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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 2, 2010  STUDY OF THE COMPUTATIONAL PARAMETERS EFFECT AT NUMERICAL SIMULATION OF THE EXPLOSIVE TRANSFORMATION PROCESS OVER MC KINETICS IN THE LEGAK TECHNIQUE
N. A. Volodina, I. Yu. Myshkina, V. F. Spiridonov VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 2. P. 314.
During numerical simulation of the detonation development and distribution process under the LEGAK technique the technology of calculations with the MC kinetics on LagrangianEulerian grids was perfected. The behavior of the calculation results with the MC kinetics was studied on the gradually thickening grids. The effect of the time step, type of the calculation quadratic viscosity and mixed cells thermodynamic parameters calculation algorithm on the numerical solution is studied. The parameters of the MC kinetics model for TATBtype explosives were specified more precisely. The calculation results for 1D and 2D problems as well as their comparison with experimental data obtained in IFV VNIIEF are presented in the paper. Key words: LEGAK technique, MC detonation kinetics, equation of state of explosive.
 ON THE DETERMINATION OF ARTIFICIAL VISCOSITY FOR MIXED CELL COMPONENTS E. A. Goncharov, V. Yu. Kolobyanin, Yu. V. Yanilkin VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 2. P. 1529.
The paper considers several ways of artificial viscosity determination for mixed cells components with two or more materials. The dependence of the calculation results on these ways is studied on test problems for three closing methods of gasdynamics equations using the following suppositions: the components` velocities divergences are equal, the components` pressure increments are equal, the components` mass velocities after passing weak perturbation are equal. Key words: EGAK technique, gas dynamics, closure methods for gas dynamics equations, artificial viscosity.
 APPLICATION OF THE TVDAPPROACH TO THE DS_{n}METHOD FOR THE HEAT RADIATION TRANSPORT EQUATION SOLUTION IN THE AXIALLYSYMMETRIC RZGEOMETRY A. D. Gadzhiev, V. V. Zavyalov, A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 2. P. 3039.
Realization of the implicit nonlinear TVDtype scheme of a higher approximation order is considered for the solution of the heat radiation transport equation in the axiallysymmetrical RZgeometry on arbitrary quadrangular grids in the frames of the discrete ordinates. A limiter is used in the scheme, which is calculated explicitly over the values known from the previous time step on a threepoint template in each direction. This property allows application of the timesaving sweep computation for the solution of the system of difference equations. The scheme combines conservativeness, smoothness in the sense of the TVDscheme methodology, first order approximation over time and second order approximation over space, except several points with extremums. The order of approximation is studied for a model transport equation. Earlier this scheme was tested for 1D geometries. The results of test problem numerical calculations are presented. Key words: radiation transport, difference scheme, method of discrete ordinates, TVD approach.
 SELFSIMILAR HEAT WAVES FROM A CONCENTRATED OR SPATIAL SOURCE IN AN ENVIRONMENT WITH NONHOMOGENEOUS THERMALPHYSICAL PARAMETERS B. P. Tikhomirov VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 2. P. 4050.
The problems about an instantaneous concentrated source in an environment with distributed physical parameters, as well as the problem about a special spatial source are considered. The issue of joining known selfsimilar solutions on the plane interface of environments with different thermalphysical characteristics is discussed in the paper. The obtained conditions of solutions` agreement allow us to estimate the part of the released energy to the left and to the right from the interface surface. In the problem about a spatial source the combustion function, proportional to the energy and inversely proportional to the time, was taken as the source. Note, that this problem includes the problem of instantaneous concentrated source as a particular case. The precise solution was built with account for the radiation energy density for setting the problems with planar, cylindrical and spherical symmetries and the mentioned combustion function. The examples of model problems for testing the calculation techniques of nonlinear thermal conductivity in nonhomogeneous environment without account and with account for the combustion function are given in the paper. Key words: concentrated and spatial sources, thermal wave, interface, matching of selfsimilar solutions, model test problems.
 SOLUTION TECHNIQUE FOR NEUTRON AND GAMMAQUANTUM TRANSPORT EQUATION AT TABULATED INPUT SCATTERING GROUP CROSSSECTIONS AND ITS APPLICATION FOR THE VVER1000 REACTOR PROTECTION O. V. Nikolayeva, L. P. Bass, V. S. Kuznetsov, V. V. Sinitsa, V. I. Tsofin VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 2. P. 5163.
An algorithm able to find solutions of the multigroup radiation transport equation in multidimensional geometries with tabulated input scattering crosssections is presented in the paper. The algorithm verification results obtained on a trivial model problem with smooth model scattering crosssections are discussed. The paper presents neutron and gamma flux densities calculated using the scattering crosssections, which satisfy the real laws of radiation/matter interaction in a small model problem with a point isotropic monoenergy source and protection of the VVER1000 reactor area. It is shown in the paper how the flux densities change when passing from the tabulated input data to their polynomial representation. Key words: transport equation, angular dependence of scattering crosssections.
 A COMPUTATIONAL MODEL OF SOLUTION CRYSTALLIZATION UNDER CONTROL ACTION OF TEMPERATURE FIELD FOR THE CASE OF BIOCRYSTAL GROWTH V. P. Ginkin, S. M. Ganina, O. M. Ginkina VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 2. P. 6474.
A computational model was built and the numerical study of the protein crystallization (lysozyme) out of a water solution under the impact of a precipitant (NaCl) concentration spatial distribution and controlling pointwise temperature impact was performed. The computational model describes the generation of the crystal nuclei and their growth depending on the oversaturation local value as well as on the heatmass transport in the whole solution area including the protein crystals. The heatmass transport is described by the NavierStokes equations in the Boussinesq approximation with account for the thermogravitation and concentration convections. Key words: protein crystallization, lysozyme, mathematical crystallization model, precipitant, equilibrium solubility, solubility as a function of temperature, oversaturation, convection, NavierStokes equation, computational algorithm, growth rate control, pointwise temperature impact.
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