Matrix MOC: The method of characteristics in matrix form

Abstract

Conventionally, tens to hundreds times of repeated characteristic sweeping is required for the Method of Characteristics (MOC) to converge within the inner-outer iteration scheme, even with the acceleration techniques like CMFD and CMR employed to improve the convergence rate. Therefore, the Matrix MOC, which converts the characteristic sweeping into a linear system, was proposed attempting to accelerate the characteristic sweeping itself. However, it is computationally intensive if not prohibitive to construct and store the coefficient matrices in the explicit form. This study proposes four principle numerical properties of the coefficient matrices in the Matrix MOC. Exploiting these properties reduces significantly the memory consumption and the computational time, making it possible to explicitly store the sparse coefficient matrices in CSR (Compressed Sparse Row) scheme for large problems. The multi-group coupling GMRES (Generalized Minimal RESidual) solver is then employed to solve the Matrix MOC equations of all groups simultaneously. Since the matrices are stored explicitly in CSR scheme, the operations involving sparse matrices and vectors are performed by taking advantage of the fully optimized Intel® MKL library. The Matrix MOC based 2D code named TIGER is developed, and verified by the BWR lattice benchmark and several variations of the C5G7 problem. Numerical results demonstrate that the Matrix MOC with the proposed numerical properties has adequate accuracy, and is feasible to solve a 2D small core problem on an ordinary PC with explicitly stored matrices. In addition, the optimal parameters of the multi-group coupling GMRES solver are investigated by sensitivity analysis to get the highest computational efficiency.