Structures convectives dans les écoulements à surface libre

Notre travail vise à évaluer le rôle de phénomènes perturbateurs dans la dynamique d'un système fluide chauffé avec surface libre. La variation des seuils primaires de déclenchement de la convection a d'abord été calculée en fonction de la taille de la cellule, l'influence de la tension de surface et du transfert de chaleur sur ces seuils de déclenchement (et au-delà) a également été traité

Stabilized finite element formulation applied to the kinematic Ponomarenko dynamo problem

International audienceA stabilized finite element (B, q) formulation is developed to solve the kinematic dynamo problem. As a test case, we solve the induction equation for a given solid body helical flow, embedded in a cylindrical conducting shell. This problem corresponds to the well-known Ponomarenko dynamo. It has the interesting property to have an exact dispersion relation giving the magnetic growth rate as a function of the flow properties. Therefore, it is a good benchmark to test our kinematic dynamo code. We calculated the dynamo threshold and plotted the geometry of the generated magnetic field. We also evaluated the residual error due to our stabilized formulation

Adapting Algebraic Recursive Multilevel Solvers (ARMS) for Solving CFD Problems

This paper presents results using preconditioners that are based on a number of variations of the Algebraic Recursive Multilevel Solver (ARMS). ARMS is a recursive block ILU factorization based on a multilevel approach. Variations presented in this paper include approaches which incorporate inner iterations, and methods based on standard reordering techniques. Numerical tests are presented for three-dimensional incompressible, compressible and magneto-hydrodynamic (MHD) problems

Multiple flow solutions in buoyancy induced convection in a porous square box

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Instabilities in a cylindrical cavity heated from below with a free surface. I. Effect of Biot and Marangoni numbers.

International audienceConvective instabilities in a cylindrical cavity heated from below, with a free surface at the top, are numerically investigated using a spectral-element code. Both buoyancy and surface tension forces are taken into account, and heat exchange is considered at the upper surface. This configuration corresponds to the Bénard-Marangoni situation. The primary thresholds associated with azimuthal eigenmodes and corresponding to the onset of convection are first given as a function of the aspect ratio of the cavity A (radius/height), the Biot number Bi, and the Marangoni number Ma. Particular attention is paid to the influence of the Biot and Marangoni numbers: a stabilizing surface tension effect (Ma>0) induces an increase of the primary thresholds, which is magnified for small values of Bi, but may also change the flow structure by creating counter-rotating rolls near the free surface. The nonlinear evolution of the convection beyond its onset is given through bifurcation diagrams for A=1.5. Two different branches of axisymmetric solutions, either with upflow or downflow at the center, emerge at the onset. The destabilization of these solutions and the further dynamical evolution of the flow has been highlighted for widely varying Biot numbers

Instabilities and bifurcations due to buoyancy in a cylindrical container heated from below with and without a free surface

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Instabilities in a cylindrical cavity heated from below with a free surface. II. Effect of a horizontal magnetic field.

International audienceThe effect of a constant and uniform horizontal magnetic field on the flow in a cylindrical cavity heated from below, with a free surface at the top, is numerically investigated. The azimuthal modes, which usually trigger convection in a cylinder, are changed by the horizontal magnetic field to oriented modes, either parallel or perpendicular to the magnetic field direction. The corresponding primary thresholds increase with the Hartmann number Ha. This increase, however, depends on the structure of the modes and is the weakest for the parallel modes and the strongest for the perpendicular modes. The changes that affect the evolution of the primary thresholds with the aspect ratio for nonzero Ha are also emphasized. The nonlinear evolution of the convection with a horizontal magnetic field is presented through bifurcation diagrams for different values of the Prandtl number Pr. For Pr=1 and small values of Ha, the structuring effect of the horizontal magnetic field, which involves modifications of the flow structures and bifurcation points, is put into light. Results are finally shown for smaller Pr values corresponding to liquid metals