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The Temetos platform is designed to conduct computational experiments at all stages of analysis and study of continuum mechanics models. A module has been developed to study the stress–strain state of a system of bodies with allowance for inelastic strains and contact interaction. It was used to analyze a fuel element that included up to 100 fuel pellets and a shell. The platform's solvers are applied to astrophysics problems. Models of the formation of accretion disks in binary star systems that allow the interpretation of observation results are constructed. [ABSTRACT FROM AUTHOR]

We consider the problem of determining the thermomechanical state of a fuel element in a nuclear reactor. A finite element algorithm for solving the thermal problem together with the problem of mechanical contact is described, and a model one-dimensional problem is studied to clarify the main features and a numerical algorithm for solving it. The leading term of the asymptotic expansion of the solution of this problem and a difference scheme for its solution, including iterative methods, are constructed. A cycle of test calculations is carried out to confirm the theoretical estimates. The comparison of calculations for real problems with theoretical predictions shows that the algorithm for solving a multidimensional nonlinear problem qualitatively corresponds to the behavior of one-dimensional calculations. [ABSTRACT FROM AUTHOR]

The results of computer simulation and full-scale modeling of gas flows injected into the plasma focus chamber using a high-speed valve (200–300 microseconds) are presented. The purpose of the work being carried out is to expand the possibility of matching plasma focus installations with an increase of discharge currents to values above 2–3 MA with the initial formation of a plasma current shell in heavy inert gases. The results of the analysis are compared with data from a series of electric discharge experiments made with a helium current shell compressing a localized region with injected deuterium. [ABSTRACT FROM AUTHOR]

Methods for the numerical solution of a problem for a mixed type equation in an unbounded domain are developed. A method for setting artificial boundary conditions is proposed that permits one to carry out calculations in a bounded domain such that the numerical solution converges to the projection of the exact solution onto this domain. The case where the solution satisfies the wave equation in a bounded domain and the Laplace equation in the remaining part of the space is considered in detail. An algorithm is presented for the case in which the process in the bounded domain is described by the heat equation. Examples of solutions in the two-dimensional case are given. The rate of convergence of the iteration algorithm is studied. [ABSTRACT FROM AUTHOR]

Computational algorithms based on the two-level additive Schwarz method (a version of the domain decomposition method with overlapping) and the Neumann–Dirichlet method (a version of the domain decomposition method without overlapping) for solving the problem of contact interaction of a system of bodies are proposed. Results of applying these algorithms for the numerical simulation of a stress-strain state of a part of a fuel element that includes 2–100 fuel pellets are presented. An axially symmetric thermoelastic approximation is used. The dependence of the number of iterations needed to ensure the desired accuracy on the number of bodies in the system, on the grid step, and on the boundary conditions on contact surfaces is investigated. [ABSTRACT FROM AUTHOR]

The problem of the contact interaction of the elements of the barrel of an electromagnetic accelerator is solved. A two-dimensional elastic approximation is used. The computational domain is a quarter of the cross-section and includes a rail, insulator, and load-bearing shell. To solve the problem, the two-level additive Schwarz method is used, with the help of which the problem in the entire domain is reduced to solving a number of local contact problems in the introduced subdomains. The results of three calculations are presented: in the first one, realistic orthotropic properties of materials are used, while in the other two, isotropic approximations are used (for the minimum and maximum values of Young's moduli). A comparative analysis of the stress-strain state of the accelerator barrel for each case is carried out. [ABSTRACT FROM AUTHOR]

An approach to mathematically model the nucleation and growth of soot particles during the diffusion combustion of hydrocarbon fuel is presented. The chain of transformations of hydrocarbon fuel is modeled using a Markov process with a finite number of states, which is described by a stiff system of Kolmogorov's ordinary differential equations (ODEs). As a result of numerical modeling, the set of functions describing the change in concentrations of various soot fractions in a laminar diffusion flame of toluene depending on time is obtained. Based on the results of the numerical solution of the ODE system, discrete particle size distributions (relative diameters) are constructed for different times. Continuous Weibull distributions approximating discrete distributions are constructed using the least squares method. The results obtained are in qualitative agreement with the experimental data. [ABSTRACT FROM AUTHOR]

We propose methods for solving an exterior boundary value problem for the Laplace equation based on the main integral Green formula. The main technique is the one of setting an artificial integral boundary condition with iterative improvement. It is shown that iterative methods converge at the rate of a geometric progression. The applicability of the methods for solving exterior problems is confirmed by computational experiments in the two- and three-dimensional cases. The algorithm is also applied to problems with an operator of the mixed type. [ABSTRACT FROM AUTHOR]

We propose a generalization of methods for solving problems for a linear elliptic operator with a known fundamental solution in an unbounded domain to the case of mixed-type problems. Two new methods are constructed, the method of setting integral boundary conditions and a three-stage iterative method. The scope of the methods constructed is limited to the cases where the operators have a known fundamental solution outside some finite domain. Numerical algorithms implemented as computer software are created to solve particular problems with the methods proposed. The applicability of the methods to differential and integro-differential equations in the two-dimensional case and the possible applicability to three-dimensional problems are demonstrated. [ABSTRACT FROM AUTHOR]

We study numerical methods for solving stiff systems of ordinary differential equations. We propose an exponential computational algorithm which is constructed by using an exponential change of variables based on the classical Runge-Kutta method of the fourth order. Nonlinear problems are used to prove and demonstrate the fourth order of convergence of the new method. [ABSTRACT FROM AUTHOR]

Processes accompanying the electrodynamic acceleration of a thin plate liner at a high accelerating current density are investigated. In addition to determining the electrical characteristics, shadow filming of the plate profile was carried out during the acceleration and the deformation of the profile in the region of fixed attachment to the current leads was monitored. A new experimentally reproducible effect in which the plate splits into three separate fragments, which is explained by nonuniform overheating by the current of the plate's cross section and the electrodynamics of the process, was found. It was detected that, on the acceleration of copper liners, the current sheath is separated from the metal body of the liner and diverges in two directions. The nature of this phenomenon has not yet been determined. [ABSTRACT FROM AUTHOR]

A method for numerical simulation of the motion of the plane liner in a magnetic compressor based on a combination of the transverse and longitudinal two-dimensional models is proposed. The method permits modeling the interaction of the liner ribbon with the rigid basement for the liner kinematic characteristics close to the experimental ones. Three different model are considered to justify the choice of the mathematical model of an elastoplastic body which would be suitable for solving similar problems. A series of computations is performed, and the results and scope of each of the models are analyzed. [ABSTRACT FROM AUTHOR]

We construct a mathematical model of electromagnetic processes in a magnetic accelerator. In the two-dimensional approximation, the Maxwell equations are reduced to a system of scalar integro-differential equations in the conductors and to the Laplace equation in the dielectric subdomains. We obtain a numerical model on the basis of the Galerkin-Petrovmethod with piecewise constant and piecewise linear basis functions. The results of computations are represented. [ABSTRACT FROM AUTHOR]

A review of methods providing the divergence-free property of the magnetic field when solving the two-dimensional problems of magnetic hydrodynamics on triangular grids by the secondorder discontinuous Galerkin method is presented. Procedures for redistributing the numerical flows corresponding to the magnetic field in the full two-dimensional formulation in the Cartesian coordinates and in the two-dimensional axisymmetric case in the cylindrical coordinates, making it possible to suppress the growth of the numerical divergence of the magnetic field, are described. Test problems of the Orszag-Tang vortex and spherical explosion are considered. [ABSTRACT FROM AUTHOR]

An obituary for professor Anton Pavlovich Favorskii is presented.

A numerical algorithm for simulating the multicontact thermoelastic interaction of a system of many bodies is developed. The algorithm is based on the iterative Schwarz alternating method modified for the class of problems under consideration. The nonlinear differential problem in question is discretized using the finite element method. Numerical results are presented, including the thermomechanical interaction of 350 bodies. [ABSTRACT FROM AUTHOR]

Experimental data for the acceleration of plate liners with a magnetic flux electromagnetic compressor are reported. The compressor is designed for peaking the power of current pulses with an initial amplitude of 3 MA. The compression zone of the liner has the form of a stripline, which makes it possible to use one current source both for the acceleration of the liner and for the generation of a magnetic flux in the compression zone. The acceleration dynamics and the deformation of plate liners during an operating cycle of the compressor are studied. In the experiments conducted, the compressor is powered by a capacitor battery. The current amplitude in the output capacitive load rises by 1.6 times, while the pulse narrows twofold. Experimental data are compared with numerical calculation data for the liner material flow, which are found to adequately describe processes taking place in such a compressor. [ABSTRACT FROM AUTHOR]

The algorithm for the construction and study of Fedorenko's finite superelements method (FSEM) is described. Different variants of Fedorenko's FSEM for simulation of media with small inclusions are presented. The algorithms are implemented and a software complex for the numerical solution of boundary value problems with singularities is developed. The theoretical substantiation of different variants of the method for elliptic equations on the example of the Laplace equation is implemented. The results of the numerical solution for several tasks are presented. [ABSTRACT FROM AUTHOR]

This article presents spatially a 2D cylindrically symmetrical, mathematical model of the MHD pump that is not stationary in time. To describe electromagnetic fields, the MHD approximation of Maxwell's equations is used; to describe the motion of heat-transfer fluid in the pump channel, the Navier-Stokes equations written in terms of vortex and flow function are used. The fluid consumption is calculated from the equation of fluid motion in a closed circuit. The calculations of different pump operating modes are presented. [ABSTRACT FROM AUTHOR]

An MHD model of the formation of astrophysical jet outflow from the vicinity of a compact object surrounded by a thin accretion disk and immersed into the nebula of a galactic plasma is considered. The numerical algorithm is based on division by physical processes and includes a difference scheme for the MHD system of equations in the two-dimensional (2D) axisymmetrical case. Triangular unstructured staggered grids are used. The modeling results show the formation of the accelerating channel in the shape of a Laval nozzle and comply with the available observation data. Computations are performed on a KIAM K-100 cluster. [ABSTRACT FROM AUTHOR]

A fundamentally new scheme of the electronuclear method based on nuclear relativistic technologies is discussed; this scheme includes the formation and utilization of a limiting hard neutron spectrum in the volume of the deep subcritical active core. It is demonstrated that the development and application of nuclear relativistic technologies can be promising for solving the problem of utilizing spent nuclear fuel and global challenges of power production. The results of the first experiments performed at the Joint Institute for Nuclear Research indicate the realistic character of the main principles of relativistic nuclear technologies, in particular, the growth of beam-power amplification by a factor of 2 for a deuteron beam irradiating a massive (315 kg) uranium target with the beam energy increasing from 1 to 4 GeV. [ABSTRACT FROM AUTHOR]

The article discusses the simulation of acceleration and deceleration of a liner in a magnetic compressor. Two-dimensional approximations are considered, corresponding to the sections of the initial spatial area of transversal and longitudinal planes. The models are presented where the liner is considered as an elastic body, elastic-plastic body, and viscous liquid. The calculated results are presented and a comparative analysis of liner motion in various models is given. [ABSTRACT FROM AUTHOR]

The work is devoted to the analytic comparison of the RKDG-method with other well-known numerical techniques. Variants of the RKDG-method are considered as well as Godunov-type finite-volume schemes. The quality of different schemes is assessed. It is found that the RKDG-method has a higher order of approximation, which ensures the better quality of the solution. [ABSTRACT FROM AUTHOR]

An MHD model for the formation of a jet in the vicinity of a compact object with a supersonic accretion regime is constructed, assuming that the plasma is perfectly electrically conducting. A stable, collimated jet of plasma along the z axis symmetric about the plane of the accretion disk is obtained. The parameters of the jet are in good agreement-with available observational data on the structure and properties of jets. [ABSTRACT FROM AUTHOR]

The temperature mode of a metal contact upon transition to a hybrid and further on to a plasma one has been studied. Spatial (three-dimensional) mathematical modeling confirmed the existence of a dependable metal contact before melting of the anchor material and transition to an arc mode of passage of the current after the onset of boiling. The possibility of destruction of the accelerated body during the acceleration time has been investigated. [ABSTRACT FROM AUTHOR]

Results of the theoretical and numerical studies of an algorithm based on the combined use of the finite element and finite superelement methods are presented. Estimates of the errors for one of the variants of the method applied to solving the Laplace equation are obtained. The method can be used to solve a problem concerning the skin layer appearing due to high velocities. [ABSTRACT FROM AUTHOR]

We investigated fluorescence and fluorescence excitation spectra of five substituted diphenylpolyenes with the number of double bonds in the chain n = 2 or n = 3 and substituents NO2, N(CH3)2, and NH2 in different media (toluene and n octane) at low (77 and 4.2 K) temperatures. The duration of fluorescence (τ) and the quantum yield of fluorescence (ϕ) of the four compounds investigated were measured at room temperature. The influence of the electron donor acceptor interaction in one of the compounds on its spectral luminescent properties has been analyzed. [ABSTRACT FROM AUTHOR]

Methods of numerical modeling of an electromagnetic field in electrodynamic launchers of the railgun type in the presence of magnetization turns have been proposed. Results of employment of different methods to model the electromagnetic field in a modular augmented staged electromagnetic launcher (MASEL) have been presented; a comparison of the results of simulation and full-scale experiments has been made. The issue of the dependence of the electromagnetic field on the configuration of magnetization turns has been investigated. [ABSTRACT FROM AUTHOR]