Evolution de la fonction de répartition d'un gaz de tourbillons 2D en présence d'un bruitEvolution of the repartition function of 2D vortex gaz in presence of noise

In this work, we study the motion of N localized vortices in the presence of ‘noise’. To apply the methods of statistical mechanics, we determine the evolution equation for the probability density function of vortices in which the presence of the ‘noise’ is accounted for by as a term similar to viscosity. This equation is isomorph to the system of equations which describe 2D turbulence with viscosity. The advantage of this formulation is that it can be numerically implemented at very large Reynolds numbers. To cite this article: S. Decossin, V. Pavlov, C. R. Mecanique 331 (2003).     

Some useful hybrid approaches for predicting aerodynamic noise

In recent years, several numerical studies have shown the feasibility of Direct Noise Computation (DNC) where the turbulent flow and the radiated acoustic field are obtained simultaneously by solving the compressible Navier–Stokes equations. The acoustic radiation obtained by DNC can be used as reference solution to investigate hybrid methods in which the sound field is usually calculated as a by-product of the flow field obtained by a more conventional Navier–Stokes solver. A hybrid approach is indeed of practical interest when only the non-acoustic part of the aerodynamic field is available. In this review, some acoustic analogies or hybrid approaches are revisited in the light of CAA. To cite this article: C. Bailly et al., C. R. Mecanique 333 (2005).     

Instabilité et particularités de l'évolution d'une nappe tourbillonnaireInstability and features of vortex sheet evolution

The instability and the features of vortex sheet evolution are studied. We consider the self-organization of localized vortices (in two-dimensional flows) into clusters-like and spiral-like structures and show that quasi-final states do not ‘forget’ conditions of their initial origin. We discuss the physical significance of the obtained results. To cite this article: V. Pavlov et al., C. R. Mecanique 330 (2002) 757–762.     

Remaillage adaptatif pour la mise en forme des tôles minces

Problems associated with finite element simulation of the forming processes are characterized by large elastoplastic deformations, evolutive contact with friction, geometrical nonlinearities inducing a severe distortion of the computational mesh of the domain. In this case, frequent remeshing of the deformed domain during computation are necessary to obtain an accurate solution and complete the computation until the termination of the numerical simulation process. This Note presents a new adaptive remeshing method of thin sheets for numerical simulation of metal forming processes. The proposed method is based on geometrical criteria and does not use the geometry of the forming tools. It is integrated in a computational environment using the ABAQUS solver. Numerical examples are given to show the efficiency of our approach. To cite this article: L. Moreau et al., C. R. Mecanique 333 (2005).     

Modified fixed point algorithm in fluid–structure interactionAccélération avec des conditions de transpiration d'un algorithme de point fixe en interaction fluide–structure

In this work, we address the numerical solution of some non-linear problems arising in the time discretization of fluid–structure interaction problems with fully implicit schemes. At each time step, we have to solve a highly non-linear coupled system, since the fluid domain depends on the unknown displacement of the structure. We propose a modified fixed-point algorithm which combines the Block-Gauss–Seidel iterations with a transpiration formulation. Numerical experiments show the great improvement in computing time with respect to the standard method. To cite this article: S. Deparis et al., C. R. Mecanique 331 (2003).     

Shape optimization of an accommodative intra-ocular lens

Cataract surgery consists in replacing the clouded or opacified crystalline lens by an Intra-Ocular Lens (IOL) having the same mean dioptrical power. Clear vision is then achieved at a given distance and glasses are needed in many situations. A new kind of IOL, potentially accommodative, is proposed. Its design is based on the deep understanding of the accommodation mechanism and on the mathematical modeling and the numerical simulation of the IOL's comportment in vivo. A preliminary version of this IOL is now commercialized by the company HumanOptics under the name ‘1CU’. In a second phase, shape optimization techniques equipped with strong mechanical and physiological constraints, are used to enhance the IOL performance and build a new design. To cite this article: F. Jouve, K. Hanna, C. R. Mecanique 333 (2005).     

Un algorithme efficace d'intégration plastique pour un matériau obéissant au critère anisotrope de HillAn efficient algorithm for plastic integration of material satisfying the Hill's anisotropic yield criterion.

This Note deals with an efficient algorithm to carry out the plastic integration and compute the stresses due to large strains for materials satisfying the Hill's anisotropic yield criterion. The classical algorithm of plastic integration such as ‘Return Mapping Method’ is largely used for nonlinear analyses of structures and numerical simulations of forming processes, but it requires an iterative schema and may have convergence problems. A new direct algorithm based on a scalar method is developed which allows us to directly obtain the plastic multiplier without an iteration procedure; thus the computation time is largely reduced and the numerical problems are avoided. To cite this article: I. Titeux et al., C. R. Mecanique 332 (2004).     

Piston Stokes flow in a semi-infinite channelL'écoulement de Stokes autour d'un piston dans un conduit semi-infini

The piston flow is bounded by rigid walls at y=±1, x>0 and generated by the uniform translation of the end wall x=0. After Katopodes, Davis and Stone [3] constructed a solution in terms of biorthogonal eigenfunctions, Meleshko and Krasnopolskaya [1] used a variation of an asymptotic technique developed by Meleshko and Gomilko [2] to examine the pointwise convergence of the non-orthogonal series. However, they overlooked the nonuniqueness of their solution and the consequent solvability condition which is shown here to necessitate a minor modification without significant harm to their contribution. To cite this article: A.M.J. Davis, C. R. Mecanique 330 (2002) 457–459.     

ADER discontinuous Galerkin schemes for aeroacoustics

In this paper we apply the ADER approach to the Discontinuous Galerkin (DG) framework for the two-dimensional linearized Euler equations. The result is an efficient high order accurate single-step scheme in time which uses less storage than Runge–Kutta DG schemes, especially for very high order of accuracy. The aim is to obtain an arbitrarily accurate scheme in space and time on unstructured grids for accurate noise propagation in the time domain in very complex geometries. We will present numerical convergence rates for ADER-DG methods up to 10th order of accuracy in space and time on structured and unstructured meshes. To cite this article: M. Dumbser, C.-D. Munz, C. R. Mecanique 333 (2005).     

Flow in wavy tube structure: asymptotic analysis and numerical simulationÉcoulement dans une structure tubulaire ondulée : analyse asymptotique et résolution numérique

This paper deals with the study of the stationary, incompressible, 2D flow of a fluid in a thin wavy tube. In this work, we consider a domain which is the union of two wavy tubes depending on a small parameter. The asymptotic expansion is constructed. The method of partial asymptotic decomposition is applied. The numerical implementation of this method for the extrusion process is developed. The new physical effects are discussed. To cite this article: A. Ainser et al., C. R. Mecanique 331 (2003).     

Verification of higher-order discontinuous Galerkin method for hexahedral elements

A high-order implementation of the Discontinuous Galerkin (dg) method is presented for solving the three-dimensional Linearized Euler Equations on an unstructured hexahedral grid. The method is based on a quadrature free implementation and the high-order accuracy is obtained by employing higher-degree polynomials as basis functions. The present implementation is up to fourth-order accurate in space. For the time discretization a four-stage Runge–Kutta scheme is used which is fourth-order accurate. Non-reflecting boundary conditions are implemented at the boundaries of the computational domain.The method is verified for the case of the convection of a 1D compact acoustic disturbance. The numerical results show that the rate of convergence of the method is of order $p+1$ in the mesh size, with p the order of the basis functions. This observation is in agreement with analysis presented in the literature. To cite this article: H. Özdemir et al., C. R. Mecanique 333 (2005).     

Pont entre les « micro » et « méso » mécaniques des composites stratifiésRelationships between ‘micro’ and ‘meso’ mechanics of laminated composites

A relatively complete bridge is built between the micromechanics of laminates for which there are numerous theoritical and experimental works and the mesomechanics of laminates introduced and developped in particular at Cachan for more than 15 years. At the ‘meso’ scale, the ply and the interface are homogeneized. To cite this article: P. Ladevèze, G. Lubineau, C. R. Mecanique 331 (2003).     

Étude des temps de chauffage et de refroidissement des alliages à mémoire de forme (AMF)Heating and cooling time studies of shape memory alloys (SMA)

The knowledge of response times of active material is essential for their efficient use as actuators. In this paper the heating and cooling times of a shape memory alloy wire (NiTi) under a constant load are predicted by the integration of the corresponding heat equation. The comparison with a ‘fictitious’ material with the same material characteristics but without phase transformation shows that the response times are longer for the SMA (around 2.7 times for heating and 1.5 times for cooling). To cite this article: N. Chaillet et al., C. R. Mecanique 332 (2004).     

Approximation uniformément valable pour l'écoulement de Falkner–SkanA uniformly valid approximation for a Falkner–Skan flow

In the context of the laminar steady two-dimensional flow of an incompressible Newtonian fluid, we propose a uniformly valid approximation in the whole domain of the flow over a flat plate with incidence. The solution is built from the asymptotic method of matched expansions at order one and has been compared with the classical boundary layer solution and the potential solution. It allows a better approximation of basic flow near the leading edge of the flat plate. The solution has been established at order two for the flow without incidence. These more realistic solutions should be employed when analysing the receptivity and the ensuing destabilisation of boundary layers. To cite this article: S. Saintlos, J. Bretteville, C. R. Mecanique 330 (2002) 673–682.     

Matrix-fracture exchange in a fractured porous medium: stochastic upscalingCoefficient d'échange matrice-fracture en milieu poreux fracturé : changement d'échelle par approche stochastique

We present in this Note a stochastic approach to the matrix-fracture exchange in a heterogeneous fractured porous medium. We introduce an intermediate scale, called the unit-scale, between the local-scale (fracture-scale) and the large-scale characteristic of the reservoir mesh (reservoir block). This paper focuses on the problem of upscaling fluid exchange phenomena from the unit scale to the reservoir mesh or block scale. Simplifying the Darcian flow terms enables us to obtain a probabilistic solution of the dual continuum problem, in continuous time, in the case of a purely random exchange coefficient. This is then used to develop several upscaling approaches to the fluid exchange problem, and to analyze the so-called ‘effective’ exchange coefficient. The results are a first contribution to the more general problem of upscaling multidimensional flow-exchange processes in space and time, in randomly heterogeneous dual continua. To cite this article: M. Kfoury et al., C. R. Mecanique 332 (2004).     

Présentation d'une méthode d'étude de la stabilité linéaire d'écoulements instationnairesPresentation of a method for linear stability analysis of unsteady flow

We propose a linear stability analysis of unsteady viscous flow. We apply this method to an oscillatory pipe flow with an axisymetric 2D perturbation which has received considerable attention. The numerical results are relevant. To cite this article: M. Siouffi et al., C. R. Mecanique 330 (2002) 641–645.     

Periodization of random media and representative volume element size for linear composites

Several existing numerical studies show that the effective linear properties of random composites can be accurately estimated using small volumes subjected to periodic boundary conditions – more suitable than homogeneous strain or stress boundary conditions – providing that a sufficient number of realizations are considered. Introducing the concept of periodization of random media, this Note gives a new definition of representative volume element which leads to estimates of its minimum size in agreement with existing theoretical results. A qualitative convergence criterion for the numerical simulations is proposed and illustrated with finite element computations. To cite this article: K. Sab, B. Nedjar, C. R. Mecanique 333 (2005).     

Second-order estimates for the large-deformation response of particle-reinforced rubbersEstimations homogénéisées pour le comportement mécanique des caoutchoucs renforcés en grandes déformations

This paper presents the application of a recently proposed ‘second-order’ homogenization method (J. Mech. Phys. Solids 50 (2002) 737–757) to the estimation of the effective behavior of hyperelastic composites subjected to finite deformations. The main feature of the method is the use of ‘generalized’ secant moduli that depend not only on the phases averages of the fields, but also on the phase covariance tensors. The use of the method is illustrated in the context of particle-, or fiber-reinforced elastomers and estimates analogous to the well-known Hashin–Shtrikman estimates for linear-elastic composites are generated. The new estimates improve on earlier estimates (J. Mech. Phys. Solids 48 (2000) 1389–1411) neglecting the use of fluctuations. In particular, the new estimates, unlike the earlier ones, are capable of recovering the exact incompressibility constraint when the matrix is also taken to be incompressible. To cite this article: O. Lopez-Pamies, P. Ponte Castañeda, C. R. Mecanique 331 (2003).     

‘Les fleurs du mal’ – an adaptive wavelet method of arbitrary lines I: convection–diffusion problems« Les fleurs du MAL » – une méthode d'ondelettes adaptive de lignes arbitraires I : problèmes de convection–diffusion

Baudelaire's ‘les fleurs du mal’ refers to various new developments (‘les fleurs’) of the method ofarbitrarylines (mal), since it was first published (in C. R. Acad. Sci. Paris, Sér. I, in 1991). Here we revisit the basic mal (semi-discretization) methodology for stationary convection–diffusion problems and develop an adaptive, wavelet-based solver that is capable of capturing the thin layers that arise in such problems. We show the efficacy and high accuracy of the wavelet-mal solver by applying it to a challenging 2D problem involving both boundary and interior layers. To cite this article: X. Ren, L.S. Xanthis, C. R. Mecanique 332 (2004).