Stabilisation des couches PML pour les équations d'Euler linéariséesPML stabilization for linearized Euler equations

The perfectly matched layer (PML) is an efficient tool to simulate propagation phenomena in free space on unbounded domain. It seems to be very efficient for Maxwell's equations, but for the linearized Euler equations, it leads to numerical instabilities. In this Note we describe a simple way to gain stability. The method consists in dissipative time perturbations of the split variables. It is illustrated by some convincing numerical tests. To cite this article: J. Métral, O. Vacus, C. R. Mecanique 330 (2002) 347–352.     

Turbulence from 1870 to 1920: The birth of a noun and of a concept

We consider here the works of French, British, and German researchers in fluid mechanics from 1870 to the beginning of the twentieth century. Our aim is to understand how the term “turbulence” introduced by William Thomson in 1887, which was not used by the main researchers of the time, including Joseph Boussinesq, Osborne Reynolds, Lord Rayleigh, Horace Lamb in the first editions of his book, became classical in the 1920s. We trace the first introductions of the terms “turbulence”, “turbulent flow” in the works of relatively unknown researchers between 1889 and 1903, until it reaches the vocabulary of mainstream researchers in fluid mechanics and physics. Our result is that the shift was in 1906–1908, when the term was used in the 1906 edition of the book of Horace Lamb, and in Lanchester's book, followed by a series of papers of German researchers before the First World War.The use of the word “turbulence”, a word used for a long time for crowds or for children, in a scientific context, corresponds to the introduction of a new concept, a new understanding of a scientific phenomenon clearly identified as being different from laminar motion. The study of the use of this term is also the study of the diffusion of a new concept among researchers of the time.     

On the slow motion of a cluster of bubbles under the combined action of gravity and thermocapillarity

The slow migration of N spherical bubbles under combined buoyancy and thermocapillarity effects is investigated by appealing solely to $3N+1$ boundary-integral equations. In addition to the theory and the associated implementation strategy, preliminary numerical results are both presented and discussed for a few clusters involving 2, 3, 4 or 5 bubbles with a special attention paid to the case of rigid configurations. To cite this article: A. Sellier, C. R. Mecanique 333 (2005).     

Hybrid schemes to compute contact discontinuities in Euler equations with any EOSSchémas hybrides pour la simulation des discontinuités de contact des équations d'Euler avec une loi d'état quelconque

We propose here some explicit hybrid schemes which enable accurate computation of Euler equations with arbitrary (analytic or tabulated) equation of state (EOS). The method is valid for the exact Godunov scheme and some approximate Godunov schemes. To cite this article: T. Gallouët et al., C. R. Mecanique 330 (2002) 445–450.     

On the connection between tug-of-war games and nonlocal PDEs on graphs

In this paper, we are interested in the connection between some stochastic games, namely the tug-of-war games, and non-local PDEs on graphs. We consider a general formulation of tug-of-war games related to many continuous PDEs. Using the framework of partial difference equations, we transcribe this formulation on graph, and show that it encompasses several PDEs on graphs such as the ∞-Laplacian, the game p-Laplacian with and without gradient terms, and the eikonal equation. We then interpret these discrete games as non-local tug-of-war games. The proposed framework is illustrated with general interpolation problems on graphs.     

Validation of averaged equations for thermal vibrational convection in near-critical fluidsValidation d'équations moyennées pour l'étude de la convection vibrationnelle dans les fluides supercritiques.

Within an averaging approach, the governing equations and effective boundary conditions describing both the average and pulsation motion of a near-critical fluid subjected to high-frequency vibrations are obtained. Vibrations induce the non-homogeneities in average temperature. Owing to these non-homogeneities, the average flows can be generated even in isothermal cavity under weightlessness. These flows are examined for 1D and 2D configurations. The direct numerical simulations fulfilled earlier confirm the averaged model, we obtain the same flow structures by essentially smaller requirements for computational time. To cite this article: A.Vorobev et al., C. R. Mecanique 332 (2004).     

Sur la fermeture des termes rapides pour des écoulements moyens rotationnelsOn the closure of rapid terms for rotational mean flows

The modelling of homogeneous turbulent flows with mean rotatio, considered in a previous Note, is handled under the form $\text{M}{}^1\text{=}\text{M}\text{[}\text{b}\text{,}\text{y}\text{,}\text{Q}{}^1\text{]}$ in terms of componental and dimensional anisotropies, and of the symmetrized stropholysis. A systematic technique of expansion is proposed. The necessary realisability conditions are then applied. It is shown that there exists no realisable functional $\text{M}$ which would be isotropic with respect to its arguments. To cite this article: J. Piquet, C. R. Mecanique 331 (2003).     

Injection de bulles en paroi d'un écoulement cisaillé visqueuxBubble injection at the wall of a viscous shear flow

Air bubble injection at the wall of a viscous shear flow is filmed using a high speed video camera. The temporal evolution of the bubbles equivalent radius and the position of their centre of mass throughout their growth are determined from image processing. The experimental results are then used to validate a model of forces acting on the bubbles during their growth and after their detachment within the limit of small bubble Reynolds numbers. To cite this article: G. Duhar, C. Colin, C. R. Mecanique 331 (2003).     

Diffusion and wave behaviour in linear Voigt modelDiffusion et comportement ondulatoire dans le modèle linéaire de Voigt

A boundary value problem $\text{P}{}_{\mathrm{\epsilon }}$ related to a third order parabolic equation with a small parameter ε is analized. This equation models the one-dimensional evolution of many dissipative media as viscoelastic fluids or solids, viscous gases, superconducting materials, incompressible and electrically conducting fluids. Moreover, the third order parabolic operator regularizes various nonlinear second order wave equations. In this paper, the hyperbolic and parabolic behaviour of the solution of $\text{P}{}_{\mathrm{\epsilon }}$ is estimated by means of slow timeτ=εt and fast timeθ=t/ε. As consequence, a rigorous asymptotic approximation for the solution of $\text{P}{}_{\mathrm{\epsilon }}$ is established. To cite this article: M. De Angelis, P. Renno, C. R. Mecanique 330 (2002) 21–26     

Direct numerical simulation of transition to turbulence in an oscillatory channel flowSimulation numérique de la transition vers la turbulence d'un ecoulement oscillant dans une conduite bi-dimensionnelle

In this Note, we present results of the numerical simulation of transition to turbulence for a purely oscillatory channel flow. These simulations were performed for various values of the Reynolds number, the so-called Stokes parameter being equal to 4. The methodology used for the flow simulation relies on a combination of finite element space approximations with time-discretization by operator splitting; it has shown to be very effective, even when it is applied to relatively complex domains with strong expansions at the inlet and outlet of the channel. The numerical results obtained agree qualitatively well with previous experiments by other investigators. To cite this article: L.H. Juárez, E. Ramos, C. R. Mecanique 331 (2003).     

On the stability of a Bingham fluid flow in an annular channelSur la stabilité de l'écoulement d'un fluide de Bingham dans une conduite annulaire

Linear stability of a fully developed Bingham fluid flow between two coaxial cylinders subject to infinitesimal axisymetric perturbations is investigated. The analysis leads to two uncoupled Orr–Sommerfeld equations with appropriate boundary conditions. The numerical solution is obtained using fourth order finite difference scheme. The computations were performed for various plug flow dimensions and radii ratios. Within the range of the parameters considered in this paper, the Poiseuille flow of Bingham fluid is found to be linearly stable. To cite this article: N. Kabouya, C. Nouar, C. R. Mecanique 331 (2003).     

A penalization method applied to the wave equation

In this Note we investigate the mathematical properties of the volume penalization method applied to the one-dimensional wave equation. Generally speaking, the penalization method allows one to handle complex geometries by simply adding a term to the equation to impose the boundary conditions. We study the convergence of the method with regards to the penalization parameter and we present error and stability analyses for the wave equation. Numerical simulations using a finite difference scheme illustrate the results. To cite this article: A. Paccou et al., C. R. Mecanique 333 (2005).     

On the Navier–Stokes equations simulation of the head-on collision between two surface solitary waves

The scope of this Note is to show the results obtained for simulating the two-dimensional head-on collision of two solitary waves by solving the Navier–Stokes equations in air and water. The work is dedicated to the numerical investigation of the hydrodynamics associated to this highly nonlinear flow configuration, the first numerical results being analyzed. The original numerical model is proved to be efficient and accurate in predicting the main features described in experiments found in the literature. This Note also outlines the interest of this configuration to be considered as a test-case for numerical models dedicated to computational fluid mechanics. To cite this article: P. Lubin et al., C. R. Mecanique 333 (2005).     

A heat transfer measurement of jet impingement with high injection temperature

Local heat transfer from an impinging high temperature jet is studied using a method based on the heat thin foil technique and on the infrared thermography. Heat thin foil technique is used to impose several heat fluxes. For each flux, the temperature distribution is recorded using infrared imaging. Local heat transfer coefficients and adiabatic wall temperatures are determined by means of a linear regression method. This procedure is validated for a single round jet impinging on a flat plate for a range of injection temperatures. To cite this article: M. Fénot et al., C. R. Mecanique 333 (2005).     

Dispersion de particules solides en mouvement de saltation dans un écoulement turbulentDispersion of solid saltating particles in a turbulent flow

The solid particle dispersion in saltating motion is studied in an homogeneous turbulence and in a turbulent boundary layer. The fluid velocity along the particle trajectory is estimated using a continuous stochastic differential equation in which the correlation integral time takes into account gravity and inertia effects. As far as the boundary layer is concerned, the aerodynamic entrainment of particles and the rebound are modelised as random variables with Gaussian probability density functions. Compared with experimental results, the numerical results show good agreement for dispersion, although velocity fluctuations are slightly under evaluated. To cite this article: C. Aguirre et al., C. R. Mecanique 332 (2004).     

Various aspects of fluid vortices

A general review of the current research in vortex dynamics is presented, based on contributions given during a workshop held in May 2003 at Porquerolles, France. This article aims at providing a picture of the work performed on this subject in the French community. Various cases are covered, from 2D vortex patches to 3D vortex tubes; from isolated vortices to shear flows. Different contexts are considered: pure Euler and Navier–Stokes flows as well as stratified, rotating and magnetic flows. To cite this article: I. Delbende et al., C. R. Mecanique 332 (2004).     

Effective equations describing the flow of a viscous incompressible fluid through a long elastic tubeEquations efficaces décrivant l'écoulement d'un fluide visqueux incompressible dans un tuyau long et élastique

We study the flow of a viscous incompressible fluid through a long and narrow elastic tube whose walls are modeled by the Navier equations for a curved, linearly elastic membrane. The flow is governed by a given small time dependent pressure drop between the inlet and the outlet boundary, giving rise to creeping flow modeled by the Stokes equations. By employing asymptotic analysis in thin, elastic, domains we obtain the reduced equations which correspond to a Biot type viscoelastic equation for the effective pressure and the effective displacement. The approximation is rigorously justified by obtaining the error estimates for the velocity, pressure and displacement. Applications of the model problem include blood flow in small arteries. We recover the well-known Law of Laplace and provide a new, improved model when shear modulus of the vessel wall is not negligible. To cite this article: S. ?ani?, A. Mikeli?, C. R. Mecanique 330 (2002) 661–666.