Consistent pCMFD Acceleration Schemes of the Three-Dimensional Transport Code PROTEUS-MOC

Abstract

This paper presents the new acceleration schemes implemented in the three-dimensional (3-D) transport solver PROTEUS-MOC in conjunction with the fixed-point iteration (FPI) methods based on a single generalized minimal residual (GMRES) iteration and one or two transport sweeps per group in each outer iteration. In order to adopt a FPI scheme that employs only one or two inner iterations, single- and two-level consistent partial current–based coarse-mesh finite difference (pCMFD) acceleration methods were implemented to remove the instability problem of the consistent coarse-mesh finite difference (CMFD) method encountered when the inner iteration convergence is not sufficiently tight. In the spatial two-level acceleration method to speed up the lower-order diffusion calculations, the first level solves a fine-mesh finite difference fixed-source problem and the second level solves a CMFD eigenvalue problem. The implemented acceleration schemes were tested using the C5G7 benchmark problems, a critical core configuration of the Transient Reactor Test Facility (TREAT), and a C5G7 transient benchmark problem. Numerical test results showed that the consistent pCMFD acceleration is always stable even for the FPI methods with one inner iteration and that the single transport sweep method is always more efficient than the single GMRES iteration method. It was also observed that the two-level pCMFD acceleration in conjunction with the FPI with single transport sweep per outer iteration is very effective in reducing the number of outer iterations and the lower-order diffusion calculation time. Compared to the current iteration scheme of PROTEUS-MOC with fully converged GMRES iteration without acceleration, this acceleration reduced the total computational time by factors of 33.7, 19.9, and 26.0 for the two-dimensional C5G7, 3-D C5G7, and TREAT M8CAL criticality problems, respectively. The gain was even much larger for transient fixed-source problems (TFSPs) that are near critical. The speedup factor was 100 for one TFSP with subcriticality level of 40 mk and 519 for another TFSP with subcriticality level of 9 mk.

Keywords:

• Method of characteristics
• coarse-mesh finite difference
• two-level acceleration method
• Krylov iteration
• transient fixed-source problem

Acknowledgments

This research is being performed using funding received from the U.S. Department of Energy Office of Nuclear Energy’s Nuclear Energy University Program. The first author would like to thank Yunlin Xu at the University of Michigan for his very helpful discussions on the HO/LO algorithm.