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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 2, 2003  SOME METHODS OF APPROXIMATION FOR 2D TRANSPORT EQUATION BY ANGLE VARIABLES
R. M. Shagaliev, A. V. Alekseev, S. V. Mzhachikh, N. P. Pleteneva VANT. Ser.: Mat. Mod. Fiz. Proc.. 2003. No 2. P. 511.
Traditional S_{n} techniques of angle variable discretization of phase space are known to require a refined angle grid. Otherwise a radiation effect, as it is called, may occur. More stringent requirements to the number of angular variable intervals may result in essentially growing consumption of CP time and PC online storage for computations. One of the resolutions of this issue may be that of developing more efficient methods of multidimensional transport equation solution in angular variables. The following four approximation schemes for the transport equation in angular variables are under consideration: a traditional method for solving 2D transport equation using DS_{n} schemes; an improved scheme, meeting such requirements as exact calculation of “moment” integrals and diffusion limit obtaining; two variants of WDD scheme, in which an output flow through faces of a phase cell is recalculated.
 NUMERICAL STUDY RESULTS FOR VARIOUS METHODS OF 2D TRANSPORT EQUATION APPROXIMATION IN ANGLE VARIABLES R. M. Shagaliev, A. V. Alekseev, O. E. Vlasova, V. V. Evdokimov, A. V. Gichuk, E. A. Irinichev, S. V. Mzhachikh, A. A. Nuzhdin, N. P. Pleteneva, H. Scott VANT. Ser.: Mat. Mod. Fiz. Proc.. 2003. No 2. P. 1220.
The paper presents numerical study results for some updated methods of solving 2D radiative transport equation in angular variables. The methods have been described in the previous paper on this line. Several model problems of radiation propagation were numerically studied. The results are discussed in terms of grid solution accuracy. The conclusions are drawn regarding the efficiency of the methods used for the class of problems under consideration.
 ON ACCELERATION OF ITERATION CONVERGENCE FOR THE SYSTEM OF HEAT RADIATION TRANSPORT IN KINETIC APPROXIMATION V. Yu. Gusev, V. V. Zavialov, M. Yu. Kozmanov VANT. Ser.: Mat. Mod. Fiz. Proc.. 2003. No 2. P. 2127.
For joint solution of implicit difference equations, which approximate a system of time dependant differential equations, including a kinetic equation of photon transfer and an equation of energy, a modification of a wellknown iteration algorithm, allowing an acceleration of iteration convergence to the solution both in a spectral case and in the case of gray substance is studied. The efficiency of the above approach is illustrated by an example.
 ANALYTICAL TESTS FOR SOLVING PROBLEMS OF PARTICLE TRANSFER USING NUMERICAL METHODS L. A. Kondakov, V. N. Seleznev, O. I. Starodumov, A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc.. 2003. No 2. P. 2843.
Every code faces a testing problem. 2D codes usually start testing with computing onedimensional problems, on which they check a property of symmetry conservation on 2D grids, the accuracy of a difference scheme, that is dependence from time and space steps, the accuracy of boundary conditions description at calculation in regions, etc. When testing codes the problems possessing analytical solutions should be chosen. In the absence of analytical solutions the problems calculated with other codes are usually used, but it does not always insure an accurate solution. Therefore analytical test construction is still burning. The paper considers 11 model problems intended for testing onedimensional and twodimensional codes of neutral particles transfer in different approximations. The problems are constructed from analytical solutions. By the way of example the results of numerical calculations using different techniques are presented for above problems.
 THERMONUCLEAR BURNING OF DEUTERIUM IN CYLINDRICAL CHANNEL WITH BERYLLIUM SHELL M. D. Churazov, E. A. Zabrodina, A. G. Aksenov, Yu.P. Arpishkin VANT. Ser.: Mat. Mod. Fiz. Proc.. 2003. No 2. P. 4447.
Series of numerical calculations in twodimensional and multitemperature approximations was carried out to study the problems of deuterium thermonuclear targets burning. The use of DT pill for igniting deuterium target offers conditions for thermonuclear burning. Cylindrical deuterium targets and heavyion beams with charge compensation are studied within Fast Ignition scheme. Special compressing ion beams with the energy E_{c} ≥ 1 000 MJ are used for obtaining the fuel density ρ ~ 30 ÷ 100 g/cm^{3} and the compression parameters ρR ~ 4 g/cm^{2}. The igniting beams with high power density J_{m} ~ 4 ⋅ 10^{6} TW/g and the energy E_{ign} ~ 24 MJ are used to gain a wave of thermonuclear burning in a compressed cylindrical channel. For igniting fuel the masses of DT pills are considered at the level m ~ 100 mg. The propagation of thermonuclear burning wave along the target and thermonuclear energyrelease E_{f} ≥ 10 000 MJ have been arrived at in calculations of targets with beryllium shell.
 MONTECARLO SIMULATION OF SPECTRAL RADIATIVE TRANSPORT AT NONEQUILIBRIUM BURNING IN MIMOZA COMPLEX (MIMMK CODE) L.Z. Morenko, N.A. Riabikina, A.A. Kibkab VANT. Ser.: Mat. Mod. Fiz. Proc.. 2003. No 2. P. 4851.
A computation technique for nonequilibrium processes in MIMOZA complex using MonteCarlo simulation for spectral radiative transport is described. The technique has been developed for solving problems of thermonuclear targets compression and burning. The computational data are given for the target proposed for the use within the laser NIF Project (USA) with simulating radiative transport in spectral diffusion approximation and with simulating radiative transport using spectral kinetic equation.
 EXPERIMENTAL STUDIES OF SHOCK COMPRESSED CARBOGAL PROPERTIES. EQUATIONS OF STATE OF CARBOGAL AND PLEXIGLASS L. F. Gudarenko, M. V. Zhernokletov, S. I. Kirshanov, A. E. Kovalev, V. G. Kudelkin, A. I. Lomaikin, M. A. Mochalov, G. V. Siniakov, A. N. Shuikin VANT. Ser.: Mat. Mod. Fiz. Proc.. 2003. No 2. P. 5262.
The paper presents experimental data for the properties of the earbogal organic compound C_{8}F_{16} (perfluorine — 1,3dimethyl cyclohexane) in high pressure and temperature region, in particular, data on single and repeated compression, temperatures and sonic speed. For plexiglass the data are given on shock compression of porous samples with initial density which is 10—60 times smaller than plexiglass density under standard conditions. Thermodynamically complete equations of state of earbogal and plexiglass have been developed using an earlier published model and wellknown experimental data. The calculations with the developed equations of state of earbogal to P ≈ 70 GPa and of plexiglass throughout the studied range are shown to agree with obtained experimental data. Formally the equation of state of earbogal can be used at the density ρ < 300 g/cm^{3} or at the temperature T < 9,510^{9} K and that of plexiglass at the density ρ < 20 g/cm^{3} or at the temperature T < 1,5 ⋅ 10^{5} K. At density and temperature higher, than the above values an unstable region of thermodynamic equilibrium exists. A detailed description of the model and an accompanied constant of the equation of state allow a practical use of the paper results.
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