Development of method based on perturbation theory for estimating and correcting errors in numerical solution of transport equation.

The numerical solution of the transport equation has the errors caused by the approximations used in the computational method. In the past estimations of these errors have been performed experimentally. In the present study, formulas to estimate the errors have been derived on the basis of the perturbation theory. This method enables us to deterministically estimate the numerical errors due to the iteration, spatial discretization and Legendre polynomial expansion of scattering transfer cross sections. Using the error estimation method developed in the present study, two examples of error analyses were carried out to confirm its validity and applicability to error estimation for a practical purpose. The errors of the calculated tritium breeding ratio for 7Li in a infinite slab geometry were estimated, and they agreed well with the values predicted from direct calculation. As the second example, error analysis was carried out for one-dimensional nuclear calculations on two types of commercial fusion reactor blankets. In this analysis the tritium breeding ratio and the fast neutron leakage flux from the inboard shield were investigated, and the errors from different causes were quantitatively compared.