Publications HAL

Journal articles

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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https://hal.science/hal-04011497/file/1-s2.0-S0021999123004370-main.pdf BibTex

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⟩
Accès au texte intégral et bibtex
https://hal.science/hal-03442180/file/TIPM-D-22B-00032R2.pdf BibTex

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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https://hal.science/hal-02976234/file/A-2021-JCP-DRP-HAL.pdf BibTex

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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https://hal.science/hal-02965451/file/10Final-AWR-HAL.pdf BibTex
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, 2020, ⟨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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https://hal.science/hal-02387321/file/Molins2020_Article_SimulationOfMineralDissolution.pdf BibTex

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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https://hal.science/hal-01718335/file/m2an180140-publie.pdf BibTex

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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https://ifp.hal.science/hal-01847035/file/noetinger-effective.pdf BibTex

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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https://inria.hal.science/hal-01476172/file/A-2017-JBM2-HAL.pdf BibTex

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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https://hal.science/hal-01996103/file/A-2016-JBM-HAL.pdf BibTex
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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https://hal.science/hal-01872062/file/m2an142.pdf BibTex

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.
Accès au texte intégral et bibtex
https://hal.science/hal-02010736/file/B-2015-ProcediaIUTAM.pdf BibTex

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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https://hal.science/hal-02010640/file/12-ChatelinPoncet-SMW-JCP.pdf BibTex

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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https://hal.science/hal-02010645/file/A-2013-SISC.pdf BibTex

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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https://hal.science/hal-02010647/file/A-2010-SIAM%20MMS.pdf BibTex
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.
Accès au texte intégral et bibtex
https://inria.hal.science/inria-00543082/file/B-2010-Numulung.pdf BibTex

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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https://hal.science/hal-02010649/file/YJCPH_2643_Poncet.pdf BibTex

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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https://hal.science/hal-00267632/file/JFM-07-FT-0401.pdf BibTex

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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https://hal.science/hal-02010650/file/A-2007-SINUM.pdf BibTex

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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https://hal.science/hal-02010666/file/Poncet-JOT-188260-SPE.pdf BibTex

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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https://hal.science/hal-02010672/file/CRAS-article.pdf BibTex
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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https://hal.science/hal-02010668/file/WK82-Revised.pdf BibTex

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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https://hal.science/hal-02010683/file/cff2003.pdf BibTex
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.
Accès au texte intégral et bibtex
https://hal.science/hal-02010675/file/poncet_jfm_final.pdf BibTex
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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https://hal.science/hal-02010686/file/2004-Poncet-JCP.pdf BibTex

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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https://hal.science/hal-02010698/file/A-2002-PoF.pdf BibTex
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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https://hal.science/hal-02010692/file/A-2002-JoT.pdf BibTex

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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https://hal.science/hal-02010704/file/A-1999-TJM.pdf BibTex

Conference papers

2023

titre
Bayesian uncertainty quantification in pore-scale imaging: how to robustly infer porous media morphological properties through reactive inverse problems ?
auteur
Sarah Perez, Philippe Poncet
article
22st Annual Conference of the International Association for Mathematical Geosciences (IAMG 2023), Aug 2023, Trondheim, Norway
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titre
Chemical and morphological uncertainty quantification by auto-weighted Bayesian Physics-Informed Neural Networks for reactive two-scale porous media at the pore scale
auteur
Sarah Perez, Philippe Poncet
article
15th Annual International conference on Porous Media - InterPore 2023, Heriot-Watt University, May 2023, Edinburgh (Scotland), United Kingdom
resume
Data-driven approaches, among them machine learning tools, have garnered increasing interest in porous media research and offer alternatives to traditional numerical methods to improve the predictive modeling based on observation data. Recently, the idea of incorporating prior physical principles within measurements to better rely on experimental data has been successfully immersed into Bayesian inference as a valuable tool for uncertainty assessments. The emergence of the Bayesian Physics-Informed Neural Networks (BPINNs) paradigm offers the opportunity to query the confidence in the predictions, the uncertainty in the measurements, and the model adequacy by providing posterior distribution of the neural network predictions [1]. In this presentation, we will show how to make BPINNs auto-weighted in order to address multi-objective IA problems, even when relying on shadow quantities. Classical BPINNs mostly rely on Markov Chain Monte Carlo methods to sample from a weighted multi-objective target distribution, whose weights are related to the scaling of the tasks, the noise magnitude, and ultimately the inherent tasks’ uncertainties. While these parameters are recognized as critical, they are mostly hand-tuned in the applications leading to pathological behaviours or biased estimation, in the sense that one of the objectives will be prevailing in the posterior distribution exploration. Actually, when dealing with real-world complex systems which involve heterogeneities and multi-scale phenomena in addition to uncertainties in the measurements, the setting of these weights can remain particularly challenging and require considerable energy in tuning. Furthermore, such dynamics also raise scale imbalances that highly disrupt the usual approaches, generating instabilities that make the sampling inoperative. We focus here on a novel adaptive strategy for unbiased uncertainty quantification in BPINNs, based on an inverse Dirichlet weighting [2] of the target posterior distribution, which remedies to the failure modes previously identified. Our approach provides enhanced convergence, stability, and balanced conditions between the different tasks which ensure an efficient exploration of the Pareto front throughout the sampling procedure. While reducing the bias in the sampling, we show that this strategy is able to automatically adjust the weights, with them the uncertainties, according to the sensitivity of each task. It then offers an interesting framework to study complex multi-scale dynamics from the Bayesian inference perspective and incorporate uncertainty quantification in multi-objective and stiff inverse problems. In this direction, we aim to capture and quantify unresolved features arising from noisy X-Ray micro tomography measurements by adding information on the predictive physical-chemical model and then compensate for the lack of knowledge on the rock matrix structure with PDE-based priors, established according to a Darcy-Brinkmann two-scale porosity model [3]. Hence, we apply our auto-weighted methodology to the simultaneous identification of chemical parameters and morphological uncertainties on the porosity field, in a reactive inverse problem at the pore scale. Altogether with the approach developed in [4] to determine the absolute permeability deviation, we will be able to provide uncertainty quantification on the main macro properties of a porous media sample based on its micro tomography and then perform more relevant direct numerical simulations with respect to the experimental data. References [1] L. Yang, X. Meng, and G.E. Karniadakis, B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data, Journal of Computational Physics, 425:109913, 2021. doi: 10.1016/j.jcp.2020.109913 [2] S. Maddu, D. Sturm, C. L Müller, and I. F Sbalzarini, Inverse Dirichlet weighting enables reliable training of physics informed neural networks, Machine Learning: Science and Technology, 3(1):015026, 2022. doi:10.1088/2632-2153/ac3712 [3] J.M. Etancelin, P. Moonen, P. Poncet, Improvement of remeshed Lagrangian methods for the simulation of dissolution processes at pore-scale, Advances in Water Resources, 146:103780, 2020. doi: 10.1016/j.advwatres.2020.103780. [4] S. Perez, P. Moonen, and P. Poncet, On the Deviation of Computed Permeability Induced by Unresolved Morphological Features of the Pore Space, Transport in Porous Media 141:151-184, 2022. doi:10.1007/s11242-021-01713-z
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2022

titre
Simulation of reactive flows on 3D pore-scale geometries using particle methods and their impact on macroscopic properties: applications to dissolution, precipitation and crystallization
auteur
Sarah Perez, Jean-Matthieu Etancelin, Philippe Poncet
article
Sixteenth International Conference Zaragoza-Pau on Mathematics and its Applications, Sep 2022, Jaca, Spain
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titre
Second order deviation of absolute permeability due to unresolved morphological features at the pore scale
auteur
Sarah Perez, Francisco J Valdés-Parada, Didier Lasseux, Philippe Poncet
article
14th Annual International Conference on Porous Media Interpore 2022, Khalifa University, May 2022, Abu Dhabi, United Arab Emirates
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titre
Particle-Strength-Exchange methods for Lagrangian 3D DNS of rheological and reactive fluids with evolving interfaces at the pore-scale
auteur
Sarah Perez, Philippe Poncet
article
14th Annual International Conference on Porous Media Interpore 2022, Khalifa University, May 2022, Abu Dhabi, United Arab Emirates
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titre
Second order deviation of permeability due to unresolved morphological features at the pore scale
auteur
Sarah Perez, Francisco J Valdés-Parada, Didier Lasseux, Philippe Poncet
article
InterPore 2022, InterPore, May 2022, Abu Dhabi, United Arab Emirates
resume
Pore-scale dynamics of one phase flow commonly involves adherence (no-slip) boundary conditions at the fluid/solid interface. However, improved modeling such as flows at moderate Knudsen numbers (i.e. for values below 0.1), or homogenization of rock matrix roughness, may require slip conditions [1,2]. It turns out that a lack of knowledge on the rock matrix wall, built by X-Ray micro tomography, leads to the same type of slip conditions v = β 2 (I nn) (∇v + ∇vT ) n where v is the pore-scale velocity, n is the unit normal vector oriented towards the fluid and β is twice the slip-length. The macroscopic model corresponding to steady one-phase flow in the creeping regime (Stokes equations) at the pore-scale with the slip condition was derived in [1, 2]. The macroscopic momentum equation corresponds to Darcy’s law in which the permeability tensor is slip-dependent. This leads to a computation of an apparent permeability that depends on β and that we denote Kβ . This apparent permeability can be expanded in a power series of a Knudsen number, the zeroth-order term identifying to the intrinsic permeability with no slip and the higher order terms to slip-correction tensors, the first one generalizing, for an ideal gas, the classical Klinkenberg correction. All the tensors are given by the solution of coupled closure problems at the successive orders [2]. While this expansion has been addressed in [1] and [2] and used in the case of synthetic geometries, it has been used in large three-dimensional real geometries in [3] in the context of isotropic permeability, that is to say Kβ = κβ I where κβ is a scalar. In this last case, the expansion κβ = κ0 + βλ1 + β2 2 λ2 + O(β3) is shown to describe the uncertainty on the permeability values that results from the gray scale uncertainty generated by micro-tomography. The coefficients λk , capturing this uncertainty estimation, are given by the solutions of the Stokes-like closure problems reported in [2] by formal expansion (from averaged equations) and re-established in [3] by asymptotic analysis (two-scale homogenization). They satisfy a non-homogeneous Dirichlet boundary condition (prescribed velocity) at the pore walls, whose value involves the immediate lower order slip momentum. While the first order of this expansion has been detailed in [3], its second order estimation is provided for the first time in this presentation for operational 3D geometries: we apply our results to the high resolution rock sample studied in [4] and show that the second order brings a significant improvement of the uncertainty estimation on the absolute permeability. These results in a real geometry confirm what was anticipated in [2] for simplified 2D geometries and are relevant as they show the importance of slip at the macroscale.
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https://hal.science/hal-04300226/file/abstract-27.pdf BibTex

2021

titre
On the estimation of permeability uncertainty due to unresolved pore-scale features
auteur
Sarah Perez, Philippe Poncet
article
XV JEMP – French Interpore Chapter, Oct 2021, Strasbourg, France
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titre
A semi-Lagrangian numerical method for the simulation of precipitation/crystallization at the pore scale of porous media
auteur
Sarah Perez, Jean-Matthieu Etancelin, Philippe Poncet
article
CrysPoM VII 2021, Jun 2021, Pau, France
resume
This talk presents advances in numerical methods for the simulation of single-phase flow, reactive transport and solid geometry evolution at the pore scale, involving dissolution, precipitation and crystallization, and will be structured in three parts. Firstly, we will present the semi-Lagrangian approach of the problem and the related models, involving particle/Lagrangian treatment of the transport phenomena and reactions, and underlying grids for the diffusion and flow computation. Frequent remeshing procedure is required in order to keep particles on a regular network, in order to avoid holes of information and particle accumulation. This remeshing technique is either high order but can generated sign changes, which is unacceptable in chemistry, or low order but leads to spurious diffusion. An a posteriori kernel selection will be provided in order deal with this difficulty. Secondly, we will describe the validation of the method by a dissolution process of 2D and 3D calcite cores (including experimental validation) with a benchmark approach. Five codes are used to obtain the solution to this benchmark problem, including Chombo-Crunch, OpenFOAM-DBS, a lattice Boltzman code, the present semi-Lagrangian method, 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. 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. Thirdly, we will focus on the simulations of precipitation and crystallization. This last aspect can include either the rheology of precipitation or the crystal growth, and the ability to manage the divergence of the velocity induced by the reaction and its related evolution of the global volumic mass. Indeed, in this context, a fast change of state from liquid to solid means incompressible but non divergence-free flows.
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2019

titre
A benchmark for the numerical simulation of pore-scale mineral dissolution with fluid-solid interface evolution
auteur
Philippe Poncet, S. Molins, Cyprien Soulaine, N Prasianakis, A. Abbasi, V. Starchenko, Sophie Roman, D. Trebotich, H. A. Tchelepi, C. Steefel
article
SITRAM 2019, Dec 2019, Pau, France
resume
This talk 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, dissolution-driven geometry evolution in two dimensions, and a three-dimensional dissolution-driven geometry evolution including an experimental validation. Five codes are used to obtain the solution to this benchmark problem, including Chombo-Crunch, OpenFOAM-DBS, a lattice Boltzman code, Vortex method, 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. Among the discretization methods, one can find finite volumes, Lagrangian methods, grid based methods (stochastic and deterministic). 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. References [1] S. Molins, C. Soulaine, N. I. Prasianakis, A. Abbasi, P. Poncet, A. J. C. Ladd, V.Starchenko, S. Roman, D. Trebotich, H. A. Tchelepi, and C. I. Steefel,Simulation ofmineral dissolution at the pore scale with evolving fluid-solid interfaces: Review of ap-proaches and benchmark problem set, to appear in Computational Geosciences, 2019.
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https://hal.science/hal-02387355/file/Congres-2019-SITRAM-Poncet.pdf BibTex
titre
Le mucus pulmonaire: impact rhéologique de la mucoviscidose
auteur
Philippe Poncet
article
Journée MucoSud, Jun 2019, Bordeaux, France
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2018

titre
Permeability estimation using vortex-based method and synthetic samples from X-ray micro-CT
auteur
Laurène Hume, Philippe Poncet, Peter Moonen
article
14me Journées d’étude des milieu poreux (JEMP), Oct 2018, Nantes, France
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https://hal.science/hal-02116155/file/JEMP2018_Hume_et_al.pdf BibTex
titre
Reactive flows at pore scale with hybrid computing
auteur
Jean-Matthieu Etancelin, Philippe Poncet
article
Fifteenth International Conference Zaragoza-Pau on Mathematics and its Applications, Sep 2018, Jaca, Spain
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titre
New trends in Vortex Methods for reactive flows
auteur
Philippe Poncet, Laurène Hume, Jean-Matthieu Etancelin
article
InterPore 2018, May 2018, New Orleans, United States
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titre
Écoulement du mucus pulmonaire: modélisation, simulation et influence de la mucoviscidose
auteur
R. Chatelin, Philippe Poncet
article
GdR CNRS 3570 MécaBio, Toulouse, 2018, Toulouse, France
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2017

titre
Pore scale modelling in porous media: diffusion-transport coupled to 3D Stokes equation at high resolution
auteur
Laurène Hume, Philippe Poncet
article
V International Conference on Particle-based Methods, Sep 2017, Hannover, Germany
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titre
Experimental and numerical cross-validation of flow in real porous media. Part 1: Experimental framework
auteur
Fabrice Guerton, Laurène Hume, Philippe Poncet, Peter Moonen
article
3rd International Conference on Tomography of Materials and Structures (ICTMS 2017), Jun 2017, Lund, Sweden
resume
The main objective of this contribution is the cross-validation of a novel approach to fluid flow simulation inside porous media. The originality of the model stands both in the use of rather raw 3D volumes from X-ray tomography and the model's computational efficiency on standard calculation means. The performance of the model is assessed in different geometries and configurations, based on reference data obtained via a dedicated experimental setup.
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https://hal.science/hal-01815893/file/ICTMS2017_Guerton_et_al.pdf BibTex
titre
Experimental and numerical cross-validation of flow in real porous media. Part 2: Numerical framework
auteur
Laurène Hume, Fabrice Guerton, Peter Moonen, Philippe Poncet
article
3rd International Conference on Tomography of Materials and Structures, Jun 2017, Lund, Sweden
resume
The main objective of this contribution is the cross-validation of a novel approach to fluid flow simulation inside porous media. The originality of the model stands both in the use of rather raw 3D volumes from X-ray tomography and the model's computational efficiency on standard calculation means. The performance of the model is assessed in different geometries and configurations, based on reference data obtained via a dedicated experimental setup.
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https://hal.science/hal-02014857/file/ICTMS2017-Hume.pdf BibTex
titre
Modélisation de l’écoulement d’un fluide miscible rhéofluidifiant à l’échelle micrométrique et applications
auteur
Laurène Hume, D. Sanchez, R. Chatelin, Philippe Poncet
article
Congrès SMAI 2017, 2017, La Tramblade, France
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titre
Pore-scale modelling in porous media: diffusion-transport coupled to 3D Stokes equation at high resolution
auteur
Laurène Hume, Philippe Poncet
article
Vth International Conference on Particle-Based Methods, 2017, Hanovre, Germany
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2016

titre
Phénomènes de transport complexe à l'échelle des pores et modélisation de la rugosité
auteur
Laurène Hume, Philippe Poncet
article
13èmes Journéess d'études des Milieux Poreux 2016, Oct 2016, Anglet, France
resume
Phénomènes de transport complexe à l'échelle des pores et modélisation de la rugosité
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https://hal.science/hal-01394580/file/JEMP_HumePoncet_Revision.pdf BibTex
titre
Numerical modeling of coupled two-phase multicomponent flow with reactive geochemical transport in porous media
auteur
Etienne Ahusborde, Brahim Amaziane, Mustapha El Ossmani, Philippe Poncet
article
13èmes Journéess d'études des Milieux Poreux 2016, Oct 2016, Anglet, France
resume
Numerical modeling of coupled two-phase multicomponent flow with reactive geochemical transport in porous media
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https://hal.science/hal-01394471/file/AHUSBORDE_JEMP2016.pdf BibTex
titre
Benchmark for coupled two-phase multicomponent flow with reactive geochemical transport in porous media
auteur
Etienne Ahusborde, Brahim Amaziane, Mustapha El Ossmani, Philippe Poncet
article
Subsurface Environmental Simulation Benchmarking Workshop V, Oct 2016, La Corogne, Spain
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titre
3D computations of mucocilliary clearance
auteur
Robin Chatelin, Dominique Anne-Archard, Philippe Poncet
article
European Congress on Computational Methods in Applied Sciences and Engineering - ECCOMAS 2016, Jun 2016, Hersonissos, Greece
resume
In this talk, an overview of the results obtained in the ANR project BioFiReaDy will be presented. This interdisciplinary project aims at understanding mucociliary clearance: the natural flow of mucus in the lung, which protects bronchus from inhaled agents such as dust, pathogens or pollution particles... 3D simulations are used, as well as experimental rheology to characterize the non-Newtonian rheological behaviour of this complex biological fluid. Using suitable numerical algorithms specially developed to compute this 3D fluid-structure interaction (FSI) problem (mucus is propelled by beating cilia), it is now possible to study the biological parameters influence on the mucus flow. These algorithms are based on (i) a novative projection method which integrates the resolution of rheological shear-thinning effects, (ii) a penalization techniques coupled to a Shermann--Morrison--Woodbury approach to compute the FSI, (iii) the use of fast solvers (FFT or multigrid) and (iv) a lagrangian discretization of the convection effects. These numerical methods are particularly suitable for 3D computations since the global computational cost is linear with respect to the number of grid points, which is very interesting for a parametric study. Several results will be presented, in particular for pathological situations such as cystic fibrosis.
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titre
Design and realization of electroactive polymer actuators for transparent and flexible haptic feedback interfaces
auteur
Philippe Poncet, F. Casset, A. Latour, S. dos Santos, R. Gwoziecki, S. Fanget
article
2016 17th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems (EuroSimE), 2016, Montpellier, France
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titre
Complex transport at pore scale and roughness modeling
auteur
Laurène Hume, Philippe Poncet
article
XIII JEMP – French Interpore Chapter, Anglet, France, 2016, Anglet, France
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2015

titre
A sequential numerical simulator for two-phase multicomponent flow with reactive transport in porous media
auteur
Etienne Ahusborde, Brahim Amaziane, Mustapha El Ossmani, Philippe Poncet
article
MoMaS Multiphase Seminar Days - Journées MoMaS Multiphasiques, Oct 2015, Nice, France
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titre
Release of fine particles from Birch pollen grains following impaction
auteur
N. Visez, G. Chassard, N. Azarkan, O. Naas, H. Sénéchal, J.P. Sutra, Philippe Poncet, M. Choël
article
Mediterranean Palynology 2015 Symposium, Sep 2015, Rome, Italy
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titre
Méthodes hybrides grille–particules pour la simulation 3D d'écoulements complexes non newtoniens
auteur
Robin Chatelin, Philippe Poncet
article
12e colloque national en calcul des structures, CSMA, May 2015, Giens, France
resume
Quelques méthodes numériques récemment développées dans le cadre du projet ANR BioFiReaDy sont regroupées dans cette communication. L'objectif est de simuler en 3D des écoulements de fluides complexes interagissant avec des obstacles immergés. L'algorithme repose sur une discrétisation hybride grille-particules, des algorithmes à pas fractionnaires et l'utilisation de solveurs rapide afin de réduire les coûts de calcul. Cela ouvre la porte à des simulations 3D de grande dimension, tout en permettant d'étudier l'influence de nombreux jeux de paramètres sur l'écoulement.
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https://hal.science/hal-01400458/file/r_0LMJKHYA.pdf BibTex
titre
An integrated two-phase ow with reactive transport model in a parallel reservoir simulator
auteur
Etienne Ahusborde, Brahim Amaziane, Mustapha El Ossmani, Philippe Poncet
article
Proceedings of the 6th MAMERN Conference, Pau, France, 2015, pau, France
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titre
Particle methods for transport in porous media at the pore scale
auteur
Etienne Ahusborde, Brahim Amaziane, Philippe Poncet
article
Complex Fluid Flow in Porous Media Conference (ComFlowPore), Bordeaux, France, 2015, Bordeaux, France
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titre
Méthodes particulaires pour le transport en milieux poreux à l’échelle des pores
auteur
Philippe Poncet
article
Journée CEA-GAMNI sur la mécanique des fluides numérique, IHP, 2015, Paris, France
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titre
Numerical simulation of flows with reactive transport in porous media: towards a validation for two-phase flow
auteur
Etienne Ahusborde, Brahim Amaziane, Mustapha El Ossmani, Philippe Poncet
article
Reactive Transport Modeling in the Geological Sciences Workshop, Institut Henri Poincaré, Paris, France, 2015, Paris, France
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2014

titre
Passive and active flow control using vortex methods
auteur
Georges-Henri Cottet, Roland Hildebrand, Petros Koumoutsakos, Chloé Mimeau, Iraj Mortazavi, Philippe Poncet
article
6th International Conference on Vortex Flows and Vortex Models, Nov 2014, Nagoya, Japan
resume
This paper deals with the application of remeshed particle methods for the simulation and control of wakes behind obstacles. We consider passive as well as active control strategies. Active control consists of jets at the boundary and we show how enhancing natural 3D instabilities of the flow can reduce the drag. Passive control strategies consist of porous coatings on the obstacle and we investigate optimal locations of the porous coating to regularize the wake downstream and reduce the drag.
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https://hal.science/hal-01063292/file/ICVFM_2014_cottet.pdf BibTex
titre
Réactions croisées entre pollen et graine de Brassica napus : implication des allergènes non hydrosolubles
auteur
O. Rivera Martos, Pierre Sutra, H. Sénéchal, S. D’andréa, Philippe Poncet
article
9ème Congrès Francophone d'Allergologie, Apr 2014, Paris, France. pp.237, ⟨10.1016/j.reval.2014.02.040⟩
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titre
Particle methods for transport at the pore scale
auteur
Philippe Poncet, R. Chatelin
article
International Conference on Numerical and Mathematical Modeling of Flow and Transport in Porous Media, Dubrovnik, Croatia, 2014, Dubrovnik, Croatia
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titre
Approche Sherman-Morrison-Woodbury pour la résolution rapide des termes de pénalisation. Application l’écoulement du mucus pulmonaire
auteur
R. Chatelin, Philippe Poncet
article
CANUM 2014, Carry-le-Rouet, France, 2014, Carry-le-Rouet, France
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titre
Méthodes particulaires pour les écoulements en milieux poreux à l’échelle des pores
auteur
Philippe Poncet
article
12èmes Journées d’Etude des Milieux Poreux (JEMP), Toulouse, 2014, Toulouse, France
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titre
Apprentissage machine pour l'étude de la mobilité du mucus dans le poumon
auteur
F. Dardalhon, Philippe Poncet
article
CANUM 2014, Carry-le-Rouet, France, 2014, Carry-le-Rouet, France
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titre
Symposium on Penalization and Applications
auteur
Gilles Carbou, P. Chatelain, Philippe Poncet, David Sanchez
article
Thirteenth International Conference Zaragoza-Pau on Mathematics and its Applications, Jaca, Spain, 2014, Jaca, Spain
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2012

titre
Particle methods for 3D biological flows with variable density and viscosity
auteur
Robin Chatelin, Philippe Poncet
article
European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), Sep 2012, Vienna, Austria
resume
This work is investigating a mechanical dysfunction of human lungs: Mucociliary clearance. The goal is to understand how diseases like cystic fibrosis impact mucus motion (by altering mucus viscosity, cilia vibrations, respiration cycle...) and to identify stagnation situations where pathogens proliferate. Strategies for computation of mucus flow around an epithelium ciliated cell are presented. Governing equations are proposed to take into account this complex geometry in motion in the surrounding highly viscous fluid. The characteristic Reynolds number of the flow is very small and mucus is modelled by Stokes problem with both variable viscosity and density. Epithelium displacement is taken into account using a penal-ization method. As density and viscosity follow a convection equation, these assumptions lead to an elliptic/hyperbolic coupling and non-linear equations. Numerical implementations are discussed to get a fast, robust and accurate algorithm in three dimension based on fast elliptic solvers and Lagrangian methods.
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https://hal.science/hal-02011145/file/B-2012-Eccomas.pdf BibTex

2010

titre
COMPUTATIONAL ASPECTS OF MUCUS PROPULSION BY CILIATED EPITHELIUM
auteur
Robin Chatelin, Philippe Poncet, Mayya Tokman
article
2nd European Conference on Microfluidics, Dec 2010, Toulouse, France
resume
This work is focused on the investigation of the mechanical dysfunction and airway clearance efficiency (or lack thereof) of the respiratory system by a quantitative analysis of mucus motion. We perform three-dimensional numerical simulations of the mucus and the ciliated cells present at lung walls (epithelium). In this preliminary work we consider a simplified configuration where the fluid is assumed to be Newtonian, the air/mucus interface is flat, and density and viscosity are constant. We formulate equations describing the simplified configuration, which are also relevant in the general context, and solve this system numerically to obtain mucus motion over a full cilia cycle. The stability condition of the explicit time integrators for the set of equations is prohibitively restrictive on the size of the integration time step. In order to begin development of effective numerical strategies for this problem we construct a one-dimensional model equation that contains the numerical challenges of a more general system. We study performance of several implicit and exponential time integrators using the model equation and use the results of the comparison to outline promising strategies for building efficient time integrators for a more complex system.
Accès au texte intégral et bibtex
https://hal.science/hal-02011153/file/B-2010-Microfluidics.pdf BibTex

2009

titre
New trends in Multi-Scale Simulation using Hybrid Grid-Particle Vortex Methods
auteur
Mustapha El Ossmani, Philippe Poncet
article
3rd International Conference on Approximation Methods and Numerical Modelling in Environment and Natural Resources, Jun 2009, Pau, France
resume
The purpose of this talk is to present a multi-scale Vortex-in-Cell method, for direct numerical simulation of three dimensional fluid flows. Vortex methods are Lagrangian. They are among the most challenging particle method, and have been dramatically improved during the last decade. This talk will present the main ideas of these methods, implemented in the open source package COMMA, funded by ANR and based on high performance packages FISHPACK and AGRIF. Among numerical methods aiming at solving the equations of fluid dynamics, the particle methods are renowned for their ability to compute accurately transport and convective effects. Most of the current challenges focus on the Navier-Stokes equations and their generalizations : multi-fluids, reactive flows, combustion, complex boundary conditions. In this short communication , one focuses on the basic three-dimensional Navier-Stokes equations, for an incompress-ible fluid, given by ∂u ∂t + u · u − ν∆u = f ρ − p ρ (1) where u is the divergence-free velocity field satisfying the no-slip condition u = 0 on Γ, p the pressure, ρ the density, ν the kinematic viscosity, and f the external force. For an incompressible fluid of constant density and viscosity, taking the curl of equation (1) and introducing the vorticity as ω = curlu, leads to ∂ω ∂t + u · ω − ω · u − ν∆ω = 0 (2) with kinematic no-slip boundary conditions u = 0, for external forces deriving from a potential (ie is the gradient of a scalar function).
Accès au texte intégral et bibtex
https://hal.science/hal-02011180/file/B-2009-Mamern09.pdf BibTex

2005

titre
Bimodal control of three-dimensional wakes
auteur
Philippe Poncet
article
ERCOFTAC Workshop DLES-6, 2005, Poitiers, France
resume
This paper investigates control strategies for drag reduction of three-dimensional wake generated by a circular cylinder at Reynolds number Re = 300, such flows presenting mode B instabilities whose main feature is streamwise finger-shaped eddies. The control is performed thanks to a field of tangential velocities on the cylinder. One first focuses on two-dimensional velocity fiels (spanwise invariant), using both a clustering genetic algorithm (see [7]) and Newton algorithm in Fourier space with five Fourier modes. Besically the same field comes out, whatever the control technique used. A square-root regression of the drag reduction versus amplitude of the control leads to the formulation of an efficiency criterion. One then considers a class of spanwise harmonic perturbation of this quasi-optimal profile, leading to a two paramater optimization problem, involving amplitude and wavelength of the perturbation. A cartography of the efficiency with respect to these two parameters is finally obtained, showing regions of interest.
Accès au texte intégral et bibtex
https://hal.science/hal-02011183/file/Poncet-DLES6-Color-HAL.pdf BibTex

2003

titre
Open-loop control of three-dimensional wakes
auteur
Philippe Poncet, Georges-Henri Cottet
article
2nd MIT Conference on Computational Fluid and Solid Mechanics, Jun 2003, Cambridge, United States
resume
We illustrate the problem of wake optimisation on the generic case of the three-dimensional cylinder. After a description of the numerical method, several optimisation strategies are presented, aiming at identifying vortex systems providing drag reduction or special topology of the flow. On the one hand, strategies as simple as cylinder rotation or bidimensional stationary profiles of velocity are considered. On the other hand, an outlook of full 3D tangential controls is presented, which may be mixed or not with the simple strategies above.
Accès au texte intégral et bibtex
https://hal.science/hal-02011187/file/Poncet_Cottet_2ndMITconf.pdf BibTex

2000

titre
A few Multiresolution Schemes for the Black-Scholes equation
auteur
Philippe Poncet, Remi Abgrall
article
CEMRACS 2000, Jul 2000, Marseille, France
resume
In this note, we apply mutliresolution technics to a discretisation of the linear Black Schole equation , which is a convection diffusion equation. In particular, we describe a few numerical schemes in order to perform one step of decimation and reconstruction. This suggests a new discretisation method of this equation, which should easily extend to more than one dimension, and lead to very efficient numerical schemes.
Accès au texte intégral et bibtex
https://hal.science/hal-02011193/file/B-2000-Cemracs.pdf BibTex

Book sections

2017

titre
Modeling Cystic Fibrosis and Mucociliary Clearance
auteur
Dominique Anne-Archard, Robin Chatelin, Marlène Murris-Espin, David Sanchez, Marc Thiriet, Alain Didier, Philippe Poncet
article
Sid M. Becker. Modeling of microscale transport in biological processes, Academic Press, pp.113-154, 2017, 978-0-12-804595-4. ⟨10.1016/B978-0-12-804595-4.00005-5⟩
resume
This chapter considers the investigation of airway clearance efficiency and dysfunction using rheological measurements, modeling and simulations of mucus flows. The work is mainly dedicated to the respiratory epithelium dysfunction subsequently to the consumption of cilia-inhibiting drugs (e.g. nicotine) or viral and/or bacterial infections, and cystic fibrosis, although many respiratory diseases are associated with an altered mucus transport.
Accès au texte intégral et bibtex
https://inria.hal.science/hal-01476216/file/18-Chapter5-CFMC.pdf BibTex

Habilitation à diriger des recherches

2007

titre
Méthodes lagrangiennes pour le calcul et le contrôle des écoulements tridimensionnels
auteur
Philippe Poncet
article
Mathématiques [math]. Université Paul Sabatier - Toulouse (France), 2007
Accès au texte intégral et bibtex
https://hal.science/tel-02010718/file/A-2007-HDR.pdf BibTex

Other publications

2022

titre
Plan de Management des Données (DMP) du projet ANR MucoReaDy "Mucoviscidose et dysfonctionnements respiratoires
auteur
Philippe Poncet, Stephanie Delage Santacreu
article
2022
Accès au texte intégral et bibtex
https://hal.science/hal-03726293/file/ANR-20-CE45-0022_PGD_Plan_de_gestion_des_donnees_a_6_mois_98624.pdf BibTex

Poster communications

2023

titre
Particle methods for the dynamics of porous biofilms with heterogeneous rheology and its interaction with lung epithelium
auteur
Jean-Matthieu Etancelin, Marlene Murris, Philippe Poncet
article
15th Annual International Conference on Porous Media (Interpore 2023), May 2023, Edimbourg, United Kingdom.
resume
In this presentation we are interested in operational applications and new numerical approaches for modeling the heterogeneous mucus bio-film of human lungs for the monitoring of cystic fibrosis (CF) therapies. At an operational level, we aim at predicting whether a therapy has a significant impact of the mucociliary clearance or not, that is to say predicting the ability of the respiratory mucus to be functional, i.e. to move together with the motion of the surrounding cells. By opposition, a non-functional mucus will not move sufficiently to clear the lung wall from allergens, toxic agents, viruses, bacteria and their residual products (DNA filaments and altered mucoid elements). In this biological configuration, the mucus is itself a porous media made of Newtonian periciliary fluid (PCL) and highly concentrated mucins produced by the goblet cells, whose motion in the mucus will allow a mixture between the mucins and the PCL leading by reaction to a polymerized mucus with a particular rheology. Among the rheological features such as visco-elasticity, visco-plasticity, yield stress and shear-thinning, we focus on this last one which has been shown to be the dominant feature leading to non-functional mucus. Moreover, the PCL is produced by the respiratory epithelium covering the lung membrane, another porous media that allows the transcytosis mechanism producing the PCL. Indeed, the PCL is not present or not working properly when the cystic fibrosis transmembrane conductance regulator protein CFTR presents a mutation responsible of CF. The numerical simulation of such configurations has two main objectives. On the one hand, one can predict whether a mucus is functional or not, with respect to the rheological features that are measured from samples. On the other hand, the numerical simulation allows to adjust the parameters of an upscaled model, including the mucus permeability and the tortuosity index that relates the effective diffusion and the molecular diffusion of chemical species by means of a power of the porosity.
Accès au texte intégral et bibtex
https://hal.science/hal-04099079/file/PosterMS05-Poncet-Interpore2023-Edimbourg-V3.pdf BibTex

2017

titre
Experimental and numerical cross-validation of flow in real porous media. Part 1: Experimental framework
auteur
F. Guerton, L Hume, Philippe Poncet, Peter Moonen
article
3rd International Conference on Tomography of Materials and Structures (ICTMS 2017), Jun 2017, Lund, Sweden
resume
In this study, we present the design of a purpose-built test cell, capable of closely mimicking boundary conditions which can be routinely imposed in fluid flow simulators. The test cell permits conducting systematic studies on the influence of unresolved pore-scale wall-roughness and pore space morphology on the hydraulic conductivity: it is therefore an ideal instrument for the generation of validation datasets for the next generation numerical flow models.
Accès au texte intégral et bibtex
https://hal.science/hal-02175583/file/Guerton_et_al_2017.pdf BibTex

Theses

2001

titre
Méthodes particulaires pour la simulation des sillages tridimensionnels
auteur
Philippe Poncet
article
Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2001. Français. ⟨NNT : ⟩
resume
Ce travail est consacré au développement des méthodes particulaires pour la résolution des équations de Navier-Stokes incompressibles en dimension 3. L'évaluation des formules de Biot-Savart ayant un coût de calcul prohibitif en dimension trois, on utilise un couplage grille-particules. On applique alors cette technique à la simulation et au contrôle de sillages produits par un cylindre. La première partie est consacrée à la méthode numérique proprement dite. On commence par présenter le modèle lagrangien et la méthode utilisée pour calculer le champ de vitesse, qui est la clef de voûte du schéma. On décrit ensuite, au chapitre 2 comment sont calculées les couches limites. Enfin, on présente au chapitre 3 l'algorithme à pas fractionnaire utilisé, ainsi que les méthodes de transfert entre jeux de particules et grilles sous-jacentes, et le calcul de la diffusion. Le code est alors validé par des simulations d'anneaux tourbillonnaires qui se propulsent sur un obstacle cylindrique, pour des nombres de Reynolds modérés (entre 400 et 2000).La seconde partie utilise la méthode numérique décrite précédemment, en l'appliquant dans un premier temps à la simulation des sillages turbulents qui se développent derrière un cylindre circulaire (chapitre 4), puis au contrôle de ces écoulements au chapitre 4.Il est connu que les solutions bidimensionnelles sont instables pour des nombres de Reynolds suffisamment élevés. Les instabilités tridimensionnelles sont identifiée grâce à leur profil spectral. Elles ont un effet important sur les forces de traînée et sur la fréquence propre de l'écoulement.Le chapitre 5, relatif au contrôle, se propose de mettre en évidence plusieurs phénomènes. On considère un contrôle en boucle ouverte, réalisé par une rotation à pulsation et amplitude constante. On étudie des rotations basse et haute fréquences. Le coefficient de traînée est alors diminué de 43% par le contrôle à haute fréquence, pour un nombre de Reynolds de 550. De plus, on montre que l'écoulement turbulent revient à un état bidimensionnel si l'amplitude de rotation est suffisamment élevée.
Accès au texte intégral et bibtex
https://theses.hal.science/tel-00004699/file/tel-00004699.pdf BibTex

Preprints, Working Papers, ...

2023

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
2023
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.
Accès au texte intégral et bibtex
https://hal.science/hal-04191804/file/2308.12864.pdf BibTex