Calculation of radiation fields in VVER shielding using approximations supporting local balance of materials mass and fission-source neutrons

The possibility of using approximations of geometry, which support the balance of materials mass on each spatial cell of a grid covering the computational region, to calculate radiation fields in VVER shielding by introducing additional mixtures of materials for cells where several initial materials are present is analyzed. The methods of combinatorial geometry, which are implemented in the MCU computer program for solving transfer equations by the Monte Carlo method, are used to specify the 3-D geometry of the shielding and a fuel-element and (or) fuel assembly fission source and the method of ray tracing is used to convert the combinatorial specification into a grid specification. A numerical experiment in which the VVER-1500 radiation shielding is calculated showed that the conservation of the materials mass/number of source neutrons in the grid cells during the conversion ensures rapid convergence of the results when the density of the spatial grid increases. Good agreement is attained between MCU Monte Carlo and KATRIN Sn calculations of VVER-1000 shielding.