An Improved Algebraic Collapsing Acceleration with General Boundary Conditions for the Characteristics Method

A detailed derivation of the algebraic collapsing acceleration (ACA), a synthetic acceleration of the characteristics method, is presented. An improvement of the synthetic hypothesis is proposed, and the corrective system is derived for general boundary conditions. Both Fourier and direct spectral analyses of the accelerated iterations for a one-dimensional slab geometry are given. The solving strategy for the corrective system along with implementation details about the method of characteristics is discussed. Numerical results for a one-group, two-dimensional benchmark are provided to illustrate the basic synthetic hypothesis and the enhancement of its robustness with the proposed two-step collapsing hypothesis. The practical performance of ACA is illustrated on a pressurized water reactor-type assembly in the context of multigroup eigenvalue calculations.