Perfectly Matched Layer for Linearized Euler Equations in Open and Ducted Domains

Recently, perfectly matched layer (PML) as an absorbing boundary condition has widespread applications. The idea was first introduced by Berenger for electromagnetic waves computations. In this paper, it is shown that the PML equations for the linearized Euler equations support unstable solutions when the mean flow has a component normal to the layer. To suppress such unstable solutions so as to render the PML concept useful for this class of problems, it is proposed that artificial selective damping terms be added to the discretized PML equations. It is demonstrated that with a proper choice of artificial mesh Reynolds number, the PML equations can be made stable. Numerical examples are provided to illustrate that the stabilized PML performs well as an absorbing boundary condition. In a ducted environment, the wave mode are dispersive. It will be shown that the group velocity and phase velocity of these modes can have opposite signs. This results in a confined environment, PML may not be suitable as an absorbing boundary condition

2-D non-periodic homogenization to upscale elastic media for P-SV waves

International audienceThe pur pose of this paper is to give an upscaling tool valid for the wave equation in general elastic media. This paper is focused on P–SV wave propagation in 2-D, but the methodology can be extended without any theoretical difficulty to the general 3-D case. No assumption on the heterogeneity spectrum is made and the medium can show rapid variations of its elastic properties in all spatial directions. The method used is based on the two-scale homogenization expansion, but extended to the non-periodic case. The scale separation is made using a spatial low-pass filter. The ratio of the filter wavelength cut-off and the minimum wavelength of the propagating wavefield defines a parameter ε0 with which the wavefield propagating in the homogenized medium converges to the reference wavefield. In the general case, this non- periodic extension of the homogenization technique is only valid up to the leading order and for the so-called first-order cor rector. We apply this non-periodic homogenization procedure to two kinds of heterogeneous media: a randomly generated, highly heterogeneous medium and the Marmousi2 geological model. The method is tested with the Spectral Element Method as a solver to the wave equation. Comparing computations in the homogenized media with those obtained in the original ones shows that convergence with ε0 is even better than expected. The effects of the leading order cor rection to the source and first cor rection at the receivers' location are shown

Interleukin-7 Regulates Adipose Tissue Mass and Insulin Sensitivity in High-Fat Diet-Fed Mice through Lymphocyte-Dependent and Independent Mechanisms

Although interleukin (IL)-7 is mostly known as a key regulator of lymphocyte homeostasis, we recently demonstrated that it also contributes to body weight regulation through a hypothalamic control. Previous studies have shown that IL-7 is produced by the human obese white adipose tissue (WAT) yet its potential role on WAT development and function in obesity remains unknown. Here, we first show that transgenic mice overexpressing IL-7 have reduced adipose tissue mass associated with glucose and insulin resistance. Moreover, in the high-fat diet (HFD)-induced obesity model, a single administration of IL-7 to C57BL/6 mice is sufficient to prevent HFD-induced WAT mass increase and glucose intolerance. This metabolic protective effect is accompanied by a significant decreased inflammation in WAT. In lymphocyte-deficient HFD-fed SCID mice, IL-7 injection still protects from WAT mass gain. However, IL-7-triggered resistance against WAT inflammation and glucose intolerance is lost in SCID mice. These results suggest that IL-7 regulates adipose tissue mass through a lymphocyte-independent mechanism while its protective role on glucose homeostasis would be relayed by immune cells that participate to WAT inflammation. Our observations establish a key role for IL-7 in the complex mechanisms by which immune mediators modulate metabolic functions

Upscaling the flow of generalised Newtonian fluids through anisotropic porous media

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 to the first-order volume averaged fluid velocity. The macroscopic dissipation potential is the volume-averaged of local dissipation potential. Using this property, guidelines are proposed to build macroscopic tensorial permeation laws within the framework defined by the theory of anisotropic tensor functions and by using macroscopic isodissipation surfaces. A quantitative numerical study is then performed on a 3D fibrous medium and with a Carreau–Yasuda fluid in order to illustrate the theoretical results deduced from the upscaling

Modelling the flow of power-law fluids anisotropic porous media at low-pore reynolds number

International audiencehe 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 the macroscopic flow law, numerical simulations have to be performed on representative elementary volume of porous media. In this paper, this has been achieved on 2D periodic arrays of parallel fibers with elliptical cross section of different aspect ratios. It is found that macroscopic flow models already proposed in the literature fail in reproducing numerical data within the whole volume fractions of fibers and aspect ratios ranges. Consequently, a novel methodology is proposed to establish the macroscopic tensorial seepage law within the framework of the theory of anisotropic tensor functions and using mechanical iso-dissipation curves. This methodology is illustrated through our numerical results

Microstructural effects on the flow law of power-law fluids through fibrous media

International audienceIn 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-dimensional periodic arrays of circular solid inclusions. The significant role of the solid fraction, the fluid rheology and the porous media anisotropy on the resulting macroscopic flow law is underlined from the simulation