Issue N^{o} 2, 1993 
SND CODE FOR 1D LASER FUSION CALCULATIONS
E.N. Antonenko, G.V. Dolgolyova, S.N. Krupina VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 2. P. 39.
The functionality оf the SND code Is described. The code la designed for numerical calculation of Controlled fusion. The system of equations is given, the numerical method is presented along with difference schemes used.

COMPARISON OF ITERATION SPEEDUP TECHNIQUES FOR RADIATION TRANSPORT EQUATION IN P_{1}APPROXIMATION AND ENERGY EQUATION A.A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 2. P. 1016.
The system of radiation transport equations and energy equations  are nonlinear so that iterative methods with nonlinear term linearization are used to solve them. The linearized system itself has a complex structure. It also uses iterative methods. The paper compares some iterative methods for radiant energy transport system based on ROMB difference scheme.

NUMERICAL SIMULATION AND ANALYSIS OF NONISOTHERMAL KINETICS V.I. Denisоv, N.B. Itкina VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 2. P. 1720.
The system of radiation transport equations and energy equations  are nonlinear so that iterative methods with nonlinear term linearization are used to solve them. The linearized system itself has a complex structure. It also uses iterative methods. The paper compares some iterative methods for radiant energy transport system based on ROMB difference scheme.

SOME NEW METHODS IN KINETIC THEORY OF GAMMA MOTION THROUGH MATERIAL G.M. Pоtetunко VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 2. P. 2124.
The kinetic theory based on Boltzmann equation is considered for highenergy gamma radiation motion through material. Given the Compton scattering anisotropy of highenergy gamma radiation, the original equation is written in small angle and diffusion approximations. The notions are introduced similar to the notions of material stapping power and energy struggling for ions. Since the energy struggling of highenergy gammaquanta is small, the gammaquanta wavelength is a singlevalued penetration depth function which allows the obtained solution in analytic form.

PL ESTIMATES OF THE FLOW ACROSS A SURFACE AND THEIR APPLICATION TO MONTE CARLO GAMMA AND CHARGED PARTICLE TRANSPORT CALCULATIONS E.N. Dоnsкоy VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 2. P. 2529.
A new class of estimates is developed for the flow over a surface based on local invariancy with respect to spatial shifts of transport equationrelated Markovian process shifts. The method of estimate development is to average the intersection estimate or its modifications over one path segment. For infinite homogeneous medium, plane layer and plane multilayer system, a specific estimation type is given, its properties are studied and finite dispertion conditions are found that are much poorer than similar conditions for intersection estimates. PL estimates of the flow across a surface are used to compute the functionals in PRIZKIE code designed for gamma and electron transport equation in plane geometry and in the energy range varying from 1 keV to 1 MeV. The paper contains some examples illustrating the advantages of PLestimates.

RECURRENT FORMULAS OBTAINED FROM BOLTZMANN EQUATION DISTRIBUTION FUNCTION EXPANSION OVER SPHERICAL HARMONICS I.A. Litvinenko, Yu.I. Matveenко VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 2. P. 3035.
The approximate solution of Boltzmann equation (in electromagnetic fields) widely uses electron or ion distribution function expansion over spherical harmonics. The higher expansion terms should be accounted when the requirement E/N* > l0^{3}Td is met (where 1 Td =10^{21} Vm^{2}). To find the distribution function within the accuracy of N order a system consisting of (N + 1)^{2} heterogeneous differential equations is solved for (N + 1)^{2} unknown expansion coefficients. This paper presents the derivation of recurrent formulas of reconstruct the differential system. A system consisting of 36 equations is written to find the distribution function within the accuracy of fifth order terns.

THE METHOD FOR A SOLUTION OF THE ENERGY AND RADIATIVE DIFFUSION EQUATIONS E.B. Raсhilоv VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 2. P. 3639.
In the paper the method for obtaining solutions of the system of nonstationary spectral radiative diffusion and the energy equations in domains with the axial symmetry is presented. The results are given for a model problem.

ACCOUNTING THE RADIATION TRANSPORT IN MAGNETOHYDRODYNAMIС HEAVYION FUSION TARGETS Yu.P. Arpishkin, M.D. Churazоv VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 2. P. 4043.
For a class of magnetchydrodynamic targets, the correctness of radiation transport is considered. The results obtained from three temperature and spectral approximations are presented and compared. The threetemperature approximation is found to be sufficient for the class of targets under consideration.

SOLUTION OF PROBLEMS OF GAS DYNAMICS AND AERODYNAMICS ON PARALLEL COMPUTERS A.V.Gusev, V.T. Zhuкоv, A.V. Zabrоdin, A.O. Latsis, A.E. Lutsку, I.L. Petrushchenkov, L.A. Pоzdnyakov, O.B. Feodoritova VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 2. P. 4454.
The creation of the multiprocessor systems of regular architecture with great possibilities in parallel data processing is perspective direction of radical efficiency increase of calculating machines. In this connection, coupling of the systems architecture with structural exception of the used calculation methods is necessary for guarantee of the real increase efficiency with the number of processors to be extended The adaptive algorithms of the calculation of the multidimensional problems of gas dynamics, gas dynamics with heat conductivity and aerodynamics were selected and tested in practice in the capacity of representative and sufficiently universal methods for employment on multiprocessor computers.

SIMULATION OF NEUTRON PROCESSES WITH THE METHOD OF SPHERICAL HARMONICS IN CRITICAL PARAMETER CALCULATIONS FOR MULTILAYER SYSTEMS (Review) I.A. Adamsкaуa VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 2. P. 5560.
The paper presents scientific data obtained by the author from critical parameter calculations for multilayer systems. The efforts were based on Godunov´s idea to apply the method of orthogonal factorization of partial solutions to differential equations of spherical harmonics. The results are motivated both by theory and by comparison with experiment, with other computational methods and with inner control technique. The results are widely used in practice. The codes are developed under the author´s guidance to calculate critical parameters of multilayer systems.

MONTE CARLO METHOD AT VNIISF E.N. Dоnsкоу, V.A. Уeltsоv, A.K. Zhitnik, N.V. Ivanоv, Yu.K. Kochubei, A.I. Mоrenкo, A.Z. Mоrenко, V.I. Rоslоv, A.B. Rоnzhin, A.N. Subbоtin VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 2. P. 6164.
The main codes of the Monte Carlo Laboratory of the VNIIEF Mathematical Division are briefly described. Typical problems are given together with the code capabilities, the method features, methods for increasing the computational efficiency.

RADIATION TRANSPORT CALCULATIONS WITHOUT LOCAL THERMODYNAMIC EQUILIBRIUM B.A. Vоinоv, P.D. Gasparyan, Yu.K. Kochubei, V.I. Rоslоv VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 2. P. 6569.
SS9 method is described which was developed to calculate the nonequilibrium radiation in onedimensional approximation. Numerical results presented are compared with theory in LTE approximation and with the data obtained elsewhere.

SIMULATION OF BREMSTRAHLUNG PHOTON ANGULAR DISTRIBUTION Ya.Z. Kandiev, V.V. Plokhoy VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 2. P. 7072.
The Monte Carlo method is used to simulate the bremstrahlung photon production during charged particlesmatter interaction. An emphasis is made on photon flight angle selection. Sampling from angular distribution of a rather complicated type is performed by superposition method combined with exclusion method.

MAXIMUM/MINIMUM PRINCIPLE FOR A RADIANT ENERGY TRANSPORT SYSTEM IN P_{1}APPROXIMATION A.A. Shestакоv VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 2. P. 7374.
Maximum/minimum principle is proved for a radiant energy transport system in P_{1}approximation. The approach used is proposed by E.S. Andreev and M.Yu. Kozmanov in proving the maximum/minimum principle for the above system in kinetic formulation.

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