Acceleration of Sn Eigenvalue Calculation with Coarse Mesh Formulation Employing Angular Flux Discontinuity Factors

Abstract

A homogenized coarse mesh SN formulation employing angular flux discontinuity factors (AnDFs) is derived as a means of efficient acceleration of the underlying two-dimensional heterogeneous fine mesh transport calculations. The homogenization parameters for the coarse mesh SN problem are generated by using the partially converged fine mesh heterogeneous SN solution and the solution of the homogenized coarse mesh SN problem provides the fine mesh problem with fast converging global fission source distributions. In order to make the coarse mesh SN problem equivalent with the reference heterogeneous problem, the angle dependent homogenized total cross sections as well as AnDFs are employed. While the angle dependent total cross sections are directly generated from the partially converged fine mesh problem solution, the AnDFs are generated by using the solution of the pilot coarse mesh calculation in which AnDFs are not used. In addition to spatial homogenization, angular condensation is employed in the coarse mesh problem for faster acceleration. It is confirmed by solving a few cases of severely heterogeneous problems that the homogenized problem can be made fully consistently with the reference heterogeneous problem with these homogenization parameters. It is observed that large errors of about 1400 pcm in reactivity and 7 % in the fission source distribution encountered in the mere volume weighted homogenization case disappear with the use of AnDFs and the angle dependent total cross sections. An alternating calculation scheme involving the fine mesh and coarse mesh SN calculations is set up to accelerate the power iteration of the fine mesh calculation by adjusting the fine mesh fission source distribution using the coarse mesh one through the modulation process. It is demonstrated from the applications to various problems with different compositions and core sizes that the performance of the acceleration scheme is outstanding in that the number of the fine mesh SN power iterations can be reduced below 10 while reproducing exactly the original solution regardless of the core size. In other words, it appears that the convergence of the coarse mesh SN formulation does not reveal any significant dependence on the problem size so that the effectiveness of the acceleration scheme becomes stronger for the larger problems having higher dominance ratios leading to a significant reduction in the computing time by a factor 84 for a 9x9 fuel assembly quarter core test problem.