Improved deterministic calculational methods for irregularly shaped shields

Abstract

A new discrete nodal transport method has been developed for general two-dimensional curvilinear geometry by using a boundary-fitted coordinate transformation from the general 'physical' coordinates to square 'computational' coordinates. The metrics which appear in the transformed transport equation are expanded using a simple polynomial function, and the angular divergence term is treated in the same way it is treated in S[sub N] methods for curved geometries. Because the metrics of the transformation depend upon the computational coordinates, the technical details of the formal development of the nodal method differ from those of ordinary nodal methods for rectangular geometry. However, the computational process in the transformed rectangular coordinate system is very similar to that used in conventional discrete nodal transport methods. A discrete S[sub N] method also has been developed to solve the boundary-fitted coordinate transformed transport equation. Simple test problems for non-simple geometries were solved using the zeroth-order nodal method, the first-order nodal method, and the S[sub N] method for the same physical and computational grids. The results for the test problems studied showed that, for most performance criteria, the computational efficiency of the zeroth-order nodal method was the highest of the three methods.