Vladimir A. Gasilov

Surface and Volume Discretization of Functionally Based Heterogeneous Objects

The presented approach to discretization of functionally defined heterogeneous objects is oriented towards applications associated with numerical simulation procedures, for example, finite element analysis (FEA). Such applications impose specific constraints upon the resulting surface and volume meshes in terms of their topology and metric characteristics, exactness of the geometry approximation, and conformity with initial attributes. The function representation of the initial object is converted into the resulting cellular representation described by a simplicial complex. We consider in detail all phases of the discretization algorithm from initial surface polygonization to final tetrahedral mesh generation and its adaptation to special FEA needs. The initial object attributes are used at all steps both for controlling geometry and topology of the resulting object and for calculating new attributes for the resulting cellular representation.

Discretization of functionally based heterogeneous objects

The presented approach to discretization of functionally defined heterogeneous objects is oriented towards applications associated with numerical simulation procedures, for example, finite element analysis (FEA). Such applications impose specific constraints upon the resulting surface and volume meshes in terms of their topology and metric characteristics, exactness of the geometry approximation, and conformity with initial attributes. The function representation of the initial object is converted into the resulting cellular representation described by a simplicial complex. We consider in detail all phases of the discretization algorithm from initial surface polygonization to final tetrahedral mesh generation and its adaptation to special FEA needs. The initial object attributes are used at all steps both for controlling geometry and topology of the resulting object and for calculating new attributes for the resulting cellular representation.

Experimental and numerical studies of structure of cluster targets for femtosecond laser pulses

A mathematical model of clusters forming in gas jets is proposed. This model concerns with the representation of the clusters by the moments of the distribution function of the clusters with respect to the radius. This model uses the kinetic theory of phase transitions presented by Frenkel for the kinetic of the clusters formation. The numerical results obtained with the help of this model are compared with the direct experimental measurements based on Mach-Zehnder interferometry and Rayleigh scattering.

Solution of the self-adjoint radiative transfer equation on hybrid computer systems

A new technique for simulating three-dimensional radiative energy transfer for the use in the software designed for the predictive simulation of plasma with high energy density on parallel computers is proposed. A highly scalable algorithm that takes into account the angular dependence of the radiation intensity and is free of the ray effect is developed based on the solution of a second-order equation with a self-adjoint operator. A distinctive feature of this algorithm is a preliminary transformation of rotation to eliminate mixed derivatives with respect to the spatial variables, simplify the structure of the difference operator, and accelerate the convergence of the iterative solution of the equation. It is shown that the proposed method correctly reproduces the limiting cases—isotropic radiation and the directed radiation with a δ-shaped angular distribution.

Development of an Apparatus for Characterization of Cluster-Gas Targets for Laser-Driven Particle Accelerations

CO\(_2\) clusters formed in supersonic expansion of a mixed-gas of CO\(_2\)/H\(_2\) or CO\(_2\)/He through a three-staged conical nozzle have been verified by measuring the angular distribution of the light scattered from cluster target. The angular distribution is fitted by convolving a lognormal size distribution with the scattering coefficients calculated based on the Mie theory. The reliability of the size measurement is verified to be within an experimental error of 10 % using standard particles. The mean sizes of CO\(_2\) clusters at the target center for the cases of CO\(_2\)/H\(_2\) and CO\(_2\)/He gas mixtures are estimated to be 0.26 and 0.22 \(\upmu \)m, respectively. For the CO\(_2\)/H\(_2\) mixed-gas target, the variation of the mean cluster size inside the gas jet is constant within the experimental error. Furthermore, the cluster density is estimated to be \(5.5 \times 10^8\) clusters/cm\(^2\) by measuring the attenuation of the laser beam intensity. In addition, total gas density profiles in radial direction are obtained via the Abel inversion from the phase shift of the light passing through the target by utilizing an interferometer. The variation of the cluster mass fraction along the radial direction of the target is almost constant, which is consistent with a Boldarev’s model.

Solution of the radiative transfer equation on parallel computer systems

A new technique for modeling three-dimensional radiative energy transfer in the framework of a code intended for the predictive simulation of high energy density plasmas on parallel computer systems is proposed. A well-scalable algorithm that takes into account the angular dependence of the radiation intensity and is free of the ray effect is constructed as based on the solution of a second-order equation with a selfadjoint operator. A feature of the algorithm is that it involves a preliminary rotation transformation, which eliminates the mixed spatial derivatives, simplifies the structure of the difference operator, and accelerates the convergence of the iterative solution of the equation. It is shown that the method proposed correctly reproduces limiting cases, namely, isotropic radiation and directed radiation with a δ-shaped angular distribution.

Experimental and numerical study of a wire-explosion POS plasma dynamics

We study possibility to design fast current switch using wire explosion. It was carried out series of experiments on explosion of single wire connecting two coaxial cylindrical electrodes. Current with the amplitude value of 80 kA and rise time of 7 μs flow through the 4-μm tungsten wire. The outer magnetic field (up to 30 kG) was directed along the electrodes. Setup design allow to us to change the amplitude of current flowing between the electrodes and to measure the total resistance of interelectrode space. So we can study POS plasma dynamics with different currents (current amplitude is changed in range of 10-80 kA, current rise rate is changed in range of 109-1010 A/s) and magnetic field. We compare experimental data with results of simulations carried out by means of the 3D radiative magnetohydro dynamic code MARPLE 3D (KIAM RAS). We simulate (i) a stage of a wire explosion and plasma stirring in the inter-electrode gap, and (ii) a stage of a plasma switch performance. Numerical simulations allow to estimate a time we need to fill the volume between the coaxial electrodes with the plasma generated from the wire and switch inhomogeneity, and to study the switch dynamics dependence on the hydromagnetic instability as well as the Hall effect. The calculated switch evolution correlates with experimental data.