An advanced nodal discretization for the quasi-diffusion low-order equations

The quasi-diffusion method was originally developed as a rapidly-convergent iterative technique for solving transport equations. In this method, the scattering source used in a given transport sweep is obtained from the solution of the quasi-diffusion low-order (QDLO) equations. The paper presents an advanced nodal discretization of the QDLO equations for global reactor core calculations. The advantage of quasi-diffusion is that it is able to capture transport effects at the surface between unlike fuel assemblies (i.e. MOX-UO₂) better than the diffusion approximation. We discretize QDLO equations with the advanced nodal methodology described by Palmtag for diffusion. The fast flux expansion consists of polynomial functions, while the thermal flux is expanded in a combination of polynomial and hyperbolic functions. The hyperbolic expansion functions proposed by Palmtag are the analytic solutions of the zero-source diffusion equation for the thermal flux. The specific form of the QDLO equations requires the derivation of new hyperbolic basis functions which are different from those proposed by Palmtag for diffusion. We have developed a discretization of the QDLO equations with node-averaged quantities, solving the 2-D equations using the weighted residual method. These node-averaged data are assumed known from single assembly transport calculations. We have written a code in 'Mathematica' that solves k-eigenvalue problems in 2-D Cartesian coordinates. The nodal quasi-diffusion low-order equations are solved numerically for several diffusion test problems, and realistic 'transport' problems. The results demonstrate the validity of the method. (author)