Some numerical methods for reactor cell, sub-critical systems and 3D models of nuclear reactors are presented. The methods are developed for steady states and spacetime calculations. Computer code TRIFON solves space-energy problem in (X, Y ) systems of finite height and calculates heterogeneous few-group matrix parameters of reactor cells. These parameters are used as input data in the computer code SHERHAN solving the 3D heterogeneous reactor equation for steady states and 3D space-time neutron processes simulation. Modification of TRIFON was developed for the simulation of space-time processes in sub-critical systems with external sources. An option of SHERHAN code for the system with external sources is under development.

A method and numerical algorithm for evaluating the computational errors in calculating the number of fission rates in small individual volumes of a reactor core, viz., fuel element, group of fuel elements, fuel assemblies, are presented. The standard error was determined by a combination of the methods of the statistical theory of errors and linear perturbation theory. An algorithm developed for calculating the value function, sensitivity coefficients, and errors of functionals which is based on the use of the MCCG3D, TRIFON, and ERRORJ software is described. The standard error, due to, for example, the relative error 1% (over the volume of a fuel element) in the microscopic fission and total cross section, of the computed fission rate in the most stressed fuel element in fuel assembly No. 10 PWR (ALMARAZ II, Spain), is evaluated as an example. The standard error of the fission reactions in this case is ε ƒ, 235 U = 5.573·10 -3 , ε ƒ, 239 Pu = 1.193·10 -3 , i.e., the total error is ~0.67%. For other isotopes, it is hundredths of a percent, i.e., approximately equal to its computational error. For the technological error ±1.2% of the density of the loaded PWR uranium-dioxide fuel, the computed uncertainty in the number of fissions is ±0.93%, and for the uncertainty ±0.5% in the fuel enrichment the error in the number fissions will be ±1.5%.Extensive information on the characteristics of the ALMARAZ II (Spain) reactor was used to study the neutronphysical characteristics of water moderated and cooled power reactors (VVER and PWR), including local heterogeneous effects [1]. The computed and experimental neutron-physical characteristics of this reactor were obtained by a large group of specialists from different countries, and many of the results can be used as tests.Local heterogeneous effects in reactors of this type are analyzed by making a computational estimate of the effect of different types of errors (uncertainties in the characteristics of the core) on the accuracy of calculations of the number of reactions in individual small volumes (fuel elements and fuel assemblies in the core). As an illustration of the method devel-

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The influence of the uncertainties in the microscopic cross sections of 238 U and 239-241 Pu on the neutron multiplication coefficient in VVÉR-1000 is studied. Data on the uncertainty of the cross sections were obtained by analyzing the ENDF/B files of the JENDL 3.3 system using the ERRORJ program. The characteristics of the reactor are calculated using the TRIFON 2.1 and SHERHAN programs. An approach associated with the calculation of the coefficients of sensitivity of the fuel assemblies and the reactor to standard samples in a small-group approximation is used.The purpose of this work is to calculate the uncertainty of the neutron multiplication coefficient in VVÉR-1000 due to the uncertainty in the microscopic cross sections of four isotopes -239 Pu, 240 Pu, 241 Pu, and 238 U. The three-dimensional model of the reactor contained 109 fuel assemblies with uranium and 54 fuel assemblies with mixed fuel, corresponding to the midpoint of the yearly fuel cycle, and uniform properties along the height. The 353 cm high core is surrounded by the elements of the compartment.The fuel assemblies were calculated using the TRIFON 2.1 program [1] in a multigroup approximation taking account of the fine structure of the neutron flux in the region of strong resonances (230 superthermal and 25 thermal groups), using a library of microscopic cross sections which is formed by the ASMS system from ENDF/B files. It has the BNAB-26 structure and includes data on the parameters of resonance levels and the dependence of the cross sections on the energy of neutrons in the thermal range. The results of the calculations were converted into data of the small-group representation with partitioning according to neutron energy 1.05·10 7 -4.65·10 3 -100-0.465-0 eV (for groups with boundaries corresponding to the lower limits of the 12th, 17th, 24th, and 26th groups of the BNAB-26 system). The calculations of the reactor were performed using the SHERHAN program [3] with four-group characteristics of the effective boundary conditions (Λ matrices), obtained from a calculation of the fuel assemblies using the TRIFON 2.1 program.Computational Method. In the base calculation of the fuel assemblies, the integrals T i m of the product of the neutron flux by radiative capture cross section of a "standard sample" σ s = 1 b and its concentration c s = 0.001·10 24 cm −3 were calculated for each type of physical zone m in each small-group energy interval i over the corresponding volumes V m of the physical zones and their relative values t i m : (1) T c F u r dUdV T T t T T i m s s U V i i m m i m i m i i m = = = ∫ ∫ ∑ σ ( , ) ; ; / .

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