Taylor projection mesh coupling between three-dimensional discontinuous grids for SN

In three-dimensional discrete ordinates (SN) transport methods, it is desirable (and at times necessary) to use discontinuous spatial grids in coarse cells or at material interfaces. On a single processor machine, variable meshing permits high definition in regions of interest, with coarse grids used in less important regions. In parallel processing, variable meshing can be used to reduce load imbalances in problems spatially decomposed over large processor arrays. In a typical SN iterative solution scheme, a source iteration is performed, followed by sweeps in angular flux for each discrete ordinate using a spatial differencing scheme. As the sweeps progress through the various spatial grids in a problem, particle conservation must be maintained at any discontinuous grid interfaces. Typically, this is accomplished using a simple balance of particles streaming across a boundary surface, resulting in a zeroth-order approximation. This procedure works well in the case of sweeps progressing from fine grids to coarse grids; however, a loss of information occurs as angular sweeps progress from coarse grids to fine grids. This paper describes a first-order Taylor Projection Mesh Coupling (TPMC) scheme for an x-y-z SN method that attempts to mitigate the loss of angular flux information as sweeps are made from coarse to fine grid surfaces