Nouvelle approche pour la discrétisation de flux diffusifs en volumes finis à forte obliquité

We propose a new approach for the discretization of diffusive flux on a non orthogonal mesh based on the Deferred correction introduced by Peric. This new method is applied successfully to the solution of a Poisson problem in quadrangular domains meshed with very distorted control volumes. The interest of this approach lies in the fact that the precision of the used schemes is conserved despite meshes distortion level. The comparative study of the value of the spectral radius of iteration matrix enables us to explain why our Deferred correction approach is better than that of Peric, which diverges on highly skewed meshes. To cite this article: Y.M. Ahipo, Ph. Traore, C. R. Mecanique 334 (2006).     

Confined buckling of inextensible rods by convex difference algorithms

In this Note we present an approach to determine the local minima of a specific class of minimization problems. Attention is focused on the inextensibility condition of flexible rods expressed as a nonconvex constraint. Two algorithms are derived from a special splitting of the Lagrangian into the difference of two convex functions (DC). They are compared to the augmented Lagrangian methods used in this context. These DC formulations are easily extended to contact problems and applied to the determination of confined buckling shapes. To cite this article: P. Alart, S. Pagano, C. R. Mecanique 330 (2002) 819–824.     

Méthode particulaire anisotropeAnisotropic particle method

A particle method has been used to simulate the vorticity transport in a two-dimensional flow of an incompressible inviscid fluid. In this method, not only the location and the circulation of the particle are used but also the moments of the internal vorticity. The transport equation for these moments has been derived from the vorticity transport equation. The method has been compared to the usual particle method as well as to Teng's elliptic vortex model. The test case is that of the evolution of two circular patches of vorticity already used by Teng. To cite this article: A. Beaudoin et al., C. R. Mecanique 330 (2002) 51–56     

Numerical simulation of corner singularities: a paradox in Maxwell-like problems

This paper sums up some recent studies related to the numerical solution of boundary value problems deriving from Maxwell's equations. These studies bring to light the theoretical origins of the ‘corner paradox’ pointed out by numerical experiments for years: In a domain surrounded by a perfect conductor, a ‘nodal’ discretization can approximate the electromagnetic field only if the domain has no reentrant corners or edges. The explanation lies in a mathematical curiosity: two different interpretations of the same variational equation, which are both well-posed and lead either to the physical or a spurious solution! Two strategies which were recently proposed to remedy this flaw of nodal elements are described. To cite this article: C. Hazard, C. R. Mecanique 330 (2002) 57–68     

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).     

Un nouveau préconditionneur pour les problèmes elliptiques à coefficients variablesA new preconditonner for general elleptic problems

In this Note we describe a preconditionner for iteratively solving the linear system arising from the discretization of a general nonseparable elliptic problem by spectral element method. This preconditionner is constructed from approximating the original problem with the closest (in some sense) separable elliptic problem. A direct method is then used to invert the preconditionner. To cite this article: M. Azaïez et al., C. R. Mecanique 331 (2003).     

Dispersion de Taylor généralisée à un fluide à propriétés physiques variablesGeneralized Taylor dispersion for heterogeneous fluid

The investigation of non-reactive miscible solute dispersion in a vertical Hele–Shaw cell is considered. An asymptotic method is used to extend Taylor model to the case of the fluid density, the dynamic viscosity and the molecular diffusion coefficient are solute concentration-dependent. It is demonstrated that the averaged variables over the gap are governed by a convection–dispersion equation in which the dispersion tensor is concentration-dependent. To cite this article: C. Felder et al., C. R. Mecanique 332 (2004).     

Complexification phenomenon in an example of sensitive singular perturbationPhénomène de complexification dans un exemple de perturbation singulière sensitive

We consider singular perturbation problems depending on a parameter ε?0 such that for ε>0 the solution u^ε belongs to a Sobolev space on a domain $\text{Ω}$, but the limit u⁰ is not a distribution on $\text{Ω}$. A very simple model problem, solvable by Fourier transform allows us to study the complexification process of u^ε as $\text{ε↘0}$. The limit holds in the topology of a space of analytical functionals. To cite this article: C.A. De Souza, É. Sanchez-Palencia, C. R. Mecanique 332 (2004).     

Étude du contrôle du décollement sur un profil d'aile par mesures PIV et analyse PODStudy of separation control on a wing profile using PIV measurements and POD analysis

The purpose of this study is the active control of flow separation on an ONERA D airfoil, using continuous blowing microjets. Particle Image Velocimetry (PIV) is used to measure velocity fields at midspan around the airfoil in both controlled and uncontrolled cases. Post-processing based on Proper Orthogonal Decomposition (POD) is developed to exhibit the main energetic features of the flow. Therefore, the detailed study of the POD modes for separated and stalled cases leads to a better understanding of the control mechanisms. Moreover, the POD basis computed for uncontrolled and controlled cases, opens the way to optimisation of control strategies. To cite this article: J. Favier, A. Kourta, C. R. Mecanique 334 (2006).