2025

titre

Modéliser mathématiquement la mucoviscidose

auteur

Philippe Poncet, Marlène Murris-Espin, Stéphanie Bui, Jean-Matthieu Etancelin, Michael Fayon, Siham Mallah, Juliette Gaudry

article

Ébullition(s) : le cahier illustré de la recherche, 2025, ⟨10.59655/ne52122995494⟩

resume

Le projet MucoReaDy vise à modéliser le transport du mucus dans les poumons pour évaluer son bon fonctionnement, en particulier chez les patients atteints de mucoviscidose. En combinant des prélèvements cliniques et des équations décrivant le mucus bronchique, le modèle identifie des paramètres permettant d’identifier un mucus sain ou pathologique. Cette cartographie permet de suivre l’évolution des patients sous trithérapie et de déterminer des signes avant-coureurs de dégradation de leur santé.

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titre

A semi-Lagrangian method for the direct numerical simulation of crystallization and precipitation at the pore scale

auteur

Sarah Perez, Jean-Matthieu Etancelin, Philippe Poncet

article

Frontiers in Earth Science, 2025, 13, pp.1493305. ⟨10.3389/feart.2025.1493305⟩

resume

This article introduces a new efficient particle method for the numerical simulation of crystallization and precipitation at the pore scale of real rock geometries extracted by X-Ray tomography. It is based on the coupling between superficial velocity models of porous media, Lagrangian description of chemistry using Transition-State-Theory, involving underlying grids. Its ability to successfully compute dissolution process has been established in the past, and is presently generalized to precipitation and crystallization by means of adsorption modeling. Numerical simulations of mineral CO 2 trapping are provided, showing evidence of clogging/non-clogging regimes, and one of the main results is the introduction of a new non-dimensional number needed for this characterization.

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2024

titre

Auto-weighted Bayesian Physics-Informed Neural Networks and robust estimations for multitask inverse problems in pore-scale imaging of dissolution

auteur

Sarah Perez, Philippe Poncet

article

Computational Geosciences, 2024, 28, pp.1175-1215. ⟨10.1007/s10596-024-10313-x⟩

resume

In this article, we present a novel data assimilation strategy in pore-scale imaging and demonstrate that this makes it possible to robustly address reactive inverse problems incorporating Uncertainty Quantification (UQ). Pore-scale modeling of reactive flow offers a valuable opportunity to investigate the evolution of macro-scale properties subject to dynamic processes. Yet, they suffer from imaging limitations arising from the associated X-ray microtomography (X-ray µCT) process, which induces discrepancies in the properties estimates. Assessment of the kinetic parameters also raises challenges, as reactive coefficients are critical parameters that can cover a wide range of values. We account for these two issues and ensure reliable calibration of pore-scale modeling, based on dynamical µCT images, by integrating uncertainty quantification in the workflow. The present method is based on a multitasking formulation of reactive inverse problems combining data-driven and physics-informed techniques in calcite dissolution. This allows quantifying morphological uncertainties on the porosity field and estimating reactive parameter ranges through prescribed PDE models with a latent concentration field and dynamical µCT. The data assimilation strategy relies on sequential reinforcement incorporating successively additional PDE constraints and suitable formulation of the heterogeneous diffusion differential operator leading to enhanced computational efficiency. We guarantee robust and unbiased uncertainty quantification by straightforward adaptive weighting of Bayesian Physics-Informed Neural Networks (BPINNs), ensuring reliable micro-porosity changes during geochemical transformations. We demonstrate successful Bayesian Inference in 1D+Time calcite dissolution based on synthetic µCT images with meaningful posterior distribution on the reactive parameters and dimensionless numbers. We eventually apply this framework to a more realistic 2D+Time data assimilation problem involving heterogeneous porosity levels and synthetic µCT dynamical observations.

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2023

titre

Adaptive weighting of Bayesian physics informed neural networks for multitask and multiscale forward and inverse problems

auteur

Sarah Perez, Suryanarayana Maddu, Ivo F. Sbalzarini, Philippe Poncet

article

Journal of Computational Physics, 2023, 491, pp.112342. ⟨10.1016/j.jcp.2023.112342⟩

resume

In this paper, we present a novel methodology for automatic adaptive weighting of Bayesian Physics-Informed Neural Networks (BPINNs), and we demonstrate that this makes it possible to robustly address multi-objective and multi-scale problems. BPINNs are a popular framework for data assimilation, combining the constraints of Uncertainty Quantification (UQ) and Partial Differential Equation (PDE). The relative weights of the BPINN target distribution terms are directly related to the inherent uncertainty in the respective learning tasks. Yet, they are usually manually set a-priori, that can lead to pathological behavior, stability concerns, and to conflicts between tasks which are obstacles that have deterred the use of BPINNs for inverse problems with multi-scale dynamics. The present weighting strategy automatically tunes the weights by considering the multi-task nature of target posterior distribution. We show that this remedies the failure modes of BPINNs and provides efficient exploration of the optimal Pareto front. This leads to better convergence and stability of BPINN training while reducing sampling bias. The determined weights moreover carry information about task uncertainties, reflecting noise levels in the data and adequacy of the PDE model. We demonstrate this in numerical experiments in Sobolev training, and compare them to analytically $\epsilon$-optimal baseline, and in a multi-scale Lokta-Volterra inverse problem. We eventually apply this framework to an inpainting task and an inverse problem, involving latent field recovery for incompressible flow in complex geometries.

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2022

titre

On the Deviation of Computed Permeability Induced by Unresolved Morphological Features of the Pore Space

auteur

Sarah Perez, Peter Moonen, Philippe Poncet

article

Transport in Porous Media, 2022, 141, pp.151-184. ⟨10.1007/s11242-021-01713-z⟩

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2021

titre

A velocity-vorticity method for highly viscous 3D flows with application to digital rock physics

auteur

Laurène Hume, Philippe Poncet

article

Journal of Computational Physics, 2021, 425, pp.109910. ⟨10.1016/j.jcp.2020.109910⟩

resume

In this article, we present a numerical iterative method for the solution of internal viscous and incompressible flows in real porous three-dimensional bodies at their pore scale. We use the penalized formulation of the problem involving velocity and vorticity: an operator splitting allows to split apart the diffusion (inherited from Stokes equation) and the penalization phenomena (which takes into account the solid matrix). By means of the numerical analysis of the splitting, we exhibit the penalization coefficient which is actually effective. This method allows to deal only with fast-evaluation operators, that is to say scaling at most as O(n log n) where n is the number of underlying grid points, such as straightforward computations of finite differences schemes or FFT solver. The numerical analysis and implementation solutions are presented, and validated on various digital rock physics geometries acquired by micro-tomography, using numerical and physical diagnostics. To enforce this validation, we also present permeability estimations of several porous samples. The simulation of transport of passive and active scalars is finally investigated in order to perform the practical upscaling to 1D models of transport and diffusion at the Darcy scale.

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titre

Simulation of mineral dissolution at the pore scale with evolving fluid-solid interfaces: review of approaches and benchmark problem set

auteur

Sergi Molins, Cyprien Soulaine, N. I. Prasianakis, Aida Abbasi, Philippe Poncet, Anthony J. C. Ladd, Vitalii Starchenko, Sophie Roman, David Trebotich, Hamdi A. Tchelepi, Carl I. Steefel

article

Computational Geosciences, 2021, 25, pp.1285-1318. ⟨10.1007/s10596-019-09903-x⟩

resume

This manuscript presents a benchmark problem for the simulation of single-phase flow, reactive transport, and solid geometry evolution at the pore scale. The problem is organized in three parts that focus on specific aspects: flow and reactive transport (part I), dissolution-driven geometry evolution in two dimensions (part II), and an experimental validation of three-dimensional dissolution-driven geometry evolution (part III). Five codes are used to obtain the solution to this benchmark problem, including Chombo-Crunch, OpenFOAM-DBS, a lattice Boltzman code, Vortex, and dissolFoam. These codes cover a good portion of the wide range of approaches typically employed for solving pore-scale problems in the literature, including discretization methods, characterization of the fluid-solid interfaces, and methods to move these interfaces as a result of fluid-solid reactions. A short review of these approaches is given in relation to selected published studies. Results from the simulations performed by the five codes show remarkable agreement both quantitatively-based on upscaled parameters such as surface area, solid volume, and effective reaction rate-and qualitatively-based on comparisons of shape evolution. This outcome is especially notable given the disparity of approaches used by the codes. Therefore, these results establish a strong benchmark for the validation and testing of pore-scale codes developed for the simulation of flow and reactive transport with evolving geometries. They also underscore the significant advances seen in the last decade in tools and approaches for simulating this type of problem.

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2020

titre

Improvement of remeshed Lagrangian methods for the simulation of dissolution processes at pore-scale

auteur

Jean-Matthieu Etancelin, Peter Moonen, Philippe Poncet

article

Advances in Water Resources, 2020, 146, pp.103780. ⟨10.1016/j.advwatres.2020.103780⟩

resume

This article shows how to consistently and accurately manage the Lagrangian formulation of chemical reaction equations coupled with the superficial velocity formalism introduced in the late 80s by Quintard and Whitaker. Lagrangian methods prove very helpful in problems in which transport effects are strong or dominant, but they need to be periodically put back in a regular lattice, a process called remeshing. In the context of digital rock physics, we need to ensure positive concentrations and regularity to accurately handle stagnation point neighborhoods. These two conditions lead to the use of kernels resulting in extra-diffusion, which can be prohibitively high when the diffusion coefficient is small. This is the case especially for reactive porous media, and the phenomenon is reinforced in porous rock matrices due to Archie's law. This article shows how to overcome this difficulty in the context of a two-scale porosity model applied in the Darcy-Brinkman-Stokes equations, and how to obtain simultaneous sign preservation, regularity and accurate diffusion, and apply it to dissolution processes at the pore scale of actual rocks.

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2019

titre

Analysis of 3D non-linear Stokes problem coupled to transport-diffusion for shear-thinning heterogeneous microscale flows, applications to digital rock physics and mucociliary clearance

auteur

David Sanchez, Laurène Hume, Robin Chatelin, Philippe Poncet

article

ESAIM: Mathematical Modelling and Numerical Analysis, 2019, 53 (4), pp.1083-1124. ⟨10.1051/m2an/2019013⟩

resume

The present study provides the analysis of the generalized 3D Stokes problem in a time dependent domain. The fluid viscosity is nonlinear and depends on a transported and diffused quantity. This is a natural model of very low Reynolds number flow, typically at the microscale, involving a heterogeneous shear-thinning miscible medium transported and diffusing in a solvent filling a deformable geometry. This one-way coupling is meaningful when the action produced by the solid on the fluid is dominant or drives the flow. Several mathematical aspects are developed. The penalized version of this problem is introduced, involving the penalization of the solid in a deformable motion but defined in a simple geometry, which is of crucial interest for many numerical methods. All the equations of this partial differential system are analyzed separately, and then the coupled model is shown to be well-posed and to converge toward the solution of the initial problem. In order to illustrate the pertinence of such models, two meaningful micrometer scale real-life problems are presented: the dynamics of a polymer inside the pores of a real rock, in practice a Xanthan biodegradable polymer percolating a Bentheimer sandstone and miscible in water, and the dynamics of the strongly heterogeneous mucus bio-film, covering the human lungs surface, propelled by the vibrating ciliated cells. For these two examples, we show that the mathematical hypothesis are satisfied.

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2018

titre

Effective viscosity of a random mixture of fluids

auteur

Benoit Noetinger, Laurène Hume, Robin Chatelin, Philippe Poncet

article

Physical Review Fluids, 2018, 3 (1), pp.014103. ⟨10.1103/PhysRevFluids.3.014103⟩

resume

We propose an estimation of the effective viscosity of a random mixture of Newtonian fluids that ignores capillary effects. The local viscosity of the mixture is assumed to be a random function of the position. Using perturbation expansions up to the second order, the resulting formula can be recast under the form of a simple power averaging mixing low. Numerical tests are used to assess the validity of the formula and the range of its applicability.

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2017

titre

Numerical and experimental investigation of mucociliary clearance breakdown in cystic fibrosis

auteur

Robin Chatelin, Dominique Anne-Archard, Marlene Murris-Espin, Marc Thiriet, Philippe Poncet

article

Journal of Biomechanics, 2017, 53, pp.56-63. ⟨10.1016/j.jbiomech.2016.12.026⟩

resume

The human tracheobronchial tree surface is covered with mucus. A healthy mucus is an heterogeneous material flowing toward the esophagus and a major defense actor against local pathogen proliferation and pollutant deposition. An alteration of mucus or its environment such as in cystic fibrosis dramatically impacts the mucociliary clearance. In the present study, we investigate the mechanical organization and the physics of such mucus in human lungs by means of a joint experimental and numerical work. In particular, we focus on the influence of the shear-thinning mucus mobilized by a ciliated epithelium for mucociliary clearance. The proposed robust numerical method is able to manage variations of more than 5 orders of magnitude in the shear rate and viscosity. It leads to a cartography that allows to discuss major issues on defective mucociliary clearance in cystic fibrosis. Furthermore, the computational rheological analysis based on measurements shows that cystic fibrosis shear-thinning mucus tends to aggregate in regions of lower clearance. Yet, a rarefaction of periciliary fluid has a greater impact than the mucus shear-thinning effects.

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2016

titre

A parametric study of mucociliary transport by numerical simulations of 3D non-homogeneous mucus

auteur

Robin Chatelin, Philippe Poncet

article

Journal of Biomechanics, 2016, 49 (9), pp.1772-1780. ⟨10.1016/j.jbiomech.2016.04.009⟩

resume

Mucus 3D computations of non-homogeneous flows Fluid-structure interaction in complex geometry a b s t r a c t Mucociliary clearance is the natural flow of the mucus which covers and protects the lung from the outer world. Pathologies, like cystic fibrosis, highly change the biological parameters of the mucus flow leading to stagnation situations and pathogens proliferation. As the lung exhibits a complex dyadic structure, in-vivo experimental study of mucociliary clearance is almost impossible and numerical simulations can bring important knowledge about this biological flow. This paper brings a detailed study of the biological parameters influence on the mucociliary clearance, in particular for pathological situations such as cystic fibrosis. Using recent suitable numerical methods, a non-homogeneous mucus flow (including non-lin-earities) can be simulated efficiently in 3D, allowing the identification of the meaningful parameters involved in this biological flow. Among these parameters, it is shown that the mucus viscosity, the stiffness transition between pericilliary fluid and mucus, the pericilliary fluid height as well as both cilia length and beating frequency have a great influence on the mucociliary transport.

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titre

Analysis of the penalized 3D variable viscosity stokes equations coupled to diffusion and transport

auteur

Robin Chatelin, David Sanchez, Philippe Poncet

article

ESAIM: Mathematical Modelling and Numerical Analysis, 2016, 50 (2), pp.565-591. ⟨10.1051/m2an/2015056⟩

resume

The analysis of the penalized Stokes problem, in its variable viscosity formulation, coupled to convection-diffusion equations is presented in this article. It models the interaction between a highly viscous fluid with variable viscosity and immersed moving and deformable obstacles. Indeed, while it is quite common to couple Poisson equations to diffusion-transport equations in plasma physics or fluid dynamics in vorticity formulations, the study of complex fluids requires to consider together the Stokes problem in complex moving geometry and convection-diffusion equations. The main result of this paper shows the existence and the uniqueness of the solution to this equations system with regularity estimates. Then we show that the solution to the penalized problem weakly converges toward the solution to the physical problem. Numerical simulations of fluid mechanics computations in this context are also presented in order to illustrate the practical aspects of such models: lung cells and their surrounding heterogeneous fluid, and porous media flows. Among the main original aspects in the present study, one can highlight the non linear dynamics induced by the coupling, and the tracking of the time-dependence of the domain.

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2015

titre

Mucus and Ciliated Cells of Human Lung: Splitting Strategies for Particle Methods and 3D Stokes Flows

auteur

R. Chatelin, Philippe Poncet, A. Didier, M. Murris-Espin, Dominique Anne-Archard, M. Thiriet

article

Procedia IUTAM, 2015, 18, pp.114-122. ⟨10.1016/j.piutam.2015.11.012⟩

resume

This work is introducing a fractional step algorithm for diffusion-transport allowing computation of flows with sharp variations of viscosity. This splitting also allows to perform transport with Lagrangian methods and diffusion with Eulerian methods, using hybrid grid-particle formulation. This splitting algorithm is globally second order. It is applied to computation of mucus mobility in human lungs, where epithelium ciliated cells are beating. A sufficient mobility is required to have healthy configurations. Our goal is to study the dependency of mucus mobility with respect to its viscosity in order to investigate mechanisms involved in pathologies such as cystic fibrosis. Scientific computing involving phenomena where transport effects are dominant, is still a challenge for realistic modeling of complex flows. Among the most famous problems, one can find Euler and Navier-Stokes equations, in velocity-pressure or velocity-vorticity formulations, with various boundary conditions. Particle and vortex methods are a well-known and efficient tool for this kind of problem. In the present paper we describe some aspects on how to use particle methods in the context of highly viscous flows. The application investigated is the propulsion of pulmonary mucus in human lungs. A meaningful model is 3D Stokes flows with a variable viscosity, depending on concentration of proteins (mucins), itself following a diffusion-transport equation. In additions to this coupling, the mucus film covering lung walls is interacting with epithelium ciliated cells, vibrating in the range of 4 to 20 Hz, as shown on figure 1. In the present study we neglect interactions between mucus and air (proven to be a non-dominant interaction), and visco-elastic effects. The aspect we aim at developing in this article is how to split diffusion and transport in this context.

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2014

titre

Hybrid grid–particle methods and Penalization: A Sherman–Morrison–Woodbury approach to compute 3D viscous flows using FFT

auteur

Robin Chatelin, Philippe Poncet

article

Journal of Computational Physics, 2014, 269, pp.314-328. ⟨10.1016/j.jcp.2014.03.023⟩

resume

Particle methods are very convenient to compute transport equations in fluid mechanics as their computational cost is linear and they are not limited by convection stability conditions. To achieve large 3D computations the method must be coupled to efficient algorithms for velocity computations, including a good treatment of non-homogeneities and complex moving geometries. The Penalization method enables to consider moving bodies interaction by adding a term in the conservation of momentum equation. This work introduces a new computational algorithm to solve implicitly in the same step the Penalization term and the Laplace operators, since explicit computations are limited by stability issues, especially at low Reynolds number. This computational algorithm is based on the Sherman-Morrison-Woodbury formula coupled to a GMRES iterative method to reduce the computations to a sequence of Poisson problems: this allows to formulate a penalized Poisson equation as a large perturbation of a standard Poisson, by means of algebraic relations. A direct consequence is the possibility to use fast solvers based on Fast Fourier Transforms for this problem with good efficiency from both the computational and the memory consumption point of views, since these solvers are recursive and they do not perform any matrix assembling. The resulting fluid mechanics computations are very fast and they consume a small amount of memory, compared to a reference solver or a linear system resolution. The present applications focus mainly on a coupling between transport equation and 3D Stokes equations, for studying biological organisms motion in a highly viscous flows with variable viscosity.

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2013

titre

A Hybrid Grid-Particle Method for Moving Bodies in 3D Stokes Flow with Variable Viscosity

auteur

Robin Chatelin, Philippe Poncet

article

SIAM Journal on Scientific Computing, 2013, 35 (4), pp.B925-B949. ⟨10.1137/120892921⟩

resume

This article presents a new approach for the resolution of large three-dimensional Stokes equations with variable viscosity fluids, coupled with transport equations. After building the model, we will write these equations in the context of highly viscous flows and penalization, in order to consider complex geometries moving in a fluid. From a mathematical point of view, the solutions show nonlinear dynamics. Beside the use of standard tools such as finite differences and staggered grids, we have built a new methodology based on large three-dimensional simulations, including operators splitting for an efficient use of fast solvers, multi-index fixed point methods, Lagrangian methods with fast and accurate grid-particle transfers, and the multiresolution description of variables. Among the main original aspects of this method, both accurate incompressibility and variable viscosity are treated in the same fixed point. Hence the computation costs for variable and constant viscosity flows are similar. Several examples are given to validate the order of convergence and conservation rates. Such models are used, among other examples, in biological computing at the cellular scale. The present article eventually describes the ciliated epithelium cells covering a mammal's lungs, beating in a mucus film. This study of human lung diseases explores the efficiency of the mucociliary clearance, a challenging problem in health sciences, especially for the investigation of cystic fibrosis and various chronic obstructive pulmonary diseases.

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2010

titre

Efficiency of Multiscale Hybrid Grid-Particle Vortex Methods

auteur

Mustapha El Ossmani, Philippe Poncet

article

Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2010, 8 (5), pp.1671-1690. ⟨10.1137/090765006⟩

resume

This article presents a study of computational cost for the vortex method, a La-grangian numerical scheme using particles of fluids for simulation of three-dimensional flows. Its main features are to compute accurately transport effects and to be very robust, that is to say, often without prohibitive stability condition. Special attention is given to hybrid grid-particle vortex methods. They are shown to scale as O(n log n), even when used in a multiscale context. Furthermore, a discussion is provided on the best strategies for simulations in complex geometry. Computational cost is shown to have the same efficiency when performing multiscale simulations of three-dimensional flows in complex geometry.

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titre

Mucus dynamics subject to air and wall motion

auteur

S. Enault, D. Lombardi, Philippe Poncet, Marc Thiriet

article

ESAIM: Proceedings, 2010, 30, pp.125-141

resume

This study presents a numerical investigation of basic interactions between respiratory mucus motion, air circulation and epithelium ciliated cells vibration. One focuses on identification of meaningful rheological parameters, physiological and numerical simulation dimensioning. These preliminary results are crucial before the study of more general configurations of respiratory mucus motion. The numerical study presented in this work aims at providing a first numerical tool able to simulate the effects of mucus mobility and its ability to carry out pathogens or to deliver aerosol therapy to membrane wall cells. Momentum diffusion is identified as the dominant effect, as expected in this micrometer scale configuration, and its associate momentum diffusion operator is shown to be extremely stiff. Furthermore, epithelium vibration is shown to be much more efficient than air circulation for mucus propulsion.

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2009

titre

Analysis of an immersed boundary method for three-dimensional flows in vorticity formulation

auteur

Philippe Poncet

article

Journal of Computational Physics, 2009, 228 (19), pp.7268-7288. ⟨10.1016/j.jcp.2009.06.023⟩

resume

This article presents numerical analysis and practical considerations for three-dimensional flow computation using an implicit immersed boundary method. The Euler equations, or half a step of the Navier-Stokes equations when using fractional step algorithms, are investigated in their vorticity formulation. The context of flow computation around an arbitrarily shaped body is especially investigated. In conventional immersed boundary methods using vorticity, singular vortex are dispatched over the body surface. In the present study, one prefers using sources of potential velocity field, dispatched on the body, whose nature is not vorticity. Such a formulation is compatible to the Euler equations. In practice, these sources of potential flow produce a velocity through this surface, aiming in practice at cancelling a flow-through velocity. This article focuses on the use of the source-to-flow-through linear application, its properties being the key points for fast convergence. Its self-adjointness, or lack thereof, conditioning and preconditioning aspects are investigated. It follows that computing a velocity field with no-flow-through conditions in complex geometry, when using the source-to-flow-through linear application, can be achieved for 4/3 of the computational cost of standard Poisson equation in a Cartesian box. The robustness of immersed boundaries is especially interesting when used together with vortex-in-cell methods, well known for their robustness in time and their ability to compute accurately convective effects. A few examples, based on real-world geometries, illustrate the method capabilities.

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2008

titre

Spatially distributed control for optimal drag reduction of the flow past a circular cylinder

auteur

Philippe Poncet, Roland Hildebrand, Georges-Henri Cottet, Petros Koumoutsakos

article

Journal of Fluid Mechanics, 2008, 599, pp.111-120. ⟨10.1017/S0022112008000177⟩

resume

We report high drag reduction in Direct Numerical Simulations of controled flows past circular cylinders at Reynolds numbers of 300 and 1000. The flow is controlled by the azimuthal component of the tangential velocity of the cylinder surface. Starting from a spanwise uniform velocity profile that leads to high drag reduction, the optimization procedure identifies, for the same energy input, spanwise varying velocity profiles that lead to higher drag reduction. The three dimensional variations of the velocity field, corresponding to the modes A and B of three dimensional wake instabilities, are largely responsible for this drag reduction. The spanwise, wall velocity variations introduce streamwise vortex braids in the wake that are responsible for reducing the drag induced by the primary spanwise vortices shed by the cylinder. The results demonstrate that extending two dimensional controllers to three-dimensional flows is not optimal as three dimensional control strategies can lead efficiently to higher drag reduction.

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2007

titre

Analysis of Direct Three-Dimensional Parabolic Panel Methods

auteur

Philippe Poncet

article

SIAM Journal on Numerical Analysis, 2007, 45 (6), pp.2259-2297. ⟨10.1137/050625849⟩

resume

Adherence boundary conditions for time dependent partial differential equations, via Chorin algorithm, can be reduced to a parabolic problem with Robin-Fourier boundary conditions in the three-dimensional context. In the spirit of panel methods, one establishes an integral formulation whose key point is the estimation of the potential density, introducing a kind of panel method for tangential kinematic boundary conditions. This paper discusses explicit estimations of this density in the general case of an arbitrarily shaped three-dimensional body, which leads to a fast numerical scheme. An error analysis is also provided, involving body smoothness, the Hölder exponent of the density, and whether the body presents torsion or not.

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2006

titre

Finite difference stencils based on particle strength exchange schemes for improvement of vortex methods

auteur

Philippe Poncet

article

Journal of Turbulence, 2006, 7, pp.N23. ⟨10.1080/14685240600595586⟩

resume

The method of Particle Strength Exchange aims at solving the viscous part of the Navier-Stokes equations, when split into diffusive and corrective parts. We present their formulation in the context of vortex methods. The present work follows the classical analysis by Degond and MasGallic whose formulas were obtained by means of integration of continuous functions. It shows that one gets different operators when integration is discrete, and leads to a substantial gain of accuracy. This scheme is then applied to several three-dimensional flows to exhibit convergence rate and impact on conservation laws at moderate Reynolds numbers. A sensitivity analysis is finally provided in order to carry out the good behavior of these schemes in both Eulerian and Lagrangian contexts.

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2005

titre

Control of three-dimensional wakes using evolution strategies

auteur

Philippe Poncet, Georges-Henri Cottet, Petros Koumoutsakos

article

Comptes Rendus. Mécanique, 2005, 333 (1), pp.65-77. ⟨10.1016/j.crme.2004.10.007⟩

resume

We investigate three-dimensional cylinder wakes of incompressible fully developed flows at Re = 300, resulting from control induced by tangential motions of the cylinder surface. The motion of the cylinder surface, in two dimensions, is optimized using evolution strategies, resulting in significant drag reduction and drastic modification of the wake as compared to the uncontrolled flow. The quasi-optimal velocity profile obtained in 2D is modified by spanwise harmonics and applied to 3D flows. The results indicate important differences in the flow physics induced by two and three dimensional control strategies.

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titre

Optimization of Vortex Shedding in 3-D Wakes Using Belt Actuators

auteur

Philippe Poncet, Petros Koumoutsakos

article

International Journal of Offshore and Polar Engineering (IJOPE), 2005, 15 (1), pp.007

resume

This paper discusses the control of cylinder wakes via tangential wall velocity modifications. The wall velocity is piecewise constant (corresponding to belt actuators), and its amplitude is optimized using a clustering real coded genetic algorithm. This type of control significantly affects the vortical structures being shed in the wake, and it is shown that the flow gets significantly modified, resulting in a 3-dimensional body shedding 2-dimensional vortical structures.

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2004

titre

Simulation and control of three-dimensional wakes

auteur

Georges-Henri Cottet, Philippe Poncet

article

Computers and Fluids, 2004, 33 (5-6), pp.697-713. ⟨10.1016/j.compfluid.2003.01.001⟩

resume

We illustrate the problem of wake optimization on two examples. In the first example, the destruction of trailing vortices, we show that stochastic optimization is a flexible tool to identify vortex systems enhancing natural instabilities. In the second example, the problem of drag reduction in a cylinder wake, a priori information on the flow dynamics is highly desirable and we give some preliminary results which should be useful to select the most efficient parameters in an optimization strategy based on differential rotation of the cylinder.

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titre

Topological aspects of three-dimensional wakes behind rotary oscillating cylinders

auteur

Philippe Poncet

article

Journal of Fluid Mechanics, 2004, 517, pp.27-53. ⟨10.1017/s0022112004000588⟩

resume

The development of a three-dimensional viscous incompressible flow generated behind an infinitely long circular cylinder, impulsively started into rectilinear motion and rotationally oscillating, is studied computationally. The numerical scheme, an hybrid vortex method, is used to integrate the velocity-vorticity formulation of the Navier-Stokes equations. The Reynolds number considered is Re = 400, which is moderate though beyond the critical values Re 2 190 and Re 2 260 for which the flow becomes spontaneously three-dimensional. The numerical method is explained and its main points are developed. This scheme is then applied to solve some two-dimensional problems, both in order to validate the method and to compute a nominal two-dimensional flow, required to measure the impact of three-dimensionality. The three-dimensional flow past a steady cylinder is also compared to benchmark simulations. Once the flow has become fully three-dimensional, beyond the transient regime and saturation of instabilities, the cylinder begins a rotary oscillation around its axis. Two kinds of rotations are considered: constant amplitude and several frequencies, and constant frequency and various amplitudes. When amplitude and frequency are high enough, the whole flow comes back to its two-dimensional state. This result gives a justification for two-dimensional computations in the literature related to rotating cylinders. For the first super-harmonic frequency of the flow, a parametric study is performed in order to find the impact of the amplitude on the topology of the flow. A bifurcation is clearly identified. Finally, the mechanisms involved in the return to a two-dimensional state are explained: the interaction between transverse instabilities and von K ´ armánarm´armán streets is quantified by means of a correlation analysis.

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titre

Advances in direct numerical simulations of 3D wall-bounded flows by Vortex-in-Cell methods

auteur

Georges-Henri Cottet, Philippe Poncet

article

Journal of Computational Physics, 2004, 193 (1), pp.136-158. ⟨10.1016/j.jcp.2003.08.025⟩

resume

This paper is devoted to the design of Vortex-In-Cell (VIC) methods for the direct numerical simulations of wall-bounded flows. A first method using body-fitted grid is presented in the particular case of a cylinder wake. This method, which has been used in [Phys. Fluids 14(6) (2002) 2021] to investigate the effect on the wake topology of cylinder rotations, is an extension of the VIC method presented in [J. Comput. Phys. 175 (2002) 702] for periodic geometries. Features of the method that are specific to wall-bounded geometries-interpolation operators, field calculations and vorticity flux formulas to enforce no-slip boundary conditions-are described in details. The accuracy of the method in the calculation of the body forces is investigated by comparisons with experiments and benchmark calculations. A second class of methods is in the spirit of the immersed boundary methods. The paper in particular shows that the no-slip conditions are very naturally handled by the vorticity flux formulas, independently of the relative locations of the particles and the body. Numerical experiments on the test-case of a ring impinging on a cylinder suggest that the method is second-order accurate.

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2002

titre

Vanishing of mode B in the wake behind a rotationally oscillating circular cylinder

auteur

Philippe Poncet

article

Physics of Fluids, 2002, 14 (6), pp.2021-2023. ⟨10.1063/1.1479344⟩

resume

This Brief Communication presents a numerical investigation of the dimensionality of a flow behind a three-dimensional rotationally oscillating circular cylinder. These computations are performed at a Reynolds number Re500, which is at a level where the mode B is the dominant three-dimensional instability. We show that a rotation of high enough amplitude makes the 3D instabilities vanish and brings the flow back to its nominal two-dimensional state.

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titre

Particle methods for direct numerical simulations of three-dimensional wakes

auteur

Georges-Henri Cottet, Philippe Poncet

article

Journal of Turbulence, 2002, 3, pp.038:1-9. ⟨10.1088/1468-5248/3/1/038⟩

resume

In this paper we describe recent advances in the development of particle methods for the direct numerical simulations of three-dimensional wakes. Both body-fitted and immersed boundary techniques are considered. The accuracy and numerical cost of the proposed numerical methods are discussed on the benchmark cases of a flow past a cylinder and of a vortex ring impinging on a cylinder.

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1999

titre

About Successive Gauss-Seidelisations

auteur

Philippe Poncet, François Robert

article

Taiwanese Journal of Mathematics, TJM, 1999, 3, pp.491 - 501. ⟨10.11650/twjm/1500407162⟩

resume

This note adresses the general problem of the dynamical behavior for successive Gauss-Seidel transformations (shortly called Gauss-Seidelisations) of a given mapping over the n-cube. Complete results are given for n = 2 and n = 3, and then a natural conjecture is proved to be false for greater n. Thus this interesting and simple problem remains still open for n ≥ 4.

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