A rebalance nonlinear iteration method for solving the neutron transport equations

A new nonlinear iteration method which can be used to solve the transport equations regardless of geometry and discretization is presented. The lower equation is derived by integrating the general discretized transport equation over coarse angular space only on cell boundaries. And the lower equation contains nonlinear correction (rebalance) factors that are angular dependent. In this paper, DP0 and DP1 expansions of the rebalance factor are tested. The method is analyzed via numerical calculations for various benchmark problems. The results show that the iterative convergence is always rapid independent of discretization schemes and that inconsistent discretizations of the higher order and lower order equations do not generate instabilities. (author)