Convergence analysis of the angular-dependent rebalance iteration method in X-Y geometry

Abstract

Recently, the angular dependent rebalance (ADR) method was developed for acceleration of the scattering source iteration (SI) and applied to various spatial differencing schemes of the discrete ordinates transport method in one- and two-dimensional geometries. In ADR, the lower-order equation is derived by integrating the rebalance form of the discretized transport equation over a coarse angular space. As a result, the lower-order equation resembles the transport equation, and the ADR method can be very easily implemented for various numerical transport methods in general geometry. However, it is difficult to theoretically analyze the stability of the ADR method since the ADR method is nonlinear. The authors study the convergence properties of the ADR iteration method via Cefus and Larsen`s approach (linearization and Fourier analysis) for step characteristic (SC) and constant-constant (C-C) spatial differencing schemes in infinite homogeneous X-Y geometry. The results show that the ADR method is unconditionally stable in such an ideal situation, giving confidence in the observed stability in finite heterogeneous problems.