Acceleration of response matrix method by cross section scaling

In this paper, a new acceleration scheme for the red-black response matrix iteration is proposed. The proposed method is easy to apply not only to newly developed codes but also to existing codes; cross section sets are input by multiplying by a scaling factor, without requiring code modification. The proposed method is called the cross-section scaling acceleration (CSA) method and is applicable to accelerating inner iteration of the response matrix calculation of second-order partial differential equations (e.g. diffusion, simplified Pn and Pn). 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. The CSA method was also used for three test problems that cover a wide range of applications: a simple one-group, one-dimensional problem, a multi-group PWR assembly problem, and a more realistic multi-group 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. The relationship between the CSA method and the discontinuity factor is also discussed in this paper. (author)