
Jean-Louis AuriaultJoseph Fourier University | UJF · Sols, Solides, Structure, Risques 3S-R
Jean-Louis Auriault
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211
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Introduction
Jean-Louis Auriault currently works at the Sols, Solides, Structure, Risques 3S-R, University Joseph Fourier - Grenoble 1. Jean-Louis does research in Materials Physics, Geophysics and Fluid Dynamics. Their most recent publication is 'Inner Resonance in Media Governed by Hyperbolic and Parabolic Dynamic Equations. Principle and Examples'.
Publications
Publications (211)
The main objective of this work is to describe reaction–diffusion of two species in a porous medium. We aim at finding the macroscopic model equivalent to the description of the physics at the pore scale, with a peculiar attention to possible shape morphogenesis as introduced in Turing’s seminal article in 1952 (Turing in Philos Trans R Soc Lond Se...
This chapter deals with the modeling and design of inner resonance media, i.e. media that present a local resonance which has an impact on the overall dynamic behaviour. The aim of this chapter is to provide a synthetic picture of the inner resonance phenomena by means of the asymptotic homogenization method (Sanchez-Palencia, 1980). The analysis i...
The Fourier equation shows infinitesimal heat disturbances that propagate at an infinite speed. To suppress this paradox, a great number of non-Fourier heat conduction models were introduced. The Fourier equation is a macroscopic description at some macroscopic length scale L large with respect to the microscopic scale l, here the atomic scale. In...
We investigate transient heat and solute transfers in liquid-saturated porous media. The macroscopic equivalent models are obtained by a homogenization process from the pore-scale description. The large value of the Lewis number in liquid mixtures introduces a possible separation of scales between the heat and solute diffusion wavelengths \(L^{\mat...
When investigating heterogeneous media such as composite materials or geological structures, it is convenient to replace them by macroscopic equivalent media, which simplifies computations a lot. In the paper, we look for the equivalent macroscopic model for describing seismic wave propagation and transient heat transfers in thermoelastic periodic...
In this paper we present the development of the macroscopic model describing the hydro-mechanical coupling of damaged porous media containing cracks or/and vugs, by using the asymptotic expansion method. The analysis starts at the mesoscopic scale at which we assume a generic microstructure and the validity of the Biot model in the micro-porous dom...
We revisit an ancient paper (Auriault and Bonnet, 1985) which points out the existence of cut-off frequencies for long acoustic wavelength in high-contrast elastic composite materials, i.e. when the wavelength is large with respect to the characteristic heterogeneity length. The separation of scales enables the use of the method of multiple scale e...
The purpose of this paper is to develop the macroscopic model of hydro‐mechanical coupling for the case of a porous medium containing isolated cracks or/and vugs. In the development, we apply the asymptotic expansion homogenization method. It is shown that the general structure of Biot's model is the same as in the case of homogeneous medium, but t...
We investigate the properties of the dispersion tensor in porous media by making use of the method of homogenization by multiple scale expansions, which gives the dispersion model from the pore scale description. Results are valid for random or periodic structures as well. By investigating the domain of relatively small Péclet numbers, we show that...
A large number of papers are adopting the Beavers and Joseph (BJ) condition (Beavers and Joseph, J Fluid Mech 30(1):197–207,
1967) for describing the boundary condition between a saturated porous medium and a free fluid, in place of the adherence
condition. The aim of the paper is to bring some insight into the domain of validity of the BJ conditio...
An increasing number of articles are adopting Brinkman’s equation in place of Darcy’s law for describing flow in porous media.
That poses the question of the respective domains of validity of both laws, as well as the question of the value of the effective
viscosityμ
e
which is present in Brinkman’s equation. These two topics are addressed in this...
Both naturally-occurring and man-made materials are often heterogeneous materials formed of various constituents with different properties and behaviours. Studies are usually carried out on volumes of materials that contain a large number of heterogeneities. Describing these media by using appropriate mathematical models to describe each constituen...
Many analytical and numerical works have been devoted to the prediction of macroscopic effective transport properties in particulate media. Usually, structure and properties of macroscopic balance and constitutive equations are stated a priori. In this paper, the upscaling of the transient diffusion equations in concentrated particulate media with...
In paper I [Vassal, Phys. Rev. E77, 011302 (2008)] of this contribution, the effective diffusion properties of particulate media with highly conductive particles and particle-particle interfacial barriers have been investigated with the homogenization method with multiple scale asymptotic expansions. Three different macroscopic models have been pro...
Fick's law expresses the proportionality of solute flux with respect to concentration gradient. Similar relations are given by Darcy's law for the fluid flow in porous media, Ohm's law for the electric flux and Fourier's law for heat transfers. When introduced in the corresponding balance equations, these flux laws yield diffusion equations of para...
Fick's law expresses the proportionality of solute flux with respect to concentration gradient. Similar relations are Darcy's law for the fluid flow in porous media, Ohm's law for the electric flux and Fourier's law for heat transfers. When introduced in the corresponding balance equations, these flux laws yield diffusion equations of parabolic cha...
Fick’s law expresses the proportionality of solute flux with respect to concentration gradi-
ent. Similar relations are given by Darcy’s law for the fluid flow in porous media, Ohm’s law for the
electric flux and Fourier’s law for heat transfers. When introduced in the corresponding balance
equations, these flux laws yield diffusion equations of pa...
The homogenisation method with multiple scale expansions is used to investigate the slow and isothermal flow of generalised Newtonian fluids through anisotropic porous media. From this upscaling it is shown that the first-order macroscopic pressure gradient can be defined as the gradient of a macroscopic viscous dissipation potential, with respect...
Using the theory of homogenization we derive macroscopic models for describing flow of gas at low pressure in dual-porosity
media. The case of a fractured porous medium is under consideration for the study, and the existence of a representative elementary
volume that consists of open connected fractures surrounded by porous matrix blocks is assumed...
L'écoulement de fluide en loi puissance à travers des milieux fibreux anisotropes est étudié en s'appuyant sur les résultats théoriques obtenus par la méthode d'homogénéisation des structures périodiques. Afin de determiner la structure de la loi d'écoulement, des simulations numériques ont été réalisées sur des volumes élémentaires représentatifs...
We investigate the high velocity flow in heterogeneous porous media. The model is obtained by upscaling the flow at the heterogeneity
scale where the Forchheimer law is assumed to be valid. We use the method of multiple scale expansions, which gives rigorously
the macroscopic behaviour without any prerequisite on the form of the macroscopic equatio...
A biporous medium is a porous medium that shows two independent connected pore systems as; e.g., heat exchanger metal foams
or organs. Wave propagation in such media is investigated by upscaling the pore scale description. We focus on the multiphasic
macroscopic behaviour which corresponds to Biot’s model for one pore system porous media. In the ca...
In this work, an asymptotic expansion homogenization is used to study the overall behaviour of a damaged elastic body with
a locally periodic distribution of growing microcracks. The microstructure evolution is represented, at the macroscopic level,
by a local internal variable related to the microcracks lengths. An evolution damage law is deduced,...
The flow of power-law fluids through fibrous media at low-pore Reynolds number is investigated using the homogenization method for periodic structures with multiple scale expansions. This upscaling process shows that the macroscopic pressure gradient is also a power-law of the volume averaged velocity field. To determine the complete structure of t...
We investigate wave propagation in elastic porous media which are saturated by incompressible viscous Newtonian fluids when the porous media are in rotation with respect to a Galilean frame. The model is obtained by upscaling the flow at the pore scale. We use the method of multiple scale expansions which gives rigorously the macroscopic behaviour...
The paper concerns macroscopic modeling of water flow in an unsaturated double-porosity soil consisting of highly conductive inclusions embedded in a less conductive matrix. The flow at the local scale in both sub-domains is assumed to be governed by the Richards equation. Application of the asymptotic homogenization method leads to a macroscopic f...
The flow of power-law fluid through anisotropic fibrous media is investigated using the homog-enization of multiple scale expansions for periodic structures. Numerical simulations were performed with 2D periodic arrays of circular solid inclusions and compared with results existing in the literature. Mechanical iso-dissipation curves were then used...
Heterogeneous media with a large number of heterogeneities cannot be described by considering each of the heterogeneities, that would yield to intractable boundary value problems. The well known method is to replace, if possible, the heterogeneous media by an homogeneous one, the description of which is valid at a very large scale (the macroscopic...
This paper aims at deriving the quasi-static filtration law in porous media, when the separation of scales is poor.We use the method of multi-scale asymptotic expansions which gives the macroscopic behaviour from the pore scale description. The first order approximation is the Darcy's law. When the separation of scales is poor, eventual correctors...
Recently, the flow law through rotating porous media was obtained by upscaling the flow equations at the pore scale. The strong influence of the Coriolis force on the flow through a rotating periodic arrays of cylinders at both the microscopic scale and the macroscopic scale is numerically investigated.
Transport in porous media is investigated by upscaling the pore scale behaviour. We use the technique of multiscale asymptotic expansions which seems to be the most efficient method to obtain macroscopic equivalent behaviours. Different transport phenomena are addressed: fluid flow through a saturated porous medium (Darcy’s law), two-phase flow (co...
We investigate the validity of Darcy's law when the separation of scales is poor. We use the method of multi-scale asymptotic expansions which gives the macroscopic behaviour from the pore scale description. The first order approximation is the Darcy's law. When the separation of scales is poor, eventual correctors to Darcy's law are obtained by in...
Recently, the filtration law of an incompressible viscous Newtonian fluid flowing through a rigid non-inertial porous medium (e.g. a soil sample placed in a centrifuge basket) which takes into account the Criolis effects was developed by using an upscaling technique (2), (3), (7). The structure of the law obtained is similar to that of the Darcy's...
In this work, the flow of power-law fluids through anisotropic fibrous media is revisited, upscaling the fluid flow at the pore scale with the homogenization method of multiple scale expansions for periodic structures. This upscaling technique permits a quantitative study of the seepage law by performing numerical simulation with simple two-dimensi...
This work is aimed at deriving and at analyzing the dynamic filtration law that describes the acoustics of a gas saturated porous medium, when a wall-slip flow occurs due to low gas pressure. The dynamic filtration law is derived by upscaling the pore-scale description that consists of the equations of linear acoustics and a wall-slip condition on...
This paper is aimed towards investigating the filtration law of an incompressible viscous Newtonian fluid through a rigid non-inertial porous medium (e.g. a porous medium placed in a centrifuge basket). The filtration law is obtained by upscaling the flow equations at the pore scale. The upscaling technique is the homogenization method of multiple...
We investigate the propagation of elastic waves through an elastic medium submitted to an angular rotation Ω. Wave propagation is shown to be directly related to the Kibel number Ki=ω/Ω, where ω is the wave frequency. Two dispersive waves W1 and W2 are obtained which tend to the classical dilatational and shear waves, respectively, when Ki tends to...
In this paper the mathematical macroscopic modeling of unsaturated water flow in a porous medium (soil) with highly permeable porous inclusions is presented. It is supposed that water flow in each sub domain can be described by the strongly non-linear Richards' equation. Gravity effects are considered. The upscaling process of this stiff problem is...
This work deals with the large-scale mathematical modelling of flow of gas at low pressure in porous media. At the pore scale, this type of flow is characterised by a wall-slip effect, which at the sample scale entails a dependence of permeability upon gas pressure. This latter property is described by Klinkenberg''s law. The goal of the present wo...
In this paper the mathematical macroscopic modeling of unsaturated water
flow in a porous medium (soil) with highly permeable porous inclusions
is presented. It is supposed that water flow in each sub domain can be
described by the strongly non-linear Richards' equation. Gravity effects
are considered. The upscaling process of this stiff problem is...
This work is aimed at deriving mathematical models that describe pollutant migration through fractured porous media. A homogenisation method is used, i.e. macroscopic models are rigorously deduced from the physical description which is valid within a Representative Elementary Volume (REV). The fundamental assumption behind homogenisation is the sep...
This work is aimed towards deriving macroscopic models that describe pollutant migration through fractured porous media. A homogenisation method is used, that is, macroscopic models are deduced from the physical description over a representative elementary volume (REV), which consists of an open fracture surrounded by a porous matrix block. No spec...
Modelling of solute transport in fractured porous media is a subject of intensive research in many engineering disciplines, such as petroleum engineering, water resources management, civil engineering. Recent field and laboratory experiments show that, in presence of strong adsorption, the behaviour of solute penetrating into the fractured porous m...
The aim of this work is to investigate the tensorial filtration law in rigid porous media
for steady-state slow flow of an electrically conducting, incompressible and viscous
Newtonian fluid in the presence of a magnetic field. The seepage law under a magnetic
field is obtained by upscaling the flow at the pore scale. The macroscopic magnetic fi...
To honour the pioneering contribution of Maurice A. Biot to the mechanics of porous media and its influence in various sciences and engineering disciplines, a Biot Conference on Poromechanics was held at the Université Catholique de Louvain in Belgium, 14-16 September 1998.
In the autumn 2000, we took the initiative of organising the Second Biot Co...
Upscaling methods aim at representing the evolution of a given physical process in a given heterogeneous medium by an equivalent macroscopic continuous behavior. In this paper, we recall the main features of the method of homogenization by multiscale asymptotic expansions. To illustrate the method, a few illustrative examples are revisited concerni...
This work is concerned with modelling steady-state slow flow of incompressible power-law fluids in porous media. The macroscopic filtration law is derived by upscaling the pore–scale description. The up-scaling technique in use is the homogenisation method of multiple scales. Then, the filtration law is in-vestigated by means of the theory of repre...
We investigate the filtration law of incompressible viscous Newtonian fluids in rigid non-inertial porous media, for example, rotating porous media. The filtration law is obtained by upscaling the flow at the pore scale. We use the method of multiple scale expansions which gives rigorously the macroscopic behaviour without any prerequisite on the f...
The objective of this work is the derivation of the wave equations for describing acoustics in a deformable porous medium saturated by a bubbly fluid, when capillary, thermal and phase change effects are accounted for. This is performed using an homogenisation technique: the macroscopic model is obtained by upscaling the bubble-scale and the pore-s...
A fractured porous medium is a dual-porosity medium, i.e., it consists of two interacting porous systems whose permeabilities are very different. The purpose of this paper is to mathematically model seismic wave propagation in saturated fractured porous media when the wavelength is large compared to the fracture characteristic length.
To obtain the effective parameters of a heterogeneous medium from the microscale description, one has to solve a boundary value problem defined on a representative cell. For practical purposes, the medium is often considered as periodic and the period represents the representative cell. In some cases the cell posesses plane symmetries. The aim of t...
We investigate the filtration law in rigid porous media for steady-state slow flow of an electrically conducting, incompressible and viscous Newtonian fluid in the presence of magnetic field. The seepage law under magnetic field is obtained by upscaling the flow at the pore scale by using the method of multiple scale expansions. The macroscopic mag...
In a previous paper (C. Boutin, J.-L. Auriault, Acoustics of a bubbly fluid at large bubble concentration, Eur. J. Mech. B/Fluids, 12(3) (1993) 367–399), the homogenization technique was used to investigate how acoustic waves propagate in a bubbly fluid at finite concentration. Three different equivalent macroscopic behaviours were shown to exist,...
This work is concerned with deriving macroscopic models for describing the propagation of shock waves in porous elastic media
saturated by a viscous Newtonian fluid. This is performed using the results that are obtained by upscaling the porous medium
behaviour from the pore scale description. This upscaling shows four different macroscopic models....
We investigate the filtration law in rigid non-Galilean porous media filled by incompressible viscous Newtonian fluid. The filtration law is obtained by upscaling the flow from the pore scale. We use the method of multiple scale expansions which gives rigorously the macroscopic behaviour without any prerequisite at the macroscopic scale. For finite...