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.

Characteristics of the equilibrium fuel cycle for the core or a blanket of ADS having the structure of the core of a fast lead-cooled reactor of type BREST (Russian abbreviation for 'Bystryy Reaktor so Svintsovym Teplonositelem') in a mode of americium transmutation are calculated. Americium loading was taken 5% of heavy atoms. Keeping the average multiplication factor the same as in a standard equilibrium cycle, reactivity swing over 1 year's microcycle is about 1%, that demands partial fuel reloading with a periodicity of about one month. For one year of operation, 61 kg of americium is destroyed, and due to increased 238 Pu content, americium is mainly converted to fission products. Thus in a system of 1 GWt (thermal), 87 kg of americium can be transmuted yearly. The estimate of the reactivity void effect has shown that it increases to 0.6% almost linearly with the void fraction increasing up to 25% and reaches its maximum of 0.7% at a void fraction of about 50%. Application of similar strategy for ADS with a sub-criticality level ≈0.96-0.98 can essentially relax safety problems related to positive void effects.