Search

Your search keyword '"Sébastien Martin"' showing total 16 results
Start Over Author "Sébastien Martin" Topic physics::fluid dynamics
16 results on '"Sébastien Martin"'

1. Existence of solutions and continuous and semi-discrete stability estimates for 3D/0D coupled systems modelling airflows and blood flows

Author

Céline Grandmont, Sébastien Martin, COmputational Mathematics for bio-MEDIcal Applications (COMMEDIA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Sorbonne Université (SU), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), and Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)

Subjects
Airflows, Energy estimates, Stokes, Computation, Airflow, Mathematics Subject Classification. 76Z05, 76D07, 65M60, 74H15, Blood flows, 010103 numerical & computational mathematics, 01 natural sciences, Stability (probability), Domain (mathematical analysis), Physics::Fluid Dynamics, Operator (computer programming), Applied mathematics, Boundary value problem, 0101 mathematics, [MATH]Mathematics [math], Mathematics, Numerical Analysis, Navier–Stokes, Applied Mathematics, Stability analysis, 010101 applied mathematics, Computational Mathematics, Stability conditions, Modeling and Simulation, Windkessel models, Implicit/explicit schemes, Analysis, Order of magnitude
Abstract

In this paper we analyse geometric multiscale models arising in the description of physiological flows such as blood flow in arteries or air flow in the bronchial tree. The geometrical complexity of the networks in which air/blood flows lead to a classical decomposition in two areas: a truncated 3D geometry corresponding to the largest contribution of the domain, and a 0D part connected to the 3D part, modelling air/blood flows in smaller airways/vessels. The fluid in the 3D part is described by the Stokes or the Navier–Stokes system which is coupled to 0D models orso-calledWindkessel models. The resulting Navier–Stokes–Windkessel coupled system involves Neumann non-local boundary conditions that depends on the considered applications. We first show that the different types of Windkessel models share a similar formalism. Next we derive existence results and stability estimates for the continuous coupled Stokes–Windkessel or Navier–Stokes–Windkessel problem as well as stability estimates for the semi-discretized systems with either implicit or explicit treatment of the boundary conditions. In all the calculations, we pay a special attention to the dependency of the various constants and smallness conditions on the data with respect to the physical and numerical parameters. In particular we exhibit different kinds of behavior depending on the considered 0D model. Moreover even if no energy estimates can be derived in energy norms for the Navier–Stokes–Windkessel system, leading to possible and observed numerical instabilities for large applied pressures, we show that stability estimates for both the continuous and semi-discrete problems, can be obtained in appropriate norms for small enough data by introducing a new well chosen Stokes-like operator. These sufficient stability conditions on the data may give a hint on the order of magnitude of the data enabling stable computations without stabilization method for the problem. Numerical simulations illustrate some of the theoretical results.

Published
2021
Full Text
View/download PDF

2. Stationary Oldroyd model with diffusive stress in thin pipes

Author

Andrei Ichim, Laurent Chupin, and Sébastien Martin

Subjects
Axisymmetric geometry, Applied Mathematics, 010102 general mathematics, Computational Mechanics, Rotational symmetry, Mechanics, 01 natural sciences, Physics::Fluid Dynamics, 010101 applied mathematics, Stress (mechanics), Cross section (physics), Classical mechanics, Stationary flow, 0101 mathematics, Asymptotic expansion, Mathematics
Abstract

The aim of this paper is to study the stationary flow of an Oldroyd fluid with particular diffusive stress, flowing through a thin 3D pipe. An asymptotic expansion with respect to a small parameter describing the ratio between the diameter of the cross section and the length is calculated and rigorously justified. The result obtained is compared against a numerical solution in the particular case of axisymmetric geometries.

Published
2017
Full Text
View/download PDF

3. Fluid-kinetic modelling for respiratory aerosols with variable size and temperature

Author

Amina Mecherbet, Céline Grandmont, Bérénice Grec, Laurent Boudin, Frédérique Noël, Sébastien Martin, Sorbonne Université (SU), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Numerical simulation of biological flows (REO), Sorbonne Université (SU)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), COmputational Mathematics for bio-MEDIcal Applications (COMMEDIA), Inria de Paris, Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Université Paris Descartes - Paris 5 (UPD5)-Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jean Alexandre Dieudonné (JAD), Université Nice Sophia Antipolis (... - 2019) (UNS), Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)

Subjects
0301 basic medicine, T57-57.97, Materials science, Applied mathematics. Quantitative methods, Airflow, Humidity, 02 engineering and technology, Mechanics, Radius, 021001 nanoscience & nanotechnology, Kinetic energy, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Aerosol, Physics::Fluid Dynamics, 03 medical and health sciences, 030104 developmental biology, Compressibility, QA1-939, Particle, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Particle size, 0210 nano-technology, Physics::Atmospheric and Oceanic Physics, Mathematics, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; In this paper, we propose a coupled fluid-kinetic model taking into account the radius growth of aerosol particles due to humidity in the respiratory system. We aim to numerically investigate the impact of hygroscopic effects on the particle behaviour. The air flow is described by the incompressible Navier-Stokes equations, and the aerosol by a Vlasov-type equation involving the air humidity and temperature, both quantities satisfying a convection-diffusion equation with a source term. Conservations properties are checked and an explicit time-marching scheme is proposed. Two-dimensional numerical simulations in a branched structure show the influence of the particle size variations on the aerosol dynamics.; Dans cet article, nous proposons un modèle couplé fluide-cinétique prenant en compte la croissance en rayon des particules d'un aérosol due à l'humidité dans les voies respiratoires. Nous nous intéressons en particulier à l'étude numérique de l'impact des effets hygroscopiques sur le comportement des particules. L'air est décrit par les équations de Navier-Stokes incompressibles, et l'aérosol par une équation de type Vlasov impliquant l'humidité et la température de l'air. Chacune de ces deux quantités vérifie une équation de convection-diffusion avec un terme source. Nous montrons que le modèle couplé vérifie de bonnes propriétés de conservation. Il est ensuite discrétisé par un schéma explicite en temps. Enfin, des simulations numériques en deux dimensions dans une bifurcation montrent l'influence de la croissance en rayon sur la dynamique de l'aérosol.

Published
2020
Full Text
View/download PDF

4. Direct simulation of rigid particles in a viscoelastic fluid

Author

Astrid Decoene, Sébastien Martin, Bertrand Maury, Laboratoire de Mathématiques d'Orsay (LM-Orsay), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Université Paris Descartes - Paris 5 (UPD5)-Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS), Département de Mathématiques et Applications - ENS Paris (DMA), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques d'Orsay ( LM-Orsay ), Université Paris-Sud - Paris 11 ( UP11 ) -Centre National de la Recherche Scientifique ( CNRS ), Mathématiques Appliquées à Paris 5 ( MAP5 - UMR 8145 ), Université Paris Descartes - Paris 5 ( UPD5 ) -Institut National des Sciences Mathématiques et de leurs Interactions-Centre National de la Recherche Scientifique ( CNRS ), Département de Mathématiques et Applications - ENS Paris ( DMA ), École normale supérieure - Paris ( ENS Paris ) -Centre National de la Recherche Scientifique ( CNRS ), Martin, Sébastien, Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), MAP5 - Mathématiques Appliquées à Paris 5 ( MAP5 - UMR 8145 ), Centre National de la Recherche Scientifique ( CNRS ) -Institut National des Sciences Mathématiques et de leurs Interactions-Université Paris Descartes - Paris 5 ( UPD5 ), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), and École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Inertial frame of reference, General Chemical Engineering, dense suspensions, fluid-structure interaction, [SPI.MECA.MEFL] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], 01 natural sciences, Viscoelasticity, characteris, 010305 fluids & plasmas, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], Physics::Fluid Dynamics, [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], 0103 physical sciences, Fluid–structure interaction, Newtonian fluid, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], General Materials Science, Penalty method, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Physics, 010304 chemical physics, penalty method, Applied Mathematics, Mechanical Engineering, Numerical analysis, Mechanics, [ MATH.MATH-NA ] Mathematics [math]/Numerical Analysis [math.NA], [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], Condensed Matter Physics, Ellipsoid, Oldroyd model, Finite element method, fictitious domain, characteristics method, tics method, [ SPI.MECA.MEFL ] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], viscoelastic fluid, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

In this paper, we present a numerical method which performs the direct simulation of 2D viscoelastic suspensions. Objectives. Interactions between viscoelastic fluids of Oldroyd type, including inertial effects, and a large number of rigid spheres or ellipsoids are addressed. Method. The numerical method is built upon a fictitious domain approach which consists in defining the fluid-structure problem over the whole domain (fluid+solid). In the Newtonian case, the resulting variational formulation, although classical, uses non-standard functional spaces which include the rigidity constraints. From the numerical point of view, these constraints can be addressed by penalty methods, leading to the possible use of standard finite elements solvers with fixed structured meshes. We show how this approach can be adapted to viscoelastic fluids of Oldroyd type. Results. Two types of configurations are investigated in dilute and dense regimes: sedimentation of spherical particles and shear flows with ellipsoidal particles.

Published
2018

5. Towards the simulation of dense suspensions: a numerical tool

Author

Sébastien Martin, Bertrand Maury, Sylvain Faure, Takéo Takahashi, Laboratoire de Mathématiques d'Orsay (LM-Orsay), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), Robust control of infinite dimensional systems and applications (CORIDA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), CORIDA, and Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est

Subjects
Materials science, Interaction forces, Stokesian dynamics, Nanotechnology, Mechanics, Viscous liquid, 01 natural sciences, 010305 fluids & plasmas, Contact force, Physics::Fluid Dynamics, Condensed Matter::Soft Condensed Matter, Rheology, 0103 physical sciences, Lubrication, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], SPHERES, 010306 general physics, Suspension (vehicle)
Abstract

International audience; We present a numerical tool which aims at investigating the rheology of dense suspensions of entities such as spheres, red blood cells, polymer chains, or any kind of rigid or deformable bodies, in a viscous fluid. We shall pay a special attention to the short-range interactions between those entities (contact forces, lubrication forces). As for the fluid itself, our strategy consists in avoiding the direct and costly solution of the Stokes equations by integrating only the interaction forces which are likely to play a significant role in the overall behaviour of the suspension, in the spirit of Stokesian Dynamics. We present some preliminary results for suspensions of spheres, Red Blood Cells, and polymer-like chains.

Published
2009
Full Text
View/download PDF

6. Viscoelastic flows in a rough channel: a multiscale analysis

Author

Laurent Chupin, Sébastien Martin, Laboratoire de Mathématiques Blaise Pascal ( LMBP ), Université Blaise Pascal - Clermont-Ferrand 2 ( UBP ) -Centre National de la Recherche Scientifique ( CNRS ), Mathématiques Appliquées à Paris 5 ( MAP5 - UMR 8145 ), Université Paris Descartes - Paris 5 ( UPD5 ) -Institut National des Sciences Mathématiques et de leurs Interactions-Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Blaise Pascal - Clermont-Ferrand 2 (UBP)-Centre National de la Recherche Scientifique (CNRS), Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), and Université Paris Descartes - Paris 5 (UPD5)-Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Scale (ratio), Truncation error (numerical integration), Applied Mathematics, 010102 general mathematics, Mathematical analysis, Surface finish, 01 natural sciences, Domain (mathematical analysis), Viscoelasticity, Physics::Fluid Dynamics, 010101 applied mathematics, Boundary layer, Mathematics - Analysis of PDEs, [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Asymptotic expansion, Mathematical Physics, Analysis, Mathematics, Communication channel, Analysis of PDEs (math.AP)
Abstract

We investigate the influence of the rough boundaries on viscoelastic flows, described by the diffusive Oldroyd model. The fluid domain has a rough wall modeled by roughness patterns of size e ≪ 1 . We present and rigorously justify an asymptotic expansion with respect to e, at any order, based upon the definition of elementary problems: Oldroyd-type problems at the global scale defined on a smoothened domain and boundary-layer corrector problems. The resulting analysis guarantees optimality with respect to the truncation error and leads to a numerical algorithm which allows us to build the approximation of the solution at any required precision.

Published
2016

7. Viscoelastic fluids in a thin domain

Author

Laurent Chupin, Guy Bayada, Sébastien Martin, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne] (LaMCoS), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Tribologie et Mécanique des Interfaces (TMI), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), and Martin, Sébastien

Subjects
Applied Mathematics, Numerical analysis, 010102 general mathematics, Mathematical analysis, Stokes-Oldroyd, MSC 76A10, 35B40, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], Stokes flow, 01 natural sciences, Viscoelasticity, Domain (mathematical analysis), Condensed Matter::Soft Condensed Matter, Physics::Fluid Dynamics, 010101 applied mathematics, Shear (sheet metal), thin films, Flow (mathematics), viscoelastic, 0101 mathematics, Thin film, complex fluids, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics, Complex fluid
Abstract

The present paper deals with viscoelastic flows in a thin domain. In particular, we derive and analyse the asymptotic equations of the Stokes-Oldroyd system in thin films (including shear effects). We present a numerical method which solves the corresponding problem and we present some related numerical tests which evidence the effects of the elastic contribution on the flow.

Published
2007
Full Text
View/download PDF

8. On the instantaneous formation of cavitation in hydrodynamic lubrication

Author

Jesús Ildefonso Díaz Díaz and Sébastien Martin

Subjects
Marketing, Physics, Strategy and Management, Fluid bearing, Mechanics, Tribology, Reynolds equation, Physics::Fluid Dynamics, Classical mechanics, Cavitation, Media Technology, Lubrication, General Materials Science, Saturation (chemistry)
Abstract

We consider the Elrod–Adams model extending the classical lubrication Reynolds equation to the case of the possible presence of a cavitation region. We show that the behaviour of the pressure and saturation depends crucially on the behaviour of the separation h ( t , x , y ) among the two surfaces. In particular, we exhibit some simple formulations for which we prove (rigorously) that a cavitation region is formed instantaneously (even for initially saturated flows). Some numerical experiences are also given. To cite this article: J.I. Diaz, S. Martin, C. R. Mecanique 334 (2006).

Published
2006
Full Text
View/download PDF

9. HOMOGENIZATION OF A NONLOCAL ELASTOHYDRODYNAMIC LUBRICATION PROBLEM: A NEW FREE BOUNDARY MODEL

Author

Carlos Vázquez, Sébastien Martin, Guy Bayada, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne] (LaMCoS), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Tribologie et Mécanique des Interfaces (TMI), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Dep. Matematicas (Universidade A Coruña) (DEP. MATEMATICAS (UNIVERSIDADE A CORUÑA)), Universidade A Coruña, and Martin, Sébastien

Subjects
Lubrication Problem, Elrod-Adams model, homogenization, two-scale convergence, Surface finish, 01 natural sciences, Homogenization (chemistry), Physics::Fluid Dynamics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, numerical simulation, ComputingMilieux_MISCELLANEOUS, Physics, Computer simulation, Applied Mathematics, 010102 general mathematics, Mechanics, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], 16. Peace & justice, piezoviscous fluid, 010101 applied mathematics, Nonlinear system, Elastohydrodynamic lubrication, Boundary model, Classical mechanics, Modeling and Simulation, Cavitation, Lubrication, AMS: 76D08, 35B40, 35J85, 76M50, 76M10, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

36 pages; The present paper deals with the homogenization of a lubrication problem, using two-scale convergence techniques and periodic unfolding methods. We study in particular the Reynolds-Hertz model, which takes into account elastohydrodynamic deformations of the upper surface, when highly oscillating roughness effects occur. The difficulty arises when considering cavitation free boundary phenomena, leading to highly nonlinear and nonlocal problems.

Published
2005
Full Text
View/download PDF

10. From the Phan–Thien–Tanner/Oldroyd-B Non-Newtonian Model to the Double Shear Thining Rabinowisch Thin Film Model

Author

Laurent Chupin, Sébastien Martin, Guy Bayada, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Blaise Pascal - Clermont-Ferrand 2 (UBP)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Institut Camille Jordan (ICJ), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Physics, Shear thinning, Mechanical Engineering, Mathematical analysis, 02 engineering and technology, Surfaces and Interfaces, 021001 nanoscience & nanotechnology, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Non-Newtonian fluid, Viscoelasticity, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], Surfaces, Coatings and Films, Deborah number, Physics::Fluid Dynamics, Shear rate, 020303 mechanical engineering & transports, 0203 mechanical engineering, Mechanics of Materials, Shear stress, Newtonian fluid, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], Statistical physics, 0210 nano-technology, Asymptotic expansion
Abstract

In this paper, an asymptotic expansion is used to derive a description of Phan–Tien– Tanner (PTT)/Oldroyd-B flows in the thin film situation without the classical “upper convective maxwell”(UCM) assumption. We begin with a short presentation of the Phan–Thien–Tanner/Oldroyd-B models, which introduce viscoelastic effects in a solute–solvent mixture. The three-dimensional flow is described using five parameters, namely the Deborah number (De) (or the relaxation parameter λ), the viscosity ratio r, the bulk fluid viscosity η, the material slip parameter a related to the “convected derivative” and an elongation number κ. Then we focus on the thin film assumption and the related asymptotic analysis that allows us to derive a reduced model. A perturbation procedure for “not too small” values of κ allows us to obtain further results such as an asymptotic “effective viscosity/ shear rate” law, which appears to be a perturbation of the double Rabinowisch model, whose parameters are completely defined by those of the original three-dimensional model. And last a numerical procedure is proposed based on a penalized Uzawa method, to compute the corresponding solution. This algorithm can also be used for any generalized double Newtonian shear thinning Carreau law.

Published
2011
Full Text
View/download PDF

11. Microscopic modelling of active bacterial suspensions

Author

Sébastien Martin, Astrid Decoene, Bertrand Maury, Martin, Sébastien, Laboratoire de Mathématiques d'Orsay (LM-Orsay), and Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Physics, Mesoscopic physics, [PHYS.PHYS.PHYS-BIO-PH] Physics [physics]/Physics [physics]/Biological Physics [physics.bio-ph], [PHYS.PHYS.PHYS-BIO-PH]Physics [physics]/Physics [physics]/Biological Physics [physics.bio-ph], Applied Mathematics, Perturbation (astronomy), 010103 numerical & computational mathematics, Mechanics, Stokes flow, Viscous liquid, 01 natural sciences, Finite element method, Quantitative Biology::Cell Behavior, Strain rate tensor, Physics::Fluid Dynamics, Classical mechanics, Modeling and Simulation, 0103 physical sciences, Fluid dynamics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Limiting oxygen concentration, 0101 mathematics, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], 010306 general physics
Abstract

We present two-dimensional simulations of chemotactic self-propelled bacteria swimming in a viscous fluid. Self-propulsion is modelled by a couple of forces of same intensity and opposite direction applied on the rigid bacterial body and on an associated region in the fluid representing the flagellar bundle. The method for solving the fluid flow and the motion of the bacteria is based on a variational formulation written on the whole domain, strongly coupling the fluid and the rigid particle problems: rigid motion is enforced by penalizing the strain rate tensor on the rigid domain, while incompressibility is treated by duality. This model allows to achieve an accurate description of fluid motion and hydrodynamic interactions in moderate to concentrated active suspensions. A mesoscopic model is also used, in which the size of the bacteria is supposed to be much smaller than the elements of fluid: the perturbation of the fluid due to propulsion and motion of the swimmers is neglected, and the fluid is only subjected to the buoyant forcing induced by the presence of the bacteria, which are denser than the fluid. Although this model does not accurately take into account hydrodynamic interactions, it is able to reproduce complex collective dynamics observed in concentrated bacterial suspensions, such as bioconvection. From a mathematical point of view, both models lead to a minimization problem which is solved with a standard Finite Element Method. In order to ensure robustness, a projection algorithm is used to deal with contacts between particles. We also reproduce chemotactic behaviour driven by oxygen: an advection-diffusion equation on the oxygen concentration is solved in the fluid domain, with a source term accounting for oxygen consumption by the bacteria. The orientations of the individual bacteria are subjected to random changes, with a frequency that depends on the surrounding oxygen concentration, in order to favor the direction of the concentration gradient.

Published
2011

12. Rigorous derivation of the thin film approximation with roughness-induced correctors

Author

Laurent Chupin, Sébastien Martin, Martin, Sébastien, Jeunes chercheuses et jeunes chercheurs - Analyse et Calcul des Effets de Rugosité sur les Ecoulements - - RUGO2008 - ANR-08-JCJC-0104 - JCJC - VALID, Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Blaise Pascal - Clermont-Ferrand 2 (UBP)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques d'Orsay (LM-Orsay), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), ANR-08-JCJC-0104,RUGO,Analyse et Calcul des Effets de Rugosité sur les Ecoulements(2008), and Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Thin films, Perturbation (astronomy), 01 natural sciences, Microscopic scale, Physics::Fluid Dynamics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Reynolds equation, 0101 mathematics, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Mathematics, Rough boundaries, Stokes system, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Lubrication approximation, Stokes flow, Lubrication theory, 010101 applied mathematics, Computational Mathematics, Boundary layer, Macroscopic scale, AMS 34K25, 34K26, 35B40, 42B05, 76D07, 76D08, 76D10, Asymptotic expansion, Analysis
Abstract

50 pages; We derive the thin film approximation including roughness-induced correctors. This corresponds to the description of a confined Stokes flow whose thickness is of order~$\eps$ (designed to be small)~; but we also take into account the roughness patterns of the boundary that are described at order~$\eps^2$, leading to a perturbation of the classical Reynolds approximation. The asymptotic expansion leading to the description of the scale effects is rigorously derived, through a sequence of Reynolds-type problems and Stokes-type (boundary layer) problems. Well-posedness of the related problems and estimates in suitable functional spaces are proved, at any order of the expansion. In particular, we show that the micro-/macro-scale coupling effects may be analysed as the consequence of two features: the interaction between the macroscopic scale (order~1) of the flow and the microscopic scale (order~$\eps$ of the thin film) is perturbed by the interaction with a microscopic scale of order~$\eps^2$ related to the roughness patterns (as expected through the classical Reynolds approximation)~; moreover, the converging-diverging profile of the confined flow, which is typical in lubrication theory (note that the case of a constant cross-section channel has no interest) provides additional micro-macro-scales coupling effects.

Published
2011

13. From 3-D Olroyd-B -PTT models to 2-D thin film non newtonian laws

Author

Laurent Chupin, Guy Bayada, Sébastien Martin, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques d'Orsay (LM-Orsay), and Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Physics::Fluid Dynamics, Law, Constitutive equation, Newtonian fluid, Perturbation (astronomy), Elongation, [SPI.MECA]Engineering Sciences [physics]/Mechanics [physics.med-ph], Asymptotic expansion, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Non-Newtonian fluid, Viscoelasticity, Mathematics, Deborah number
Abstract

International audience; The PTT-OLROYD-B model for solute-solvent mixtures introduces visco elastic effects by way of five parameters, namely Deborah number De , a viscosity ratio r ,a viscosity , a parameter related to the convected derivation and an elongation parameter ?. Asymptotic expansion is used to gain a description of the flow in the thin film situation . Two cases are considered depending of the relative magnitude of the parameters De and ? with respect to the thickness ratio. In the first situation, the elongation effects disappear at the limits and the constitutive law of the film flow is a double Newtonian Rabinowitch model whose parameters are completely described by those of the original 3-D model. In the second case in which the elongation parameter is of order zero with respect of the film thickness ratio, however small, a perturbation procedure allows to retain this parameter in the asymptotic constitutive law. This law appears to be a small modification of the double Newtonian Rabinowisch law. At last a new numerical procedure is proposed. Numerical examples will be presented for 3-D flows

Published
2010

14. Influence of Multiscale Roughness Patterns in Cavitated Flows: Applications to Journal Bearings

Author

Sébastien Martin

Subjects
Materials science, Computer simulation, Article Subject, General Mathematics, lcsh:Mathematics, General Engineering, Thin film flow, Surface finish, Mechanics, lcsh:QA1-939, Lubrication theory, Homogenization (chemistry), Physics::Fluid Dynamics, lcsh:TA1-2040, Cavitation, Saturation (chemistry), Anisotropy, lcsh:Engineering (General). Civil engineering (General), Simulation
Abstract

This paper deals with the coupling of two major problems in lubrication theory: cavitation phenomena and roughness of the surfaces in relative motion. Cavitation is defined as the rupture of the continuous film due to the formation of air bubbles, leading to the presence of a liquid-gas mixture. For this, the Elrod-Adams model (which is a pressure-saturation model) is classically used to describe the behavior of a cavitated thin film flow. In addition, in practical situations, the surfaces of the devices are rough, due to manufacturing processes which induce defaults. Thus, we study the behavior of the solution, when highly oscillating roughness effects on the rigid surfaces occur. In particular, we deal with the reiterated homogenization of this Elrod-Adams problem, using periodic unfolding methods. A numerical simulation illustrates the behavior of the solution. Although the pressure tends to a smooth one, the saturation oscillations are not damped. This does not prevent us from defining an equivalent homogenized saturation and highlights the anisotropic effects on the saturation function in cavitated areas.

Published
2008
Full Text
View/download PDF

15. Micro-Roughness Effects in (Elasto)Hydrodynamic Lubrication Including a Mass-Flow Preserving Cavitation Model

Author

Carlos Vázquez, Sébastien Martin, Guy Bayada, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne] (LaMCoS), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Tribologie et Mécanique des Interfaces (TMI), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Dep. Matematicas (Universidade A Coruña) (DEP. MATEMATICAS (UNIVERSIDADE A CORUÑA)), Universidade A Coruña, and Martin, Sébastien

Subjects
Materials science, Scale (ratio), Mass flow, Fluid bearing, [SPI.MECA.MEFL] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], 02 engineering and technology, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], Physics::Fluid Dynamics, 0203 mechanical engineering, Scale analysis (mathematics), Lubrication, [PHYS.MECA.MEFL] Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], Elastohydrodynamic, ComputingMilieux_MISCELLANEOUS, Mechanical Engineering, Surfaces and Interfaces, Mechanics, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], Physics::Classical Physics, 021001 nanoscience & nanotechnology, Roughness, Reynolds equation, Surfaces, Coatings and Films, 020303 mechanical engineering & transports, Classical mechanics, Mechanics of Materials, Macroscopic scale, Cavitation, 0210 nano-technology, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

An average Reynolds equation is proposed for predicting the effects of deterministic periodic roughness, taking JFO mass flow preserving cavitation model and elastohydrodynamic effects into account. For this, the asymptotic model is based upon a double scale analysis approach. The average Reynolds equation can be used both for the description of cavitation on a macroscopic scale in widening gap regions as well as for cavitation on the microscopic interasperity scale. Results of numerical simulations based on the model are presented for the case of a hydrodynamically lubricated journal bearings and an elasto-hydrodynamically lubricated point contact.

Published
2007

16. An Average Flow Model of the Reynolds Roughness Including a Mass-Flow Preserving Cavitation Model

Author

Guy Bayada, Carlos Vázquez, Sébastien Martin, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne] (LaMCoS), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Tribologie et Mécanique des Interfaces (TMI), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Dep. Matematicas (Universidade A Coruña) (DEP. MATEMATICAS (UNIVERSIDADE A CORUÑA)), Universidade A Coruña, and Martin, Sébastien

Subjects
Materials science, Mechanical Engineering, Mass flow, Thermodynamics, 02 engineering and technology, Surfaces and Interfaces, Mechanics, Surface finish, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], Tribology, 021001 nanoscience & nanotechnology, Reynolds equation, Surfaces, Coatings and Films, Physics::Fluid Dynamics, 020303 mechanical engineering & transports, 0203 mechanical engineering, Mechanics of Materials, Cavitation, Scale analysis (mathematics), Surface roughness, [PHYS.MECA.MEFL] Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], Boundary value problem, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], 0210 nano-technology, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

An average Reynolds equation for predicting the effects of deterministic periodic roughness, taking Jakobsson, Floberg, and Olsson mass flow preserving cavitation model into account, is introduced based upon the double scale analysis approach. This average Reynolds equation can be used both for a microscopic interasperity cavitation and a macroscopic one. The validity of such a model is verified by numerical experiments both for one-dimensional and two-dimensional roughness patterns.

Published
2004

Catalog

Books, media, physical & digital resources
See catalog results