Discrete Ordinates Methods for Transport Problems with Curved Spatial Grids.

Abstract

The method of characteristics (MOC) has been favored for many recent whole core transport codes; some current research codes are: the nTRACER code from Seoul National University, the MPACT code from the University of Michigan, and the Dragon code from Ecole Polytechnique de Montreal. However, it is well-known that whole core transport with MOC is both computational expensive and requires significant storage. On the other hand, discrete ordinates (SN) methods have been successfully applied to large systems, as has been demonstrated by the computer code Attila.

However, all previous discrete-ordinates methods implemented in available production computer codes were formulated only for problems containing spatial cells with planar boundaries. This creates geometric approximations and inefficiencies for modeling any physical system with curved boundaries â the curved boundaries must be approximated using a greatly many very fine spatial cells, each fine cell having a planar boundary.

In this thesis, we derive, implement, and test 2-D discrete ordinates methods, which are applicable for systems having curved interfaces between material regions, and which treat these curved surfaces analytically. The key benefits of "these" discrete ordinates methods on curved spatial grids over the MOC method include: (i) the ability to use standard highly-optimized quadrature sets, (ii) a single user-specified spatial grid, (iii) a simple extension to 3-D transport, and (iv) a small memory footprint for the computer.