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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 4, 2016  DS_{n} METHOD WITH TVD RECONSTRUCTION AND SYNTHETIC P_{1}SA ITERATION ACCELERATION FOR NUMERICAL SOLUTION OF THE TWODIMENSIONAL THERMAL RADIATION TRANSPORT EQUATION IN THE AXIALLY SYMMETRIC RZ GEOMETRY
A. D. Gadzhiev, D. A. Koshutin, A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc. 2016. No 4. P. 319.
Development of an efficient numerical solver for the thermal radiation transport equation is a challenging problem. We consider a new technique for numerical solution of the twodimensional thermal radiation transport equation. The idea of the new approach is to use the discrete ordinate method with TVD reconstruction for solving the kinetic equation and a synthetic method based on a P_{1}approximation for accelerated convergence of iterations in joint solution of the transport and energy equations. Key words: radiation transport, TVD reconstruction, iteration method.
 PRACTICAL STABILITY CONDITIONS FOR A DIFFERENCE SCHEME FOR SOLVING THE HEAT TRANSFER EQUATION WITH DOUBLE THERMAL CONDUCTIVITY REMAPPING Yu. A. Bondarenko, A. A. Gorbunov, B. P. Tikhomirov VANT. Ser.: Mat. Mod. Fiz. Proc. 2016. No 4. P. 2025.
In some codes, the nonlinear heat transfer equation is solved numerically using implicit conditionally stable difference schemes with a fixed maximum permissible number of iterations with respect to the nonlinearity of thermal conductivity having the value of 1, 2 or 3. In this paper, the von NeumannFourier method is combined with the Newton numerical method for initial data stability analysis of a scheme with double remapping of the field of thermal conductivities. From the stability condition we derived a time step constraint suitable for practical simulations. It is shown that the dependence of the time step on the mesh spacing is not quadratic. Key words: radiant heat transfer, implicit difference scheme, thermal conductivity, initial data stability, von NeumannFourier method, iterative Newton method, time step, test simulations.
 STRUCTURE OF THREEDIMENSIONAL STATIONARY ISOBARIC DOUBLE WAVES IN AN IDEAL INCOMPRESSIBLE FLUID. PART 2. SOLUTION OF REDUCED SYSTEM AND LOCAL CLASSIFICATION OF DOUBLE WAVES V. E. Shemarulin VANT. Ser.: Mat. Mod. Fiz. Proc. 2016. No 4. P. 2639.
Studies of the structure of isobaric threedimensional stationary waves in an ideal incompressible fluid are coming to an end. In the first part of the work, the system of functional equations implicitly defining these waves was reduced to an equivalent system, which is more convenient for research. The present part shows that the solutions of the reduced system have a simple geometric structure and provides an explicit description of the diversity of local solutions of this system. As a result, all isobaric threedimensional stationary double waves are proven to be clusters of flow regions of thee major types: shear, conical and tangential. Shear flows are the well known flows in parallel planes; for each plane, in parallel right lines. Conical flows are the flows along sets of tangent semiplanes of arbitrary convex conical surfaces; for each semiplane, in right lines parallel to the generatrix of the conical surface belonging to the semiplane. Tangential flows are the flows along sets of tangent surfaces (surfaces generated by right tangents of arbitrary space curves) governed by certain convexity conditions (ensuring that there are no intersections of tangent semiplanes); for each semiplane, in right lines parallel to the generatrix of the tangent surface (tangent to the curve) belonging to the semiplane. A similar explicit description of the structure of isobaric threedimensional steadystate simple waves and twodimensional nonsteadystate isobaric flows has been given by the author before. Thus, the present work finalizes the local classification of isobaric flows of an ideal incompressible fluid for the case of three independent variables: three space variables or two space variables and time. Key words: isobaric flows, threedimensional stationary double waves, local flow classification, shear, conical and tangential flows.
 COMPARISON OF TWO SWEEP PARALLELING METHODS FOR HYBRID COMPUTERS WITH GRAPHICS PROCESSING UNITS A. A. Fedorov, A. N. Bykov VANT. Ser.: Mat. Mod. Fiz. Proc. 2016. No 4. P. 4050.
The paper describes two methods (the parallel pipeline and the Yanenko method) for solving a system of linear algebraic equations with a tridiagonal matrix on GPUaccelerated parallel computes. Specific features of their implementation both on parallel computers having no accelerators and on hybrid computers are discussed. Arithmetic complexity of the Yanenko method is analyzed, and results of numerical scalability experiments are reported. Key words: system of linear algebraic equations with tridiagonal matrix, sweep method, parallel pipeline, Yanenko method, GPUaccelerated parallel computers, code RAMZESKP.
 PROTON FAST IGNITION OF A CYLINDRICAL DT TARGET ENCLOSED IN A STATIONARY HEATINSULATED SHELL K. V. Khishchenko, A. A. Charakhchian VANT. Ser.: Mat. Mod. Fiz. Proc. 2016. No 4. P. 5159.
The paper considers a twodimensional axiallysymmetric problem of fast ignition of a precompressed cylindrical target with a DT mixture enclosed in a stationary heatinsulated shell. The target is ignited on the end by a proton beam, the intensity of which does not depend on the radial coordinate. The difference from the onedimensional problem is that the fusion alpha particles and the selfradiation of plasma freely emerge from the fuel through the side boundary with the shell. The threshold ignition energy for the mixture densities of 22 and 110 g/cm^{3} is shown to be about one tenth of that in the known case without the shell and with a beam radius much smaller than the target radius. As compared to the problem of interest, the quasionedimensional model developed earlier understates the threshold ignition energy with respect to the radius by a factor of four for the given beam intensity. Key words: cylindrical ICF target, fast ignition, ignition energy.
 INVESTIGATION OF THE INFLUENCE OF AUSTENITIC STEEL SURFACING ON CRACK OPENING IN A PEARLITIC STEEL PIPELINE DN800 D. A. Kuzmin VANT. Ser.: Mat. Mod. Fiz. Proc. 2016. No 4. P. 6065.
The object of the study is a straight section of the main circulation pipeline from pearlitic steel with austenitic steel cladding. These steels have different linear expansion coefficients. The influence of the cladding on the opening of a through crack in the pipeline is studied. The size of crack opening and the shape of crack faces are determined for various crack lengths. A comparative analysis of the crack opening area for the pipeline with cladding and without it is made. Key words: main circulation pipeline, austenitic cladding, crack opening.
 A TECHNIQUE FOR CALCULATING RADIATION LOSSES IN THE INITIAL SECTION OF A BENT SINGLEMODE OPTICAL FIBER Yu. V. Malykh, V. V. Shubin VANT. Ser.: Mat. Mod. Fiz. Proc. 2016. No 4. P. 6677.
A technique for calculating optical radiation losses in the initial section of a bent singlemode optical fiber as a function of the bending angle is presented. Known techniques and formulas for calculating radiation losses in bent optical fibers are discussed in terms of their applications. As far as the techniques considered cannot describe the losses in the initial bend section, we have developed a new approach. The resulting technique was used to calculate radiation losses as a function of the bending angle for an SMF28 optical fiber. The calculated results are compared with experimental data. Key words: bend of singlemode optical fiber, transition radiation losses, bending radiation losses, conformal mapping method, length and angle of bending.
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