by numerical aspects rather than by physical ones. The rupture of thin films occurs when their thickness reaches the order of the grid size and by refining the grid the breakup events are delayed. When thin filaments rupt...

We present high-resolution three-dimensional (3-D) direct numerical simulations of breaking waves solving for the two-phase Navier–Stokes equations. We investigate the role of the Reynolds number ( Re , wave inertia relative to viscous effects) and Bond number ( Bo , wave scale over the capillary length) on the energy, bubble and droplet statistics...

We present a numerical solver for the incompressible Navier-Stokes equations that combines fourth-order-accurate discrete approximations and an adaptive tree grid (i.e. h-refinement). The scheme employs a novel compact-upwind advection scheme and a 4th-order accurate projection algorithm whereby the numerical solution exactly satisfies the incompre...

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 th...

Theoretical source models of underwater explosions are often applied in studying tsunami hazards associated with subaqueous volcanism; however, their use in numerical codes based on the shallow water equations can neglect the significant dispersion of the generated wavefield. A non-hydrostatic multilayer method is validated against a laboratory-sca...

Mesoscale eddies, although being on the scales of O (20–100km), have a dispro-portionate role in shaping the mean stratification, which varies on the scale of O (1000km). With the increase in computational power, we are now able to partially resolve the eddies in basin-scale and global ocean simulations, a model resolution often referred to as meso...

In this paper, we introduce a novel way to represent the interface for two-phase flows with phase change. We combine a level-set method with a Cartesian embedded boundary method and take advantage of both. This is part of an effort to obtain a numerical strategy relying on Cartesian grids allowing the simulation of complex boundaries with possible...

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 wave steepness $ak$ from 0.1 to 0.25; the two being varied independently. The turbulent win...

Mass transfer between liquid steel and slag is an important physical phenomenon during secondary metallurgy for prediction of the chemical reaction rate and adjustment of liquid steel composition. We study this phenomenon at ambient temperature with a water experiment and perform Direct Numerical Simulations, aiming to reproduce an argon-gas bottom...

Bubbles bursting at the ocean surface are an important source of sea-spray aerosol. Indeed, a bubble bursting at the surface of a liquid produces a jet that then breaks up leading to several droplets. Here we simulate the bursting of a single bubble by numerical simulation of the axisymmetric two-phases air-water Navier-Stokes equations in the pres...

The French Riviera is very often threatened by flash floods. These hydro-meteorological events, which are fast and violent, have catastrophic consequences on life and property. The development of forecasting tools may help to limit the impacts of these extreme events. Our purpose here is to demonstrate the possibility of using b-flood (a subset of...

The tsunami generation potential of pyroclastic density currents (PDCs) entering the sea is poorly understood, due to limited data and observations. Thus far, tsunami generation by PDCs has been modeled in a similar manner to tsunami generation associated with landslides or debris flows, using two‐layer depth‐averaged approaches. Using the adaptive...

A well-known drawback of the Volume-Of-Fluid (VOF) method is that the breakup of thin liquid films or filaments is mainly caused by numerical aspects rather than by physical ones. The rupture of thin films occurs when their thickness reaches the order of the grid size and by refining the grid the breakup events are delayed. When thin filaments rupt...

A series of benchmarks based on the physical situation of “phase inversion” between two immiscible liquids is presented. These benchmarks aim at progressing towards the direct numerical simulation of two-phase flows. Several CFD codes developed in French laboratories and using either Volume-of-Fluid or Level-Set interface tracking methods are used...

Theoretical source models of underwater explosions are often applied in studying tsunami hazards associated with submarine volcanism; however, their use in numerical codes based on the shallow water equations can neglect the significant dispersion of the generated wavefield. A non-hydrostatic multilayer method is validated against a laboratory-scal...

Mesoscale eddies, the weather system of the oceans, although being on the scales of O(20-100 km), have a disproportionate role in shaping the mean jets such as the separated Gulf Stream in the North Atlantic Ocean, which is on the scale of O(1000 km) in the along-jet direction. With the increase in computational power, we are now able to partially...

Bubbles bursting at the ocean surface are an important source of sea-spray aerosol. We describe jet drop production, from ensembles of high fidelity numerical simulations of bubble bursting, validated against experimental results. The number of jet drops, their size, and velocity are controlled by the ratio of the bubble size, Rb, and the visco-cap...

Bubble-mediated gas exchange in turbulent flow is critical in bubble column chemical reactors as well as for ocean-atmosphere gas exchange related to air entrained by breaking waves. Understanding the transfer rate from a single bubble in turbulence at large Péclet numbers (defined as the ratio between the rate of advection and diffusion of gas) is...

The French Riviera is very often threatened by flash floods. These hydro-meteorological events, which are fast and violent, have catastrophic consequences on life and properties. The development of forecasting tools may help to limit the impacts of these extreme events. Our purpose here is to demonstrate the possibility of using b-flood (a subset o...

[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 t...

As a consequence of the remarkable advances in computational sciences realized over the past decades, complex physical processes can now be simulated. To insure fidelity and accuracy, precise convergence criteria must be satisfied. While efforts have been dedicated towards the validation of the computational tools specialized in two-phase flows, th...

In this work, we use Direct Numerical Simulation (DNS) through a Volume of Fluid (VOF) solver with Adaptive Mesh Refinement (AMR) to analyze the atomization of a pulsating round liquid jet with a narrow length scale range configuration. We propose three grid sizes based on characteristic scales we estimate from the deformation and fragmentation pro...

In this article, we extend our Distributed Lagrange Multiplier/Fictitious Domain method previously implemented on simple regular Cartesian grids to quadtree/octree adaptive grids. The objective is to improve both the accuracy and efficiency of our DLM/FD particle-resolved simulation method by extending its computing capabitilies through dynamic loc...

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...

We numerically study the retraction of an axisymmetric viscous filament in a passive surrounding fluid. The analysis focuses on the evolution of the tip velocity, from the early stage of the filament retraction until it reaches its final equilibrium spherical shape. The problem is governed by two control parameters: the Ohnesorge number, Oh, which...

In this paper, we present a detailed example of numerical study of film formation in the context of metal coating. Subsequently we simulate wiping of the film by a planar jet. The simulations have been performed using Basilisk, a grid-adapting, strongly optimized code. Mesh adaptation allows for arbitrary precision in relevant regions such as the c...

We numerically study the retraction of an axisymmetric viscous filament in a passive surrounding fluid. The analysis focuses on the evolution of the tip velocity, from the early stage of the filament retraction until it reaches its final equilibrium spherical shape. The problem is governed by two control parameters: the Ohnesorge number, Oh, which...

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 i...

The injection and atomization of gasoline fuels are critical to the performance of gasoline direct injection engines. Due to the complex nature of the primary breakup of the liquid jet in the near field, high-level details are often difficult to measure in experiments. In the present study, detailed numerical simulations are performed to investigat...

The injection and atomization of gasoline fuels are critical to the performance of gasoline direct injection engines. Due to the complex nature of the primary breakup of the liquid jet in the near field, high-level details are often difficult to measure in experiments. In the present study, detailed numerical simulations are performed to investigat...

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...

When a bubble bursts at the surface of a liquid, it creates a jet that may break up and produce jet droplets. This phenomenon has motivated numerous studies due to its multiple applications, from bubbles in a glass of champagne to ocean/atmosphere interactions. We simulate the bursting of a single bubble by direct numerical simulations of the axisy...

We report on a numerical 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 important enough, the bubble motion may induce a collec...

In this work, we use Direct Numerical Simulation (DNS) through a Volume of Fluid (VOF) solver with Adaptive Mesh Refinement (AMR) to analyze the atomization of a pulsating round liquid jet with a narrow length scale range configuration. We propose three grid sizes based on characteristic scales we estimate from the deformation and fragmentation pro...

We studied experimentally the discharge of a vertical silo filled by spherical glass beads and assisted by injection of air from the top at a constant flow rate, a situation which has practical interest for nuclear safety or air-assisted discharge of hoppers. The measured parameters are the mass flow rate and the pressure along the silo, while the...

We study the flow of a thin layer of fluid over a flat surface. Commonly, the 1-D Shallow-water or Saint-Venant set of equations are used to compute the solution of such flows. These simplified equations may be obtained through the integration of the Navier–Stokes equations over the depth of the fluid, but their solution requires the introduction o...

In this paper, we present a detailed example of numerical study of flm formation in the context of metal coating. Subsequently we simulate wiping of the film by a planar jet. The simulations have been performed using Basilisk, a grid-adapting, strongly optimized code. Mesh adaptation allows for arbitrary precision in relevant regions such as the co...

In this work we present experimental results of the gravity-driven discharge of poppy seeds from three-dimensionally (3D) printed silos. The velocity fields of the flowing poppy seeds are measured using magnetic resonance imaging (MRI) velocimetry techniques. Crucially, this approach allows the velocity field to be determined throughout the flow do...

This work studies the breakup of finite-size liquid filaments, when also including substrate effects, using direct numerical simulations. The study focuses on the effects of three parameters: Ohnesorge number, the ratio of the viscous forces to inertial and surface tension forces, the liquid filament aspect ratio, and where there is a substrate, a...

We propose an adaptive numerical solver for the study of viscoelastic 2D two-phase flows using the volume-of-fluid method. The scheme uses the robust log conformation tensor technique of Fattal and Kupferman (2004, 2005) [1,2] combined with the time-split scheme proposed by Hao and Pan (2007) [3]. The use of such a time-split scheme has been proven...

We propose an adaptive numerical solver for the study of viscoelastic 2D two-phase flows using the volume-of-fluid method. The scheme uses the robust log conformation tensor technique of Fattal & Kupferman (2004,2005} combined with the time-split scheme proposed by Hao & Pan (2007}. The use of this time-split scheme has been proven to increase the...

Introduction In the process of coating-such as found in photography, lamination or metallurgy, a moving flat sheet of coated material (e.g. steel) emerges-usually moving vertically-from a bath of liquid coating material. Depending on parameters the resulting film formation process may be entirely laminar or turbulent [1]. This first stage process o...

We investigate droplet impact on a solid substrate in order to understand the influence of the gas in the splashing dynamics. We use numerical simulations where both the liquid and the gas phases are considered incompressible in order to focus on the gas inertial and viscous contributions. We first confirm that the dominant gas effect on the dynami...

Sea spray is the main source of aerosols above the ocean. One of the pathways for sea spray production is through bubble bursting, which ejects myriads of droplets. We present a detailed description of the velocity of jets formed by bubble bursting, obtained through extensive comparison between experimental results and numerical simulations for a w...

The utilization of biodiesel is an effective approach to reduce pollution from internal combustion engines and thushas attracted steadily increasing interest in the recent years. As the viscosity of biodiesel is much higher than that of standard diesel, the atomization characteristics of a biodiesel jet can significantly deviate from those of a sta...

Using an incompressible Navier-Stokes solver with a modified non-Newtonian viscosity, we implement the μ(I)-rheology and study the transient arrest for thick granular layers. In order to study the stopping height phenomenology Hstop, we implement the steady-state-only approximate version of the non-local model from [6, 7] and successfully incorpora...

Granular material flowing on complex topographies are ubiquitous in industrial and geophysical situations. Even model granular flows are difficult to understand and predict. Recently, the frictional rheology μ(I) -describing the ratio of the shear stress to the normal stress as a function of the inertial number I, that compares inertial and confine...

Industrial storage of granular material using silos is common, however, improved understanding of silo flow is needed. Various continuum models attempt to describe the velocity of dense granular flow in silos. Kinematic, and recently, stochastic models, based upon the diffusion of some quantity, perform well when there is a single orifice, and when...

The thin layer (or Boundary Layer scaling) approximation of the Navier Stokes equation with μ(I) rheology for dry granular flows over an inclined plate is presented. It is called “Granular RNS/P” (Reduced Navier Stokes/ Prandtl). Integrated over the depth, it gives the classical depth averaged equations (Shallow Water type equations, popularized by...

Modeling and simulating overland flow fed by rainfall is a common issue in watershed surface hydrology. Modelers have to choose among various friction models when defining their simulation framework. The purpose of this work is to compare the simulation quality for the Manning, Darcy-Weisbach, and Poiseuille friction models on the simple case of a...

The Cook Strait Canyon is a submarine canyon which lies within 10 km of Wellington, the capital city of New Zealand. The canyon flanks are scarred with the evidence of past landslides that may have caused large local tsunamis. City planning and civil defence management require information on the magnitude and frequency of these tsunamis to adequate...

Droplet migration in a Hele–Shaw cell is a fundamental multiphase flow problem which is crucial for many microfluidics applications. We focus on the regime at low capillary number and three-dimensional direct numerical simulations are performed to investigate the problem. In order to reduce the computational cost, an adaptive mesh is employed and h...

Droplet migration in a Hele--Shaw cell is a fundamental multiphase flow problem which is crucial for many microfluidics applications. We focus on the regime at low capillary number and three-dimensional direct numerical simulations are performed to investigate the problem. In order to reduce the computational cost, an adaptive mesh is employed and...

Droplet-based microfluidics is a promising tool for performing biochemical or chemical assays. Droplets are unit systems of controlled volume and content, within which mixing, reacting and/or transferring can be achieved. Therefore, a comprehensive understanding of droplet migration in confined microchannels is essential to many microfluidics appli...

Modeling and simulating overland flow fed by rainfall is a common issue in watershed surface hydrology. Modelers have to chose among various friction models when defining their simulation framework. The purpose of this work is to compare the simulation quality for the Manning, Darcy-Weisbach, and Poiseuille friction models on the simple case of a c...

We propose a numerical approach to study the mechanics of a flowing bubble in a constraint micro channel. Using an open source two phase flow solver (Gerris, gfs.sourceforge.net) we compute solutions of the bubble dynamics (i.e. shape and terminal velocity) induced by the interaction between the bubble movement, the Laplace pressure variation, and...

We present a study of viscous fingering using the Volume Of Fluid method and a central injection geometry, assuming a Laplacian field and a simple surface tension law. As in experiments we see branched structures resulting from the Saffman-Taylor instability. We find that the area A of a viscous-fingering cluster varies as a simple power law A∼L α...

Using a continuum Navier-Stokes solver with the μ(I) flow law implemented to model the viscous behavior, and the discrete Contact Dynamics algorithm, the discharge of granular silos is simulated in two dimensions from the early stages of the discharge until complete release of the material. In both cases, the Beverloo scaling is recovered. We first...

This article investigates the appearance of instabilities in two planar coflowing fluid sheets with different densities and viscosities via experiments, numerical simulation and linear stability analysis. At low dynamic pressure ratios a convective instability is shown to appear for which the frequency of the waves in the primary atomization region...

Bingham plastics exhibit complex behaviors, depending on both geometrical and rheological factors, and are difficult to characterize systematically. This is particularly true in the case of transient flows, where solidlike and fluidlike behaviors coexist in an intermittent fashion. The aim of this contribution is to study the slump of Bingham colum...

Implementing a plastic rheology (using the μ(I)-rheology [5]) in a 2D Navier-Stokes solver, we simulate the continuum counterpart of the granular silo. Doing so, we observe a constant flow rate during the discharge and recover the Beverloo scaling. The results suggest that the constant discharge rate is due to the existence of a friction-dependent...

The granular silo is one of the many interesting illustrations of the thixotropic property of granular matter: a rapid flow develops at the outlet, propagating upwards through a dense shear flow while material at the bottom corners of the container remains static. For large enough outlets, the discharge flow is continuous; however, by contrast with...

We present a robust and computationally efficient numerical scheme for simulating steady electrohydrodynamic atomization processes (electrospray). The main simplification assumed in this scheme is that all the free electrical charges are distributed over the interface. A comparison of the results with those calculated with a volume-of-fluid method...