A practical implementation of the higher-order transverse-integrated nodal diffusion method

• A practical higher-order nodal method is developed for diffusion calculations.
• The method resolves the issue of the transverse leakage approximation.
• The method achieves much superior accuracy as compared to standard nodal methods.
• The calculational cost is only about 50% greater than standard nodal methods.
• The method is packaged in a module for connection to existing nodal codes.

Transverse-integrated nodal diffusion methods currently represent the standard in full core neutronic simulation. The primary shortcoming of this approach is the utilization of the quadratic transverse leakage approximation. This approach, although proven to work well for typical LWR problems, is not consistent with the formulation of nodal methods and can cause accuracy and convergence problems. In this work, an improved, consistent quadratic leakage approximation is formulated, which derives from the class of higher-order nodal methods developed some years ago. Further, a number of iteration schemes are developed around this consistent quadratic leakage approximation which yields accurate node average results in much improved calculational times. The most promising of these iteration schemes results from utilizing the consistent leakage approximation as a correction method to the standard quadratic leakage approximation. Numerical results are demonstrated on a set of benchmark problems and further applied to a realistic reactor problem, particularly the SAFARI-1 reactor, operating at Necsa, South Africa. The final optimal solution strategy is packaged into a standalone module which may simply be coupled to existing nodal diffusion codes.