An optimal penalty method for a hyperbolic system modeling the edge plasma transport in a tokamak

The penalization method is used to take account of obstacles, such as the limiter, in a tokamak. Because of the magnetic confinement of the plasma in a tokamak, the transport occurs essentially in the direction parallel to the magnetic field lines. We study a 1D nonlinear hyperbolic system as a simplified model of the plasma transport in the area close to the wall. A penalization which cuts the flux term of the momentum is studied. We show numerically that this penalization creates a Dirac measure at the plasma-limiter interface which prevents us from defining the transport term in the usual distribution sense. Hence, a new penalty method is proposed for this hyperbolic system. For this penalty method, an asymptotic expansion and numerical tests give an optimal rate of convergence without spurious boundary layer. Another two-fields penalization has also been implemented and the numerical convergence analysis when the penalization parameter tends to $0$ reveals the presence of a boundary layer

Asymptotic-preserving methods for an anisotropic model of electrical potential in a tokamak

A 2D nonlinear model for the electrical potential in the edge plasma in a tokamak generates a stiff problem due to the low resistivity in the direction parallel to the magnetic field lines. An asymptotic-preserving method based on a micro-macro decomposition is studied in order to have a well-posed problem, even when the parallel resistivity goes to $0$. Numerical tests with a finite difference scheme show a bounded condition number for the linearised discrete problem solved at each time step, which confirms the theoretical analysis on the continuous problem.Comment: 8 page

An experimental study of particle sedimentation using ultrasonic speckle velocimetry

Ultrasonic speckle velocimetry (USV) is a non-invasive technique that allows the measurement of fluid velocity in flow and also that of powders under sedimentation. To improve the USV method, we studied the sedimentation of polymethyl methacrylate and silica particles in water. Then, we built a sedimentation cell and characterized the diameter distribution of the particles. Subsequently, we carried out a specific study to optimize the USV procedure, the signal processing and data analysis. Space and temporal resolution and USV dynamics are also discussed with regard to the optimization conditions. We found that USV is a useful technique to measure velocities between 10−5 and 1 m s−1, using appropriate ultrasonic transducers. The space resolution is fixed by the length and the percentage of overlapping of the analyzed speckle windows and varies between 48 and 536 μm for the different studied particle families. Furthermore, we found that a 0.1 ns temporal resolution could be obtained after a zero padding signal processing. In the context of our sedimentation experiments, we showed that the velocities measured by USV are in close agreement with those measured by particle image velocimetry and theory

Excitation and resonant enhancement of axisymmetric internal wave modes

To date, axisymmetric internal wave fields, which have relevance to atmospheric internal wave fields generated by storm cells and oceanic near-inertial wave fields generated by surface storms, have been experimentally realized using an oscillating sphere or torus as the source. Here, we use a novel wave generator configuration capable of exciting axisymmetric internal wave fields of arbitrary radial form to generate axisymmetric internal wave modes. After establishing the theoretical background for axisymmetric mode propagation, taking into account lateral and vertical confinement, and also accounting for the effects of weak viscosity, we experimentally generate and study modes of different order. We characterize the efficiency of the wave generator through careful measurement of the wave amplitude based upon group velocity arguments. This established, we investigate the ability of vertical confinement to induce resonance, identifying a series of experimental resonant peaks that agree well with theoretical predictions. In the vicinity of resonance, the wave fields undergo a transition to non-linear behaviour that is initiated on the central axis of the domain and proceeds to erode the wave field throughout the domain.Comment: 15 pages, 9 figure

Investigation of flow structures involved in sound generation by two- and three-dimensional cavity flows

Proper Orthogonal Decomposition and Stochastic Estimation are combined to shed some light on the link between organized flow structures and noise generation by turbulent flows. Proper Orthogonal Decomposition (POD) is firstly used to extract selected flow events. Based on the knowledge of these structures, the Quadratic Stochastic Estimation of the acoustic pressure field is secondly performed. Both procedures are successively applied to two- and three-dimensional numerical databases of a flow over a cavity. It is demonstrated that POD can extract selected aerodynamic events which can be associated with selected frequencies in the acoustic spectra. Reconstructed acoustic fields also indicate the aerodynamic events which are responsible of the main energy of the noise emission. Such mathematical tools offer new perspectives in analysing flow structures involved in sound generation by turbulent flows and in the experimental design of a flow control strategy

Effective material parameter retrieval for thin sheets: theory and application to graphene, thin silver films, and single-layer metamaterials

An important tool in the field of metamaterials is the extraction of effective material parameters from simulated or measured scattering parameters of a sample. Here we discuss a retrieval method for thin-film structures that can be approximated by a two-dimensional scattering sheet. We determine the effective sheet conductivity from the scattering parameters and we point out the importance of the magnetic sheet current to avoid an overdetermined inversion problem. Subsequently, we present two applications of the sheet retrieval method. First, we determine the effective sheet conductivity of thin silver films and we compare the resulting conductivities with the sheet conductivity of graphene. Second, we apply the method to a cut-wire metamaterial with an electric dipole resonance. The method is valid for thin-film structures such as two-dimensional metamaterials and frequency-selective surfaces and can be easily generalized for anisotropic or chiral media.Comment: 5 pages, 5 figure