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

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

Probabilistic analysis of the upwind scheme for transport

We provide a probabilistic analysis of the upwind scheme for multi-dimensional transport equations. We associate a Markov chain with the numerical scheme and then obtain a backward representation formula of Kolmogorov type for the numerical solution. We then understand that the error induced by the scheme is governed by the fluctuations of the Markov chain around the characteristics of the flow. We show, in various situations, that the fluctuations are of diffusive type. As a by-product, we prove that the scheme is of order 1/2 for an initial datum in BV and of order 1/2-a, for all a>0, for a Lipschitz continuous initial datum. Our analysis provides a new interpretation of the numerical diffusion phenomenon

Design and RF measurements of a 5 GHz 500 kW window for the ITER LHCD system

International audienceCEA/IRFM is conducting R&D efforts in order to validate the critical RF components of the 5 GHz ITER LHCD system, which is expected to transmit 20 MW of RF power to the plasma. Two 5 GHz 500 kW BeO pill-box type window prototypes have been manufactured in 2012 by the PMB Company, in close collaboration with CEA/IRFM. Both windows have been validated at low power, showing good agreement between measured and modeling, with a return loss better than 32 dB and an insertion loss below 0.05 dB. This paper reports on the window RF design and the low power measurements. The high power tests up to 500kW have been carried out in March 2013 in collaboration with NFRI. Results of these tests are also reported. In the current ITER LHCD design, 20 MW Continuous Wave (CW) of Radio-Frequency power at 5 GHz are expected to be generated and transmitted to the plasma. In order to separate the vacuum vessel pressure from the cryostat waveguide pressure, forty eight 5 GHz 500kW CW windows are to be assembled on the waveguides at the equatorial port flange. For nuclear safety reasons, forty eight additional windows could be located in the cryostat section, to separate and monitor the cryostat waveguide pressure from the exterior transmission line pressure. These windows are identified as being one of the main critical components for the ITER LHCD system since first ITER LHCD studies [1] [2] [3] or more recently [4] [5] , and clearly require an important R&D effort. In this context and even if the LHCD system is not part of the construction baseline, the CEA/IRFM is conducting a R&D effort in order to validate a design and the performances of these RF windows. In order to begin the assessment of this need, two 5 GHz 500 kW/5 s pill-box type windows prototypes have been manufactured in 2012 by the PMB Company in close collaboration with the CEA/IRFM [6]. The section 2 of this paper reports the RF and mechanical design of a 5 GHz window. Some features of the mechanical design and the experimental RF measurements at low power are reported in section 3. High power results, made in collaboration with NFRI, are detailed in section 4. The development of CW windows is discussed in the conclusion. 2-RF AND MECHANICAL DESIGN The proposed 5 GHz RF window is based on a pill-box design [2] , i.e. a ceramic brazed in portion of a circular waveguide, connected on either side to a rectangular waveguide section. Typical design rules of thumb of such device are circular section diameter about the same size of the diagonal of the rectangular waveguide (cf. FIGURE 1). Without taking into account the ceramic, the circular section length is approximately half a guided wavelength of the circular TE 11 mode, in order for the device to act as a half-wave transformer. Once optimized, taking into account the ceramic, matching is correct only for a narrow band of frequency and is very sensitive to the device dimensions and the ceramic relative permittivity. The heat losses in the ceramic, which have to be extracted by an active water cooling, depends on the inside electric field topology and of ceramic dielectric loss (loss tangent). Undesirable modes due to parasitic resonances can be excited in the ceramic volume, raising the electric field an