Comparison of 1-D/1-D Fusion Method and 1-D/1-D Hybrid Method in Two-Dimensional Neutron Transport Problems: Convergence Analysis and Numerical Results

Two two-dimensional/one-dimensional (2-D/1-D) methods, fusion and hybrid, have been developed and reported in the literature to deal with three-dimensional (3-D) heterogeneous reactor problems and to avoid direct 3-D transport calculations. The 2-D/1-D fusion method transforms a 3-D transport problem into 2-D and 1-D transport problems that have a smaller computational burden than the original problem. The hybrid method uses an additional diffusion (or SP₃) approximation in the axial direction to enhance the efficiency of the calculation.

This paper presents and compares the stability and the accuracy of the two methods. To this end, a 2-D transport problem is considered by reducing one dimension in the radial direction, leading to 1-D/1-D fusion or hybrid method. Fourier stability analysis is used to study the stability and the convergence behaviors of the two methods. With respect to accuracy, the two methods are compared via numerical solutions on a typical 2-D reactor problem. The results indicate that the fusion method is stable and gives a very accurate transport solution. On the other hand, the hybrid method requires a stabilizing scheme, and the diffusion approximation in the axial calculation causes significant errors.