Bertrand Maury

Micro-Macro Modelling of an Array of Spheres Interacting ThroughLubrication Forces

by Bertrand Maury and Aline Lefebvre-Lepot

We consider here a discrete system of spheres interacting through a lubrication force. This force... more We consider here a discrete system of spheres interacting through a lubrication force. This force is dissipative, and singular near contact: it behaves like the reciprocal of interparticle distance. We propose a macroscopic constitutive equation which is built as the natural continuous counterpart of this microscopic lubrication model. This model, which is of the newtonian type, relies on an elongational viscosity, which is proportional to the reciprocal of the local fluid fraction. We then establish the convergence in a weak sense of solutions to the discrete problem towards the solution to the partial differential equation which we identified as the macroscopic constitutive equation.

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Multiscale modelling of the respiratory tract

We propose here a decomposition of the respiratory tree into three stages which correspond to dif... more We propose here a decomposition of the respiratory tree into three stages which correspond to different mechanical models. The resulting system is described by the Navier-Stokes equation coupled with an ODE (a simple spring model) representing the motion of the thoracic cage. We prove that this problem has at least one solution locally in time for any data and, in

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MULTISCALE MODELLING OF THE RESPIRATORY TRACK: A THEORETICAL FRAMEWORK

by Bertrand Maury and A. Soualah

We propose here a decomposition of the respiratory tree into three stages which correspond to dif... more We propose here a decomposition of the respiratory tree into three stages which correspond to different mechanical models. The resulting system is described by the Navier-Stokes equation coupled with an ODE (a simple spring model) representing the motion of the diaphragm muscl. We prove that this problem has at least one solution locally in time for any data and, in

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A discrete contact model for crowd motion

The aim of this paper is to develop a crowd motion model designed to handle highly packed situati... more The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: We first define a spontaneous velocity which corresponds to the velocity each individual would like to have in the absence of other people; The actual velocity is then computed as the projection of the

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One Time-step Finite Element Discretization of the Equation of Motion of Two-fluid Flows

ABSTRACT We discretize in space the equations obtained at each time step when discretizing in tim... more ABSTRACT We discretize in space the equations obtained at each time step when discretizing in time a Navier-Stokes system modelling the two-dimensional flow in a horizontal pipe of two immiscible fluids with comparable densities, but very different viscosities. At each time step the system reduces to a generalized Stokes problem with nonstandard conditions at the boundary and at the interface between the two fluids. We discretize this system with the “mini-element” and establish error estimates. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005

Crowd motion from the granular standpoint

Mathematical Models and Methods in Applied Sciences, 2015

ABSTRACT Following the approach initially proposed in Maury and Venel,30,31 we consider here crow... more ABSTRACT Following the approach initially proposed in Maury and Venel,30,31 we consider here crowd motion from the standpoint of granular media, and we investigate how theoretical and numerical tools in nonsmooth analysis can help better understanding some paradoxical features. We shall be especially interested in evacuation processes, jams, and we will detail how the granular nature of the flow helps to understand two well-known phenomena, the so-called &quot;Faster is Slower&quot; effect, and &quot;Stop-and-Go&quot; waves.

Simulation of self-propelled chemotactic bacteria in a stokes flow

ESAIM: Proceedings, 2010

A congestion model for cell migration

This paper deals with a class of macroscopic models for cell migration in a saturated medium for ... more This paper deals with a class of macroscopic models for cell migration in a saturated medium for two-species mixtures. Those species tend to achieve some motion according to a desired velocity, and congestion forces them to adapt their velocity. This adaptation is modelled by a correction velocity which is chosen minimal in a least-square sense. We are especially interested in

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Handling of Contacts in Crowd Motion Simulations

Traffic and Granular Flow ’07, 2009

Special issue: Selected papers based on the presentations at the CEMRACS annual summer school, Marseille, France, July 21st to August 29th, 2008

ESAIM Proceedings

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Un Modèle de Mouvements de Foule

ESAIM: Proceedings, 2007

ESAIM: PROCEEDINGS, July 2007, Vol.18, 143-152 Jean-Frédéric Gerbeau & Stéphane Labbé, Editor... more

A PENALTY METHOD FOR THE SIMULATION OF THE AORTIC VALVE

by Bertrand Maury and A. Lefebvre

We present a method to simulate the motion of a rigid body in a fluid governed by the Navier-Stok... more We present a method to simulate the motion of a rigid body in a fluid governed by the Navier-Stokes equations. Numerical simulations of such a problem can be carried out in many different ways, which we may classify into two main classes. The first one relies on a moving mesh which fits the moving part of the boundary (see em

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The Fat Boundary Method: Semi-Discrete Scheme and Some Numerical Experiments

by Silvia Bertoluzza and Bertrand Maury

Lecture Notes in Computational Science and Engineering, 2005

The Fat Boundary Method (FBM) is a fictitious domain like method for solving partial differential... more The Fat Boundary Method (FBM) is a fictitious domain like method for solving partial differential equations in a domain with holes Ω \ Bwhere B is a collection of smooth open subsets -that consists in splitting the initial problem into two parts to be coupled via Schwartz type iterations: the solution, with a fictitious domain approach, of a problem set in the whole domain Ω, for which fast solvers can be used, and the solution of a collection of independent problems defined on narrow strips around the connected components of B, that can be performed fully in parallel. In this work, we give some results on a semi-discrete FBM in the framework of a finite element discretization, and we present some numerical experiments.

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Handling congestion in crowd motion modeling

Networks and Heterogeneous Media, 2011

We address here the issue of congestion in the modeling of crowd motion, in the non-smooth framew... more We address here the issue of congestion in the modeling of crowd motion, in the non-smooth framework: contacts between people are not anticipated and avoided, they actually occur, and they are explicitly taken into account in the model. We limit our approach to very basic principles in terms of behavior, to focus on the particular problems raised by the non-smooth character of the models. We consider that individuals tend to move according to a desired, or spontanous, velocity. We account for congestion by assuming that the evolution realizes at each time an instantaneous balance between individual tendencies and global constraints (overlapping is forbidden): the actual velocity is defined as the closest to the desired velocity among all admissible ones, in a least square sense. We develop those principles in the microscopic and macroscopic settings, and we present how the framework of Wasserstein distance between measures allows to recover the sweeping process nature of the problem on the macroscopic level, which makes it possible to obtain existence results in spite of the non-smooth character of the evolution process. Micro and macro approaches are compared, and we investigate the similarities together with deep differences of those two levels of description.

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Multiscale modelling of the respiratory track: a theoretical framework

ESAIM: Proceedings, 2008

We propose here a decomposition of the respiratory tree into three stages which correspond to dif... more We propose here a decomposition of the respiratory tree into three stages which correspond to different mechanical models. The resulting system is described by the Navier-Stokes equation coupled with an ODE (a simple spring model) representing the motion of the diaphragm muscl. We prove that this problem has at least one solution locally in time for any data and, in the special case where the external forces are equal to zero and if the initial conditions are small enough, that the solution exists globally in time. Note moreover that, in the case where the spring stiffness is equal to zero, we obtain an existence result globally in time provided, once again, that the data are small enough. The behaviour of the global model is illustrated by two-dimensional simulations.

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Moving meshes with freefem++

An integrated, nonlinear model for oxygen transfer into the blood

Modeling of the air flow in the human respiratory tract

Modeling of flow limitation phenomena in the human respiratory tract during forced expiration

A smooth extension method

by Benoît Fabrèges and Bertrand Maury

ABSTRACT In this note, we present a smooth extension method for the simulation of the motion of i... more ABSTRACT In this note, we present a smooth extension method for the simulation of the motion of immersed rigid bodies. It is a method of the fictitious domain type, which uses Cartesian meshes and recovers the optimal order of the error by finding a smooth extension of the exact solution defined in the domain with holes. We first present the method with a Poisson problem and show next how it can be adapted to the case of immersed rigid bodies. Finally, the method is validated in both the scalar and the vector cases.

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