Convergence Analysis of Additive Angular Dependent Rebalance Acceleration for the Discrete Ordinates Transport Calculations

In solving the discrete ordinates neutron transport equation, the additive angular dependent rebalance (AADR) acceleration method proposed by the authors previously is simple to implement, unconditionally stable, and very effective. For slab geometry problems, it is demonstrated via Fourier analysis that the spectral radii of the AADR acceleration in S₄-like and DP₁-like rebalances as well as DP₀-like rebalance are less than that of diffusion synthetic acceleration (DSA). This AADR acceleration method is easily extendable to DP_N-like and low-order S_N-like rebalancing, and it does not require consistent discretizations between the high-order and low-order equations as does DSA. The continuous Fourier analysis is also performed for rectangular geometry. This Fourier analysis shows that the AADR with directional S₂-like weighting functions, which uses two different rebalance factors for the x and y directions per octant, provides better results than the AADR with the normal S₂-like weighting functions, which uses a single weighting function per octant. The low-order equation in AADR is solved by a preconditioned Bi-CGSTAB algorithm, which reduces computational burden significantly.