Asymptotic description of solutions of the exterior Navier Stokes problem in a half space

We consider the problem of a body moving within an incompressible fluid at constant speed parallel to a wall, in an otherwise unbounded domain. This situation is modeled by the incompressible Navier-Stokes equations in an exterior domain in a half space, with appropriate boundary conditions on the wall, the body, and at infinity. We focus on the case where the size of the body is small. We prove in a very general setup that the solution of this problem is unique and we compute a sharp decay rate of the solution far from the moving body and the wall

Existence of global strong solutions to a beam-fluid interaction system

We study an unsteady non linear fluid-structure interaction problem which is a simplified model to describe blood flow through viscoleastic arteries. We consider a Newtonian incompressible two-dimensional flow described by the Navier-Stokes equations set in an unknown domain depending on the displacement of a structure, which itself satisfies a linear viscoelastic beam equation. The fluid and the structure are fully coupled via interface conditions prescribing the continuity of the velocities at the fluid-structure interface and the action-reaction principle. We prove that strong solutions to this problem are global-in-time. We obtain in particular that contact between the viscoleastic wall and the bottom of the fluid cavity does not occur in finite time. To our knowledge, this is the first occurrence of a no-contact result, but also of existence of strong solutions globally in time, in the frame of interactions between a viscous fluid and a deformable structure

Weak solutions to a thin film model with capillary effects and insoluble surfactant

The paper focuses on a model describing the spreading of an insoluble surfactant on a thin viscous film with capillary effects taken into account. The governing equation for the film height is degenerate parabolic of fourth order and coupled to a second order parabolic equation for the surfactant concentration. It is shown that nonnegative weak solutions exist under natural assumptions on the surface tension coefficient

ANSYS HFSS as a new numerical tool to study wave propagation inside anisotropic magnetized plasmas in the Ion Cylotron Range of Frequencies

The paper demonstrates the possibility to use ANSYS HFSS as a versatile simulating tool for antennas facing inhomogeneous anisotropic magnetized plasmas in the Ion Cyclotron Range of Frequencies (ICRF). The methodology used throughout the paper is first illustrated with a uniform plasma case. We then extend this method to 1D plasma density profiles where we perform a first benchmark against the ANTITER II code. The possibility to include more complex phenomena relevant to the ICRF field in future works like the lower hybrid resonance, the edge propagation of slow waves, sheaths and ponderomotive forces is also discussed. We finally present a 3D case for WEST and compare the radiation resistance calculated by the code to the experimental data. The main result of this paper - the implementation of a cold plasma medium in HFSS - is general and we hope it will also benefit to research fields besides controlled fusion.Comment: 15 pages, 14 figure

On discretization in time in simulations of particulate flows

We propose a time discretization scheme for a class of ordinary differential equations arising in simulations of fluid/particle flows. The scheme is intended to work robustly in the lubrication regime when the distance between two particles immersed in the fluid or between a particle and the wall tends to zero. The idea consists in introducing a small threshold for the particle-wall distance below which the real trajectory of the particle is replaced by an approximated one where the distance is kept equal to the threshold value. The error of this approximation is estimated both theoretically and by numerical experiments. Our time marching scheme can be easily incorporated into a full simulation method where the velocity of the fluid is obtained by a numerical solution to Stokes or Navier-Stokes equations. We also provide a derivation of the asymptotic expansion for the lubrication force (used in our numerical experiments) acting on a disk immersed in a Newtonian fluid and approaching the wall. The method of this derivation is new and can be easily adapted to other cases

L∞L^\infty bounds for numerical solutions of noncoercive convection-diffusion equations

International audienceIn this work, we apply an iterative energy method à la de Giorgi in order to establish $L^\infty$ bounds for numerical solutions of noncoercive convection-diffusion equations with mixed Dirichlet-Neumann boundary conditions