Convergence and Acceleration of Void Iterations in Boiling Water Reactor Core Calculations

A theoretical background for the convergence of void iterations in boiling water reactor (BWR) core calculations is considered. First, the process of each void-iteration step is interpreted as a transformation in a set of vectors representing the characteristics of the core, and the condition for convergence is derived in terms of the spectral radius of the transformation operator. Second, to visualize the convergence condition, the concept of a trajectory of channel power is introduced. Third, it is explained that the spectral radius of the transformation operator can be changed by changing the number of source iterations within each void iteration step. Based on this analysis, an optimum number of source iterations, when the Chebyshev polynomial acceleration technique is employed, is estimated for a typical BWR core. Numerical examples, presenting both divergent and convergent cases, show the validity of the present theoretical analysis.