A rebalance approach to nonlinear iteration 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. This method uses a lower equation at each iteration to improve the result of the higher equation. 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. The rebalance factor is expanded by DPN method. In this paper, DPo 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 discretization of the higher order and lower order equations do not generate instabilities. From the numerical calculations, we also show that the converged solution is highly tilted toward the solution of the lower order equation but with higher order angular quadrature set. Therefore, an inconsistent combination that consists of an accurate discretization of the lower order equation and a crude discretization of the higher order equation offers advantages over the consistent combination