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This study presents a parallel meshless approach for time-fractional equations in the axisymmetric geometry. In the present parallel meshless approach, the method of approximate particular solutions (MAPS), in conjunction with Laplace transform, extended precision arithmetic (EPA) and multiple scale technique (MST) is implemented. In this application, the Laplace transform is employed to eliminate the dependence on time. The MAPS is used to obtain the solution of time-independent equation in Laplace space. Furthermore, the solution of time dependent equation is restored by Stehfest’s algorithm. Here the multiple scale technique (MST) and extended precision arithmetic (EPA) are applied to alleviate the effect of an ill-conditioned matrix on a numerical inverse Laplace transform. Then multi-cores parallel computing can improve effectively computing speed of the proposed meshless approach. In the numerical implementation, both the 2D axisymmetric equations and the original 3D equations are considered and compared.

Obtaining distributions of current density, magnetic field, and ac loss in coils is essential for practical applications. However, simulating large-scale 2-generation high-temperature-superconducting, YBCO coils is a challenging task. In this paper, we employ a multiscale model to successfully implement electromagnetic modeling of large-scale YBCO solenoid coils in two-dimensional axisymmetric geometry with the approximation of infinite turns (J infinite-turn). Based on the approximation, current penetration, magnetic field, and ac loss of coils can be obtained. The calculation results of multiscale models with J infinite-turn and uniform current density (J uniform) are compared with those from reference models which consider superconducting characteristics on each turn of coils with actual size based on H-formulation. Compared with J uniform, J infinite-turn improves the quality of current density and background magnetic field significantly and demonstrates good accuracy with errors less than 10% in terms of ac loss, whilst speeding up calculation by two orders of magnitudes than reference model. Also, the approximation shows more reliability if the coil is larger with more turns in pancakes.

The aim of this paper is to study the stationary flow of an Oldroyd fluid with particular diffusive stress, flowing through a thin 3D pipe. An asymptotic expansion with respect to a small parameter describing the ratio between the diameter of the cross section and the length is calculated and rigorously justified. The result obtained is compared against a numerical solution in the particular case of axisymmetric geometries.

Control valves, nozzles, and other mechanical flow constricting constructions often introduce highly turbulent flow downstream of vena contracta. When solid particles are present in the fluid stream erosion can occur due to the high fluid velocity and turbulence, both in the converging and diverging section of a constriction. This paper presents an experimental study of such flow structure in a converging–diverging valve geometry. The purpose of the study is to obtain velocity profiles downstream of vena contracta by the use of particle image velocimetry measurements. Profiles and flow structure, with and without introduced swirl component, is investigated and discussed with respect to erosion in such specific geometries.

Dynamic compaction (DC) is widely used to improve the mechanical properties of soils and other granular fill material upon which foundations or other structures are to be built. To calculate the inner deformation induced by DC, a computational model based on stochastic medium theory was developed to deduce the amount of deformation in the fill from the geometry of the DC crater. For this model, the tamper-soil system was simplified to an axisymmetric geometry and the probability of any unit of material below the crater being deformed can be calculated. Subsequently, the deformation at any point can be obtained by integration. Input parameters for the model were established by back analysis using the results from a DC field test and published data. Comparing the model results to results from actual and simulated DC programs shows that the computational model is useful for calculating deformation induced by DC without the need to consider the constitutive model of the soil.

International audience; A new method based on topology optimization is proposed for solving a three-dimensional axisymmetric inverse problem regarding the configuration of electric currents used in the electromagnetic casting technique of the metallurgical industry. These electric currents must generate an electromagnetic field such that when certain mass of liquid metal is placed in the field it levitates acquiring a predefined axisymmetric shape. The method proposed is able to obtain a suitable configuration of electric currents, and is very attractive from the computational point of view, since it is based on a sparse convex quadratic programming formulation for which there are very efficient interior-point solution algorithms.

International audience; This paper deals with the study of axisymmetric wave propagation in various acoustic / porous stratified media coupling configurations. It presents the theoretical development of a semi-analytical method, its validation for a limit test-case half-space ground, and an extension to a realistic multilayered seabed, when spherical waves are emitted from a transient point source in water.

This paper presents a numerical model of High Pressure Sodium (HPS) lamps including the acoustic streaming. The model is implemented in COMSOL and based on the finite elements method using a 2D axi-symmetric geometry. Moreover, a revision concerning AR experimental characterizations of HPS lamps will also be provided. The results presented in this paper will contribute to the understanding of AR phenomena and help in the electronic ballast design methods for AR avoidance.

The use of electrostatic ion beam traps require to set many potentials on the electrodes (ten in our case), making the tuning much more difficult than with quadrupole traps. In order to obtain the best trapping conditions, an analytical formula giving the electrostatic potential inside the trap is required. In this paper, we present a general method to calculate the analytical expression of the electrostatic potential in any axisymmetric set of electrodes. We use conformal mapping to simplify the geometry of the boundary. The calculation is then performed in a space of simple geometry. We show that this method, providing excellent accuracy, allows to obtain the potential on the axis as an analytic function of the potentials applied to the electrodes, thus leading to fast, accurate and efficient calculations. We conclude by presenting stability maps depending on the potentials that enabled us to find the good trapping conditions for oxygen 4+ at much higher energies than what has been achieved until now., 9 pages

International audience; A finite element model including plasma simulation is used to calculate the amplitude of acoustic resonances in HID lamps in a 2D axisymmetric geometry. Simulation results are presented for different operation parameters and are compared with experimental data.

We present a single epoch of high signal-to-noise ratio spectropolarimetry of the Type Ia supernova (SN Ia) 2004S taken nine days after maximum light. The flux spectrum is normal, but with the additional presence of high-velocity (HV) line features in both Ca II and Fe II. The object shows continuum polarization at the 0.4% level in the red, a value which appears to be typical of SNe Ia. The continuum data are consistent with a ~10% global asphericity in an axisymmetric geometry. Unlike previous observations of other SNe Ia with HV features, the HV features in SN 2004S show no strong polarimetric signature, though this may be due to the timing of our observations. Instead, the object shows line polarization features (P < 0.5%) that are rotated with respect to the axis of symmetry of the continuum. The line features are visible in Si II, Fe II, and Ca II, and appear to be narrowly confined in velocity space just above the photosphere. These polarization features are a result of compositional inhomogeneities in the ejecta. They may represent newly synthesized elements whose clumpy spatial distribution within the ejecta is distinct from that of the globally aspherical ejecta as a whole., 25 pages, 6 figures, AJ, minor revisions to match accepted journal version

Hypothesis Predicting formation mode of double emulsion drops in microfluidic emulsification is crucial for controlling the drop size and morphology. Experiments and modelling A three-phase Volume of Fluid-Continuum Surface Force (VOF–CSF) model was developed, validated with analytical solutions, and used to investigate drop formation in different regimes. Experimental investigations were done using a glue-free demountable glass capillary device with a true axisymmetric geometry, capable of readjusting the distance between the two inner capillaries during operation. Findings A non-dimensional parameter ( ζ ) for prediction of double emulsion formation mode as a function of the capillary numbers of all fluids and device geometry was developed and its critical values were determined using simulation and experimental data. At log ζ > 5.7, drops were formed in dripping mode; the widening jetting occurred at 5 log ζ log ζ ζ criterion was correlated with the ratio of the break-up length to drop diameter. The transition from widening to narrowing jetting was achieved by increasing the outer fluid flow rate at the high capillary number of the inner fluid. The drop size was reduced by reducing the distance between the two inner capillaries and the minimum drop size was achieved when the distance between the capillaries was zero.

The expansion of a rarefied axisymmetric plume emitted by a plasma thruster is analyzed and compared with a 3D Cartesian-type and a 2D cylindrical-type simulation code, both based on a particle-in-cell formulation for the heavy species and a simple Boltzmann-type model for the electrons. The first part of the paper discusses the 2D code numerical challenges in the moving of particles, their generation within the cells, and the weighting to the nodes, caused by the radial non-uniformity and the singular and boundary character of the symmetry axis. The second part benchmarks the 2D code against the 3D one for a high-energy, unmagnetized plume with three major species populations (injected neutrals, singly-charged and doubly-charged ions) and three minor species populations (constituted by particles coming from collisional processes, such as the charge-exchange reactions). The excellent agreement found in the results proves that both plume codes are capable of simulating, with a reasonable noise level, heavy particle populations differing by several orders of magnitude in number density. For simulations with a comparable level of accuracy, the 2D code presents a ten-fold gain in computational cost, although the symmetry axis remains its weakest point, due to particle depletion there and the related weighting noise.