Improved discrete nodal transport method for treating void regions

To solve neutron transport problems with void regions accurately and efficiently, the legacy discrete nodal transport method (DNTM) was improved in three-dimensional Cartesian geometry. Firstly, the efficient nodal-equivalent finite difference (NEFD) algorithm was modified, named M-NEFD, to directly treat the zero total cross section in the denominator for void nodes. Furthermore, an angle projection discrete-ordinates (APSN) method was proposed to combine with the NEFD algorithm, named APSN-NEFD, to treat the void regions without sweeping the void nodes one by one. Thirdly, the angular sweeps within one octant of both M-NEFD and APSN-NEFD were parallelized using OpenMP. Based on these improvements, a discrete-ordinates nodal transport code named NECP-HONESTY has been developed in three-dimensional Cartesian geometry. To test the performance of the method and the code, a fission-source problem with two small void regions and a fixed-source problem with one large void region were presented in this paper by comparing with the Monte Carlo method. It has been demonstrated by the numerical results that the improved DNTM can provide accurate eigenvalue and scalar flux, no matter directly sweeping the void nodes with M-NEFD or skipping the void regions with APSN. In addition, compared with M-NEFD, APSN-NEFD can efficiently reduce both computing time and storage requirement for problem with large void regions.