Acceleration of Response Matrix Method Using Cross-Section Scaling

Abstract

In this paper, an acceleration scheme for the red-black response matrix iteration is proposed. The proposed method is easily applied not only to newly developed codes but also to existing ones; cross-section sets are input by multiplying by a scaling factor, without requiring any code modification. The proposed method is called the cross-section scaling acceleration (CSA) method and is applicable to accelerate inner iteration of the response matrix calculation of second-order partial differential equations (e.g., diffusion, simplified P_N, and P_N). An eigenvalue analysis of the proposed method was carried out for one-group homogeneous problems. The analysis showed that the maximum eigenvalue of the red-black response matrix strongly depends on the scaling factor, and that the convergence of iteration becomes faster when an appropriate scaling factor is used. In the derivation of the response matrix, it was found that the CSA method is viewed as an alternative form of the acceleration method proposed by Lewis and Palmiotti. Although their method requires modifications of the response matrix, application of the CSA method is much easier. The CSA method was used for three test problems that cover a wide range of applications: a simple one-group, one-dimensional problem; a multigroup pressurized water reactor (PWR) assembly problem; and a more realistic multigroup PWR quarter-core problem. The calculation results of the test problems showed that the number of iterations can be reduced from 30 to 80% by utilizing the CSA method.