Resolution of linear viscoelastic equations in the frequency domain using real Helmholtz boundary integral equations

Boundary integral equations are well suitable for the analysis of seismic waves propagation in unbounded domains. Formulations in elastodynamics are well developed. In contrast, for the dynamic analysis of viscoelastic media, there are very seldom formulations by boundary integral equations. In this Note, we propose a new and simple formulation of time harmonic viscoelasticity with the Zener model, which reduces to classical elastodynamics if a compatibility condition is satisfied by boundary conditions. Intermediate variables which satisfy the classical elastodynamic equations are introduced. It makes it possible to utilize existing numerical tools of time harmonic elastodynamics. To cite this article: S. Chaillat, H.D. Bui, C. R. Mecanique 335 (2007).     

Asymptotics of Neumann harmonics when a cavity is close to the exterior boundary of the domain

We construct the asymptotics (as ε→0) of solutions to the Neumann problem for the Laplace equation and of the corresponding Dirichlet integral. The problem concerns a three-dimensional domain having two connected components of the boundary at the distance ε>0. To cite this article: G. Cardone et al., C. R. Mecanique 335 (2007).     

Homogenization of an elasticity problem in domains with a net of slender bars near surface

We consider an elasticity problem in a domain Ω⁽⁾=ΩF⁽⁾, where Ω is an open bounded domain in R³, F⁽⁾ is a connected nonperiodic set in Ω like a net of slender bars, and is a parameter characterizing the microstructure of the domain. We consider the case of a surface distribution of the set F⁽⁾, i.e., for sufficiently small , the set F⁽⁾ is concentrated in arbitrary small neighbourhood of a surface Γ. Under a hypothesis on the asymptotic behaviour of the energy functional, we obtain the macroscopic (homogenized) model. To cite this article: M. Goncharenko, L. Pankratov, C. R. Mecanique 331 (2003).     

Analytical development of disturbed matrix eigenvalue problem applied to mixed convection stability analysis in Darcy media

This work consists in evaluating algebraically and numerically the influence of a disturbance on the spectral values of a diagonalizable matrix. Thus, two approaches will be possible; to use the theorem of disturbances of a matrix depending on a parameter, due to Lidskii and primarily based on the structure of Jordan of the no disturbed matrix. The second approach consists in factorizing the matrix system, and then carrying out a numerical calculation of the roots of the disturbances matrix characteristic polynomial. This problem can be a standard model in the equations of the continuous media mechanics. During this work, we chose to use the second approach and in order to illustrate the application, we choose the Rayleigh–Bénard problem in Darcy media, disturbed by a filtering through flow. The matrix form of the problem is calculated starting from a linear stability analysis by a finite elements method. We show that it is possible to break up the general phenomenon into other elementary ones described respectively by a disturbed matrix and a disturbance. A good agreement between the two methods was seen. To cite this article: H.B. Hamed, R. Bennacer, C. R. Mecanique 336 (2008).     

Relevance of a thermal contact resistance depending on the solid/liquid phase change transition for sprayed composite metal/ceramic powder by direct current plasma jets

The thermal contact between layers plays a key role in the behaviour of composite particles (mechanofused) subjected to a high temperature jet (example of two layers metal/ceramic particles under plasma spraying). This work underlines the interest of considering a thermal contact resistance varying with the melting state of the two components along the full process. The computational model considers the time-dependent state of the particle during its flight with coupled transfers and solid/liquid/vapor phase changes. To cite this article: M. Bouneder et al., C. R. Mecanique 336 (2008).     

A two-dimensional effective model describing fluid–structure interaction in blood flow: analysis, simulation and experimental validation

We derive a closed system of effective equations describing a time-dependent flow of a viscous incompressible Newtonian fluid through a long and narrow elastic tube. The 3D axially symmetric incompressible Navier–Stokes equations are used to model the flow. Two models are used to describe the tube wall: the linear membrane shell model and the linearly elastic membrane and the curved, linearly elastic Koiter shell model. We study the behavior of the coupled fluid–structure interaction problem in the limit when the ratio between the radius and the length of the tube, , tends to zero. We obtain the reduced equations that are of Biot type with memory. An interesting feature of the reduced equations is that the memory term explicitly captures the viscoelastic nature of the coupled problem. Our model provides significant improvement over the standard 1D approximations of the fluid–structure interaction problem, all of which assume an ad hoc closure assumption for the velocity profile. We performed experimental validation of the reduced model using a mock circulatory flow loop assembled at the Cardiovascular Research Laboratory at the Texas Heart Institute. Experimental results show excellent agreement with the numerically calculated solution. Major applications include blood flow through large human arteries. To cite this article: S. Čanić et al., C. R. Mecanique 333 (2005).     

On the slow gravity-driven migration of arbitrary clusters of small solid particles

A new approach is advocated to compute at a low cpu time cost the rigid-body motions of settling solid particles when inertial effects are negligible. In addition to the relevant boundary-integral equations, the numerical implementation and a few convincing benchmark tests we address two configurations of equivalent spheres and spheroids, i.e. that exhibit when isolated the same settling velocity. To cite this article: A. Sellier, C. R. Mecanique 332 (2004).

Résumé

On propose une approche originale pour déterminer le mouvement d'une assemblée de particules solides et de formes arbitraires soumise à l'action de la pesanteur dans l'approximation de Stokes. Outre les intégrales de frontière et la méthode numérique associées on présente quelques comparaisons et examine le cas de deux configurations de sphères et ellipsoides de révolution équivalents, c'est-à-dire dotés lorsqu'ils sont seuls de la même vitesse de sédimentation. Pour citer cet article : A. Sellier, C. R. Mecanique 332 (2004).     

A criterion of the continuous spectrum for elasticity and other self-adjoint systems on sharp peak-shaped domains

The spectra of the elasticity and piezo-electricity systems for a solid with a sharp peak point on the boundary, which is free of traction, are not discrete. An algebraic criterion of non-empty continuous spectrum is found for the Neumann problem for rather arbitrary formally self-adjoint elliptic systems of second-order differential equations on a sharp peak-shaped domain. To cite this article: S.A. Nazarov, C. R. Mecanique 335 (2007).     

Direct simulation of the motion of neutrally buoyant balls in a three-dimensional Poiseuille flow

In a previous article the authors introduced a Lagrange multiplier based fictitious domain method. Their goal in the present article is to apply a generalization of the above method to: (i) the numerical simulation of the motion of neutrally buoyant particles in a three-dimensional Poiseuille flow; (ii) study – via direct numerical simulations – the migration of neutrally buoyant balls in the tube Poiseuille flow of an incompressible Newtonian viscous fluid. Simulations made with one and several particles show that, as expected, the Segré–Silberberg effect takes place. To cite this article: T.-W. Pan, R. Glowinski, C. R. Mecanique 333 (2005).     

Parallelization of the algorithm of asymptotic partial domain decomposition in thin tube structures

The method of asymptotic partial domain decomposition for thin tube structures (finite unions of thin cylinders) is revisited. Its application to the Newtonian and non-Newtonian flows in great systems of vessels is considered. The possibility of a parallelization of its algorithm is discussed for linear and non-linear models.     

Simultaneous measurements of equivalence ratio and flame structure in multipoint injectors using PLIF

Simultaneous measurements of PLIF-kerosene and PLIF-OH have been successfully performed in a multipoint injection system for various overall equivalence ratio, air inlet temperature between 480 and 730 K and pressure up to 2.2 MPa. Single shot 2D-maps of the spatial distribution of kerosene vapour and OH radical in the combustor have been recorded with good signal-to-noise ratio. Results show that depending on the split between the pilot and the main injectors, the flame front exhibits a single or a double structure. Good spatial correlation between the repartition of the kerosene vapour and the position of the flame front was observed; in particular, no “dark zone” is observed between the fuel and the flame front. As temperature and pressure increase, fuel evaporation improves and the spatial distribution of OH radical becomes more homogeneous in the combustor, suggesting a partially-distributed combustion. To cite this article: M. Orain et al., C. R. Mecanique 337 (2009).     

Adaptive finite elements for the steady free fall of a body in a Newtonian fluid

The numerical simulation of the free fall of a solid body in a viscous fluid is a challenging task since it requires computational domains which usually need to be several order of magnitude larger than the solid body in order to avoid the influence of artificial boundaries. Toward an optimal mesh design in that context, we propose a method based on the weighted a posteriori error estimation of the finite element approximation of the fluid/body motion. A key ingredient for the proposed approach is the reformulation of the conservation and kinetic equations in the solid frame as well as the implicit treatment of the hydrodynamic forces and torque acting on the solid body in the weak formulation. Information given by the solution of an adequate dual problem allows one to control the discretization error of given functionals. The analysis encompasses the control of the free fall velocity, the orientation of the body, the hydrodynamic force and torque on the body. Numerical experiments for the two dimensional sedimentation problem validate the method. To cite this article: V. Heuveline, C. R. Mecanique 333 (2005).