Modeling the diffusion yield of radioactive fission products from uranium dioxide fuel

The numerical aspects of a systematic solution of the problem of diffusion and yield of radioactive fission products from a homogeneous sphere, simulating a uranium dioxide fuel kernel, with realistic boundary conditions are discussed. The numerical scheme is based on a one-group method of calculating the production and radioactive mutual transmutations of fission products in combination with the standard expansion of the radial dependence of the concentration in terms of the eigenfunctions of the Laplace operator. It is demonstrated on illustrative examples that the approach is highly economical.