Development of a cross section self-shielding method in arbitrary geometry

We are developing a neutron transport calculation code based on the Iso-Geometric Analysis (IGA) method that can resolve the multi-group neutron transport equation for any arbitrary spatial domain. The energy variable is treated with multi-group theory. Therefore, self-shielding calculations become necessary. We have decided to adopt the subgroup method because this method does not rely on any specific geometrical domain and should be used in combination with the IGA method. Some basic theory of the IGA method is given to introduce the concept of basis function and NURBS for the representation of the spatial domain. Validation of the implementation of the subgroup method for IGA and S-N transport calculations is presented. The result is that the combination of S-N transport theory, IGA and the subgroup method gives correctly shielded cross-sections. Thus, effective multi-group cross-sections can be generated for any arbitrary spatial domain.