Neutron Diffusion Variational Nodal Method Based on Arbitrary Triangular Mesh

The traditional core calculation code based on rectangular and hexagonal geometry cannot be applied to the calculation of new type reactors with complex geometry, the study of multigroup neutron diffusion variational nodal method based on arbitrary triangular meshes was carried out in this paper. Firstly, ANSYS program was used to divide the calculation area into arbitrary triangular meshes, which was then transformed into regular triangles by coordinate transformation method. Secondly, the Galerkin variation technique was employed to establish the functional containing the nodal neutron balance equation and the internal variables of the triangular nodal were expanded using the orthogonal basis functions of the regular triangle. Finally, the variational principle was used to obtain the response relationship between the neutron flux and the surface neutron current, and then the traditional source iteration method was carried out to solve the equations. The code named TriVNM was developed based on the above theoretical model, and verified by diffusion benchmark with different geometries. The results show that the keff and relative power distribution calculated by TriVNM agree well with the reference results, and this method can be applied to diffusion calculation for reactor core with complex geometry.