The response matrix acceleration: A new non-linear method for the 3D discrete-ordinate transport equation

Abstract

In this paper, we propose a new non-linear technique for accelerating the solution of the discrete ordinates transport equation. The new method, called Response Matrix Acceleration (RMA), has been designed to complement the Coarse-Mesh Finite Difference method (CMFD) by offering better stability and improved performance in cases where CMFD fails. To accomplish this, RMA uses knowledge of the transport operator along with nonlinear coefficients and solves for the interface partial currents to maintain consistency with the transport operator. Two distinct variants of RMA are derived. The convergence properties of both variants of RMA applied the source iteration schemes are investigated for the one-group transport operator. Analysis of the results indicates that both variants of RMA have improved effectiveness and stability relative to CMFD, for optically diffusive materials. To achieve optimal numerical performance, a combination of RMA and CMFD is suggested. Improvements in the performance of RMA are expected with ongoing development and optimization. Further investigation into the use of RMA for accelerating outer iterations, parallel problems, and different transport operators is proposed. The results of a spectral radius analysis are presented, along with a strong scaling benchmark using the 3D C5G7 MOX problems. Furthermore, two real-scale problems, the whole-core EOLE reactor simulation and a PWR assembly simulation, are studied to assess the performances of the new method in a parallel computing framework using the constant and linear short characteristics of the IDT solver in APOLLO3®.