Nodal SN method for neutron transport equation in triangular geometry

Using the theory of area coordinate, arbitrary triangles were transformed into regular triangles. The transverse integration was done on the regular triangle. The spatial distribution of intra-node flux and source were approximated by a new orthogonal quadratic polynomial expansion, and a second-order polynomial provided the spatial expansion of transverse-leakage. The neutron angular distribution of flux and transverse-leakage were represented by the SN quadrature set. Additionally, the nodal-equivalent finite difference algorithm was applied in order to establish a stable and efficient iterative scheme. A two-dimension triangular nodal SN transport calculation program (DNTR) was coded according to the model. A series of numerical results for the test problems demonstrate that this triangular nodal SN method is faster 5 to 7 times than the fine mesh difference code (DOT4.2) with the same precision and faster 1 to 3 times than the rectangular discrete nodal transport method (DNTM) with the same precision and equal mesh width. However, this method can be applied to solve the unstructured neutron transport problems, and has an unexampled advantage of the nodal SN methods used on the structured meshes, such as DNTM. (authors)