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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 1, 2006  TECHNIQUE OF DIAGONAL MATRIX DEFINITION FOR COMPUTATIONAL SOLUTION OF RADIATIVE TRANSFER EQUATIONS IN P_{1}APPROXIMATION BY ROMB SCHEME
A. D. Gadzhiev, A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc. 2006. No 1. P. 313.
Technique of diagonal matrix definition for iteration acceleration at numerical solution of the radiative transfer equation in P_{1}approximation by ROMB scheme is considered. The essence of the technique lies in assigning oneway flux of radiation from the previous iteration on difference meshes and getting diagonal matrix for temperature definition.
 EXPLICITIMPLICIT CALCULATION ALGORITHM OF GASDYNAMIC FLOWS IN LEGAK3D TECHNIQUE S. M. Bakhrakh, S. V. Velichko, S. S. Kosarim, O. N. Kulygina, M. V. Luchinin, A. O. Naumov, V. F. Spiridonov, I. Yu. Taradai, K. V. Tsiberev VANT. Ser.: Mat. Mod. Fiz. Proc. 2006. No 1. P. 1422.
Explicitimplicit calculation algorithm of 3D gasdynamic flows realized in LEGAK3D technique is described, which allows to reduce the time of calculations. The idea of the algorithm lies in the increase of a counting time step owing to the use of Kurant number multiplied by the given number of times, in condition of stability. Here, the groups of “poor” cells which “keep” the step are calculated by implicit scheme. Other cells are calculated explicitly. Method implementation lies in diffusion equation solution. Two implicit difference schemes approximating this equation are given. The algorithm is parallelized. The examples of some test problems are given as a demonstration of its capacity.
 MATHEMATICAL SIMULATION OF RUNAWAY PROCESSES OF A REACTOR ON PROMPT NEUTRONS M. V. Kashcheev, I. A. Kuznetsov VANT. Ser.: Mat. Mod. Fiz. Proc. 2006. No 1. P. 2338.
Mathematical model of runaway processes of the reactor on prompt neutrons is developed. The model is realized in the new 2D program ANPEX which allows to simulate accident scenario at appearance of secondary criticality in molten active zone as well as at fast input of large abundant reactivity to the undamaged reactor with its subsequent runaway on prompt neutrons. When creating ANPEX program a series of improvements possessing newness was introduced. A large amount of variant calculations of damage processes was carried out by ANPEX program as well as calculation of prompt criticality stage in a damaged active zone BN600 was realized.
 DIRECT 3D NUMERICAL SIMULATION OF TURBULENT MIXING IN A BUOYANT PLUME V. P. Statsenko, O. G. Sin’kova, Yu. V. Yanilkin VANT. Ser.: Mat. Mod. Fiz. Proc. 2006. No 1. P. 3949.
Development of a turbulent buoyant plume in the field of gravity under statistically stationary outflow of a more light fluid to the homogeneous incompressible medium from a local source is numerically studied. Calculations are carried out using direct numerical simulation of turbulence by 3D gasdynamic technique TREK. Calculation results are compared with the known experimental data.
 DIRECT NUMERICAL SIMULATION OF TURBULENT MIXING IN BENJAMIN EXPERIMENTS V. P. Statsenko, I. N. Chistyakova, Yu. V. Yanilkin, V. Yu. Kolobyanin VANT. Ser.: Mat. Mod. Fiz. Proc. 2006. No 1. P. 5060.
The process of turbulent mixing in Benjamin experiments is numerically investigated. The calculations were carried out with the help of direct numerical simulation by twodimensional EGAK technique and threedimensional TREK technique. Calculation results are compared among themselves as well as with certain calculation and experimental data.
 NUMERICALANALYTICAL METHOD FOR SOLVING THE PROBLEM OF BRINE TRANSFER IN A WATERBEARING STRATUM V. M. Konyukhov, A. N. Chekalin VANT. Ser.: Mat. Mod. Fiz. Proc. 2006. No 1. P. 6176.
Numericalanalytical method for solving nonlinear equation of hyperbolic type describing brine filtration is suggested. Exact solutions of problems on initial characteristic problem of desired function are used at method development. Method testing is carried out on model problems. High performance and accuracy of the suggested method are shown.
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