Analytical spatial reconstruction scheme for the coarse-mesh solutions generated by the constant spectral nodal method for monoenergetic discrete ordinates transport calculations in X,Y geometry fission–chain reacting systems

Nodal methods are widely regarded as forming an accurate class of coarse-mesh methods for neutron transport problems in the discrete ordinates (SN) formulation. They are also viewed as efficient methods, as the number of floating point operations generally decrease, as a result of the reduced number of mesh points; therefore they generate accurate results in shorter running time. However, the coarse-mesh numerical solutions do not yield detailed information on the solution profile, as the grid points can be located considerably apart from each other. In this paper, we describe an analytical spatial reconstruction of coarse-mesh solutions of the SN transverse integrated nodal equations with constant approximations for the transverse leakage terms, as generated by the hybrid spectral diamond–spectral Green’s function–constant nodal (SD–SGF–CN) method for monoenergetic SN eigenvalue problems in X,Y geometry for neutron multiplying systems. Numerical results for typical model problems are given and we close with general concluding remarks and suggestions for future work.

► The hybrid SD–SGF–CN spectral nodal method.
► Accurate coarse-mesh solution to SN eigenvalue problems in X,Y geometry.
► Analytical spatial reconstruction scheme within each discretization node.
► Accurate flux profile generated from the spatial reconstruction scheme.