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Abstract: In this article electroconvective phenomenon, which take place in a dielectric liquid layer submitted to an unipolar injection, are studied by numerical simulations means. For the first time the full and coupled resolution of the Electro-Hydro-Dynamic equations are achieved. The results are compared with those coming from stability analysis especially for the linear and non-linear criteria in strong and weak injection cases. The hysterical behavior of the development of this instability is accurately reproduced. To cite this article: P. Traoré et al., C. R. Mecanique 337 (2009). [Copyright &y& Elsevier]

Abstract: The effect of acoustic streaming (more precisely the Eckart streaming) on the linear stability of a laterally heated fluid layer confined between two horizontal infinite walls (Hadley flow) has been studied. In the considered range of Prandtl number (), three types of instabilities prevail in the absence of acoustic streaming: two-dimensional stationary instabilities for low Prandtl numbers, and three-dimensional oscillatory and then stationary instabilities for higher Prandtl numbers. When an acoustic beam of width (normalized by the layer depth) is applied, the thresholds of the two-dimensional modes, which become oscillatory, increase with the acoustic intensity (monitored through the parameter A) before strongly decreasing to reach the pure acoustic streaming instability threshold. Concerning the three-dimensional instabilities, the thresholds of the oscillatory modes increase while those of the stationary modes strongly decrease. For , these evolutions induce the crossing of the critical curves of these two modes when A is increased, so that the oscillatory modes which are dominant for small values of A are replaced by the stationary modes for larger values of A. The position of the crossing depends on the width of the acoustic beam. To cite this article: W. Dridi et al., C. R. Mecanique 337 (2009). [Copyright &y& Elsevier]

Abstract: We introduce an hyperbolic two-fluid two-pressure model to compute unsteady two-phase flows in porous media. The closure laws comply with the entropy inequality, and a unique set of jump conditions holds within each field. To cite this article: J.-M. Hérard, C. R. Mecanique 336 (2008). [Copyright &y& Elsevier]

Abstract: In this Note, we present a method to solve numerically the Stokes equation for the incompressible flow between two immiscible fluids presenting very different viscosities. The resolution of the finite element systems of equations is performed using Uzawa''s method. The stiffness matrix conditioning problems related to the very important viscosity ratios are circumvented using an new iterative scheme. A numerical example is proposed to show the efficiency of this approach. To cite this article: T.T.C. Bui et al., C. R. Mecanique 336 (2008). [Copyright &y& Elsevier]

Abstract: In the context of the laminar steady two-dimensional flow of an incompressible Newtonian fluid, we propose, with the matched asymptotic expansions method, a uniformly valid approximation in the whole domain for a disturbed flow over a flat plate with incidence. Following Libby and Fox''s ideas, two-dimensional disturbances generated in the boundary layer, without disturbed pressure gradient, have been studied for a basic flow without incidence. The established theoretical perturbation is then validated from the numerical simulation of the Navier–Stokes equations linearized in the vicinity of the basic flow. To cite this article: S. Saintlos Brillac, K. Debbagh, C. R. Mecanique 336 (2008). [Copyright &y& Elsevier]

Abstract: Flow simulations over two circular cylinders in tandem are carried out at a Reynolds number of 100, using a fully coupled resolution method for solving the two-dimensional Navier–Stokes equations. A critical cylinder spacing was found between 3.95 and 4.0 cylinder diameters. The fluctuating forces jumped appreciably at this critical gap, like the shedding frequency and the mean drag. To cite this article: E. Didier, C. R. Mecanique 335 (2007). [Copyright &y& Elsevier]

Abstract: The linear stability of acoustic streaming flows induced by ultrasound waves (Eckart streaming), for both isothermal and laterally heated fluids confined between two parallel horizontal infinite walls has been studied. The basic profiles were determined analytically, and the eigenvalue problem derived for the temporal stability analysis was solved by a spectral Tau Chebyshev method. In the isothermal case, a critical acoustic parameter leading to an oscillatory instability was determined. is minimum for an acoustic beam width (normalized by the height of the fluid layer) and increases when either is decreased or increased. The other result concerns the influence of the acoustic streaming flow on the stability of the laterally heated layer (Hadley flow). For rather small beam widths, the acoustic streaming flow destabilizes the Hadley flow, but for large beam widths (), a range of acoustic parameter values was found for which the Hadley flow is stabilized (increase of the thresholds), before a sharp decrease of the thresholds for larger A. Let us underline that the stability of such flows has not been yet studied in the literature. To cite this article: W. Dridi et al., C. R. Mecanique 335 (2007). [Copyright &y& Elsevier]

Abstract: In this Note, the pressure drop of non-Newtonian thermodependent fluids flowing between two parallel plates is considered. The effects of different parameters on the evolution of local friction factor are numerically investigated in two heating cases and correlations are proposed to compute the pressure drop. To cite this article: V.T. Nguyen, M. Lebouche, C. R. Mecanique 335 (2007). [Copyright &y& Elsevier]

Abstract: A polynomial chaos (PC) expansion a the Lagrangian model for the stochastic incompressible inviscid flow around an airfoil is presented. The flow field is modeled using a distribution of lumped vortices on the airfoil surface while the wake is modeled with Lagrangian point vortices. An original technique is proposed for the computation of the PC coefficients of the velocities induced by the vortices. Two computational examples for random airfoil motions are provided to illustrate the capability of the method to deal with complex situations. To cite this article: O. Le Maître, C. R. Mecanique 334 (2006). [Copyright &y& Elsevier]

Abstract: We present low complexity models for the transport of passive scalars for environmental applications. The model uses partial observations assimilation. Similitude solutions are proposed in a non symmetric metric based on travel times. The approach does not require the solution of any PDE and is mesh free. Also, the solution can be computed in one point only without computing the whole solution. To cite this article: B. Mohammadi, J.-M. Brun, C. R. Mecanique 334 (2006). [Copyright &y& Elsevier]

Abstract: In this Note, we present direct numerical simulation results of a spatial mixing layer generated behind an upstream plate separating two boundary layers. The effect of the shape of the trailing edge of the plate is considered through comparisons between flows obtained from a bevelled or a blunt plate. In the former case, a spatial mixing layer consistent with previous experimental and numerical observations is obtained. In the latter case, the self-excited state that establishes in the near wake region dominates primary and secondary instability mechanisms while understating the importance of inflow perturbations. This behaviour is interpreted in terms of convective or absolute instability. The effects on turbulent statistics are also discussed. To cite this article: S. Laizet, E. Lamballais, C. R. Mecanique 334 (2006). [Copyright &y& Elsevier]

Abstract: 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). [Copyright &y& Elsevier]

Abstract: A numerical tool is developed for coupling natural convection in cavities with surface radiation and computations are performed for an air-filled square cavity whose four walls have the same emissivity. Compared to the adiabatic case without radiation, the top wall is cooled, the bottom wall is heated, air flow along the horizontal walls are reinforced and thermal stratification in cavity core is reduced. Detailed analysis shows that net radiative heat flux is linear with ΔT if , which is the case at low Rayleigh number, and that radiative Nusselt number is a linear function of the cavity height. Surface radiation induces an early transition to time-dependent flows: for and a cavity height of 0.335 m the critical Rayleigh number is equal to and the corresponding Hopf bifurcation is supercritical. Furthermore, multiple periodic solutions are observed between and . To cite this article: H. Wang et al., C. R. Mecanique 334 (2006). [Copyright &y& Elsevier]

Abstract: A model for the simulation of boiling flow with phase change in a closed cavity is presented. A front-tracking method is used to deal with the liquid–vapor interface. The liquid phase is incompressible while the vapor phase is weakly compressible and obeys to the perfect gas law. This model can deal with large density ratio () flows while accounting for the saturation curve. Computations are performed on a 1D validation case, idealizing a pressure cooker. Results are compared with a low Mach number approximation. To cite this article: V. Daru et al., C. R. Mecanique 334 (2006). [Copyright &y& Elsevier]

Abstract: In this Note, we propose a way to obtain two-fluid two-pressures multiphase models that satisfy an entropy inequality. We first notice that the continuous model associated to the discrete model of Abgrall and Saurel (2003) satisfies the entropy principles. Thanks to this, we show how to modify existing models in order to achieve the second law of thermodynamics. To cite this article: M. Papin, R. Abgrall, C. R. Mecanique 333 (2005). [Copyright &y& Elsevier]

Abstract: This work proposes a procedure of finite difference discretized in a system of curvilinear coordinates adapted to the shape of the saturated zone, to simulate a flow in the LCM (Liquid Composites Molding) process. Formulation and the numerical application of the procedure are described. We describe two configurations of injections. A good agreement is found between numerical, analytical and literature experimental results. To cite this article: M. Hattabi et al., C. R. Mecanique 333 (2005). [Copyright &y& Elsevier]

Abstract: On the basis of simple conformal mappings, we present a method to describe a two-dimensional potential flow around a rotating obstacle of arbitrary section. As a result, a simplified expression of the matrix of added mass and added moment of inertia is obtained. We also underline the need to determine this perturbation potential all over the fluid domain. Indeed, this is of practical interest in order to express the hydrodynamic moment in incompressible viscous flow. To cite this article: Y.-M. Scolan, C. R. Mecanique 333 (2005). [Copyright &y& Elsevier]

Abstract: In this Note, a numerical investigation of laminar convection wake above a heated plate placed in a channel is carried out. An analytical study based on a three region structure is proposed in the immediate neighbourhood of the trailing edge. Velocity and temperature at the centerline channel as well as the pressure gradient are presented in asymptotic expressions. Comparison of these results with numerical solutions enhances the analytical study. To cite this article: Z. Doulfoukar, A. Achiq, C. R. Mecanique 333 (2005). [Copyright &y& Elsevier]

Abstract: This Note describes a computational method for three dimensional unsteady flows around a submerged body with forward speed. The two free-surface boundary conditions are written under their non linear form. The calculations are carried out in the time domain using a mixed Euler–Lagrange scheme based on the knowledge, at each time step, of the potential on the free surface and of the location of this surface. A mixed problem with a Neumann condition on the body and a Dirichlet one on the free surface is then solved. The panel method uses desingularized sources to represent free surface effects. Validations are carried out on steady flows. To cite this article: A. Rebeyrotte et al., C. R. Mecanique 333 (2005). [Copyright &y& Elsevier]

The anisotropic particle method has been extended to the case of viscous flows. The moment transport equation is modified to account for viscous effects. The diffusion term has been evaluated by using the PSE method and the particle moments. The modified transport equation includes geometrical moments for which a specific transport equation has been introduced. The study of the evolution of two corotating vortices allowed the comparison of the anisotropic particle method with the usual particle method. To cite this article: A. Beaudoin et al., C. R. Mecanique 332 (2004). [Copyright &y& Elsevier]

Convective instabilities of low Prandtl number fluids are subject to various studies. The purpose here is an extension to hydrodynamic transitions in the fluid phase with a free or rigid surface under phase change and to construct the corresponding bifurcation diagram. Investigations interesting the process control by using the latent heat and the solid/liquid thermal conductivity difference are considered. The solution methodology is based on a front localisation approach showing a very good ability to describe convection regimes coupled to the phase change transition in the case of vertical solidification with confinement. To cite this article: E.A. Semma et al., C. R. Mecanique 331 (2003). [Copyright &y& Elsevier]

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. Azai¨ez et al., C. R. Mecanique 331 (2003). [Copyright &y& Elsevier]

Flow through a cylindrical flat chamber, a model of some particular heat exchanger, is investigated numerically using the CFD-ACE code. Turbulence is modelled using the classical k–ϵ model. A better understanding of the secondary flow is then obtained: the k–ϵ model shows a strong dependence of the secondary flow velocity field with Reynolds number as was pointed out with precedent experimental results. Variations of the number of vortexes composing the secondary flow, giving a symmetrical or asymmetrical aspect, will influence the fluid particle trajectories and time residence. To cite this article: S. Petitot et al., C. R. Mecanique 330 (2002) 749–756. [Copyright &y& Elsevier]

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. [Copyright &y& Elsevier]

The convective instability of a horizontal liquid layer confined in an annular Hele–Shaw cell subject to a constant rotation and submitted to a centrifugal gradient of temperature is investigated. Using a linear stability analysis, we study the effects of both Coriolis forces and curvature aspect on the stationary convective threshold when the Prandtl number is of the order of unity or larger than unity. We show that the Coriolis forces have a stabilizing effect, and the wave number is independent of these forces. However, a multicellular regime in the radial direction is observed for small Ekman numbers. The results related to the influence of the curvature are also shown. To cite this article: S. Ramezani et al., C. R. Mecanique 330 (2002) 633–640. [Copyright &y& Elsevier]

A diffuse approximation based collocation method is used for the study of the flow over a half-circular cylinder. We give some results on the instationary wake at a Reynolds number Re=65. To cite this article: T. Sophy et al., C. R. Mecanique 330 (2002) 193–198. [Copyright &y& Elsevier]

The aim of this work is a priori evaluation and improvement of a non-linear model for turbulent flows using the results from direct numerical simulation of Navier–Stokes equations. The algebraic explicit non-linear model recently proposed by Rumsey C.L. et al. [1] is studied. The data base used here comes from a direct numerical simulation of a turbulent flow through a square duct. For this flow, this study shows that the hypothesis of equilibrium state for the anisotropic tensor is correct. The analysis is made using the maps of the second and third invariants of the Reynolds stress tensor. The approach used permits to conclude that the model using a wall function improves the numerical prediction of the anisotropy. To cite this article: O. El Yahyaoui et al., C. R. Mecanique 330 (2002) 27–34 [Copyright &y& Elsevier]

Abstract: This Note is a generalization of the work presented in Comptes Rendus Mécanique (Vol. 333, 6). Now two-dimensional multi-bodies configurations are considered. Simple conformal mappings of the fluid region are used to describe the potential flow around an array of bodies with arbitrary shape. By revisiting this problem, a compact expression of the coupled matrix of added masses and moment of inertia is elaborated. The corresponding solution in term of velocity potential, has another purpose. It is used as a basis of functions to formulate the loads acting on the same body arrangement but now placed in a viscous and incompressible fluid flow. To cite this article: Y.-M. Scolan, C. R. Mecanique 335 (2007). [Copyright &y& Elsevier]