Unstructured coarse mesh finite difference method to accelerate k-eigenvalue and fixed source neutron transport calculations

Unstructured coarse mesh finite difference (CMFD) method was implemented to accelerate the k-eigenvalue and fixed source neutron transport calculations in the nodal SN transport code DNTR, which was based on arbitrary triangular-z meshes. The same triangular-z meshes were adopted in the CMFD calculation to accommodate the arbitrary problem boundaries and simplify the coarse mesh generation and mapping processes. Two-level CMFD formulations were derived for the k-eigenvalue problems, and the few-group CMFD calculation was used to speed up the convergence of the multigroup CMFD calculation. For the fixed source problems in the neutronics analyses of subcritical reactors or transient neutron transport calculations, a special ks iteration method by introducing the source multiplication factor ks was employed in the SN transport calculation to remove the dependence of the convergence rate on the subcriticality. Multigroup CMFD formulations were established to accelerate the convergence of the ks iteration procedure in the fixed source neutron transport calculation. The acceleration effects of CMFD on the k-eigenvalue and fixed source calculations were verified using four representative neutron transport problems, i.e. the small fast breeder reactor with Cartesian boundaries, the BN-600 fast reactor with hexagonal boundaries, the space nuclear power reactor with cylindrical boundaries, and the accelerator driven subcritical reactor with hexagonal boundaries. The numerical results showed that for the first three eigenvalue problems, the multigroup CMFD achieved a speedup of total computation time by a factor of 2-5, and the two-level CMFD reduced the computation time by a factor of 3-7. It was also shown that the multigroup CMFD was able to accelerate the ks iteration procedure in the fixed source problems by a factor of about 6. The implementation of the unstructured CMFD method turns the DNTR code into an efficient neutron transport solver with flexible geometry treatment capability for both k-eigenvalue and fixed source problems.