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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]

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]

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]

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]

In this work finite superelements method (FSEM) for solution of biharmonic equation in bounded domains is proposed and developed. The method is based on decomposition of domain into subdomains with the solution of a number of intermediary problems, every of which is a boundary value problem for biharmonic equation with boundary condition being basis for interpolation of solution at superelements boundaries. The initial problem solution is found as an expansion on the constructed function system. It is shown that the solution of general problem can be recovered using functions and traces found above. Error estimates for one case of FSEM are obtained. [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]

Abstract. The results of numerical investigation of the Finite Superelement Method (FSEM) for the solution of 3D elasticity problems are given. A definition of FSEM is proposed, and the general theory is briefly explained. Then the variants of FSEM are considered for the model problem. Their comparative analysis is being carried out. These variants are based on the finite element interpolation techniques on superelements boundaries. FSEM and FEM efficiency comparison is presented for the model problem. Quantative error data are obtained. A certain example of a 3D elasticity problem is considered in conclusion. A notable advantage of a higher degree FSEM approximation technique is illustrated. [ABSTRACT FROM AUTHOR]

A Fedorenko Finite Superelements Method (FSEM) for 3D linear elasticity problems is considered. We present special weak statement for traces of original problem solution which natural Bubnov-Galerkin approximation leads to the FSEM. Some applications of the FSEM for the problems of mechanics of composites are considered and results of numerical experiments are presented. [ABSTRACT FROM AUTHOR]

Presents a method of numerical experiment for investigating the use of currents induced within a conducting shield for railgun performance control. Statement of the problem; Discussion of the numerical simulation and its results; Conclusions.

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]

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 scheme of a multi-objective installation 'Baikal', a multi-megajoule source of X-ray emission with a temperature of 250-300 eV and a power of 500-1000 TW, is described in this article. The Project of the 'Baikal' installation is based on an inductive energy store, which in the process of step-by-step energy transmission with increasing power generates an electric pulse with parameters required for compression of liners. Electric parameters of the 'Baikal' installation are: current -50 MA, voltage 8-10 MV, pulse duration -150 ns, pulse energy 30 MJ. An installation 'MOL' is intended for testing the scheme of one of 'Baikal' modules. It consists of an inductive store IN-1 with accumulated energy of 12,5 MJ, capacitor banks, a magnetic amplifier, a magnetic compressor with a capacitor bank for generation of initial magnetic flow, a plasma opening switch (POS) and a load simulator. [ABSTRACT FROM AUTHOR]