A preconditioning for the spectral solution of incompressible variable-density flows

In the present study, the efficiency of preconditioners for solving linear systems associated with the discretized variable-density incompressible Navier-Stokes equations with semiimplicit second-order accuracy in time and spectral accuracy in space is investigated. The method, in which the inverse operator for the constant-density flow system acts as preconditioner, is implemented for three iterative solvers: the General Minimal Residual, the Conjugate Gradient and the Richardson Minimal Residual. We discuss the method, first, in the context of the one-dimensional flow case where a top-hat like profile for the density is used. Numerical evidence shows that the convergence is significantly improved due to the notable decrease in the condition number of the operators. Most importantly, we then validate the robustness and convergence properties of the method on two more realistic problems: the two-dimensional Rayleigh-Taylor instability problem and the three-dimensional variable-density swirling jet

Stabilité des écoulements de canal à densité variable

On s'intéresse à la stabilité des écoulements de deux fluides miscibles en canal plan sous l'hypothèse d'incompressibilité et pour de grandes variations de la masse volumique. On considère deux types d'écoulements de base : un écoulement de Poiseuille ainsi que deux couches limites de blaisus pour le cas de deux et trois couches superposées en négligeant les effets de gravités. Il a été observé que l'instabilité est accrue lorsque la zone de mélange se rapproche des parois, de même qu'en diminuant l'épaisseur de celle-ci. Finalement, cette instabilité n'est pas une instabilité de Kelvin Helmholtz classique

Analysis of transient growth using an orthogonal decomposition of the velocity field in the Orr-Sommerfeld Squire equations

Despite remarkable accomplishment, the classical hydrodynamic stability theory fails to predict transition in wall-bounded shear flow. The shortcoming of this modal approach was found 20 years ago and is linked to the non-orthogonality of the eigenmodes of the linearised problem, defined by the Orr Sommerfeld and Squire equations. The associated eigenmodes of this linearised problem are the normal velocity and the normal vorticity eigenmodes, which are not dimensionally homogeneous quantities. Thus non-orthogonality condition between these two families of eigenmodes have not been clearly demonstrated yet. Using an orthogonal decomposition of solenoidal velocity fields, a velocity perturbation is expressed as an L2 orthogonal sum of an Orr Sommerfeld velocity field (function of the perturbation normal velocity) and a Squire velocity field (function of the perturbation normal vorticity). Using this decomposition, a variational formulation of the linearised problem is written, that is equivalent to the Orr Sommerfeld and Squire equations, but whose eigenmodes consist of two families of velocity eigenmodes (thus dimensionally homogeneous). We demonstrate that these two sets are non-orthogonal and linear combination between them can produce large transient growth. Using this new formulation, the link between optimal mode and continuous mode transition will also be clarified, as the role of direct resonance. Numerical solutions are presented to illustrate the analysis in the case of thin boundary layers developing between two parallel walls at large Reynolds number. Characterisations of the destabilizing perturbations will be given in that case

A spectral fictitious domain method with internal forcing for solving elliptic PDEs

International audienc

On the spectral accuracy of a fictitious domain method for elliptic operators in multi-dimensions

International audienc

LES of a compressed Taylor vortex flow using a finite volume/finite element method on unstructured grids

International audienc

Non modal subcritical transition of channel entry flow

International audienceDeveloping channel flows are of interest in a large number of application areas. Many aspects of these flows are not yet fully understood, such as the stability characteristics at subcritical Reynolds number. Using massively parallel supercomputers, it is now possible to device new numerical experiments to study this kind of flow, that would have been impossible a few years ago. This work presents DNS of bypass transition of a subcritical channel entrance flow where transition occurs inside the boundary layers of the developing entry flow. The two boundary layers are perturbed near the entrance and streaks are generated inside the boundary layers through the classical linear lift-up mechanism (transient growth). The streaks strongly modify the velocity profile, which become inflectional at some distant downstream in the low-speed regions of the streaks. It is generally expected that the local inflectional velocity profiles associated with the low-speed streak are unstable with two kind of instability modes: a symmetric varicose mode and an antisymmetric sinuous mode [1]. In zero pressure gradient boundary layer, the low-speed streaks are more unstable with respect to the latter. On the contrary, in the present channel entrance flow, the varicose mode is favored. The streaks occupy almost half of the channel height when they are subjected at their top head to a Kelvin-Helmholtz instability. Furthermore, instabilities at the top of a low speed streak on one wall are found to be coupled with the instabilities of the streaks on the opposite wall. This observation is confirmed by a local linear stability analysis of the streaky velocity profile. Further downstream, a turbulent transition is observed and the flow evolves towards a fully turbulent channel flow. Simulations corresponding to a larger channel height have also been performed with an inlet perturbation located at the same position. In that case the boundary layers are thinner respectively to the channel height, and a sinuous mode precedes the streaks breakdown and the turbulent transition of the boundary layers

Visualisation in-situ pour l'étude de la transition sous-critique

National audienceno abstrac

Asymptotic and numerical analysis of an inviscid bounded vortex flow at low Mach number

International audienc

An efficient spectral method based on an orthogonal decomposition of the velocity for transition analysis in wall bounded flow

International audienc