The Slice Balance Approach (SBA) is an approach for solving geometrically-complex, neutralparticle transport problems within a multi-group discrete ordinates (SN) framework. The salient feature is an angle-dependent spatial decomposition. We approximate general surfaces with arbitrary polygonal faces and mesh the geometry with arbitrarily-shaped polyhedral cells. A celllocal spatial decomposition divides cells into angle-dependent slices for each SN direction. This subdivision follows from a characteristic-based view of the transport problem. Most balancebased characteristic methods use it implicitly; we use it explicitly and exploit its properties. Our mathematical approach is a multiple balance approach using exact spatial moments balance equations on cells and slices along with auxiliary relations on slices. We call this the slice balance approach; it is a characteristic-based multiple balance approach. The SBA is intentionally general and can extend differencing schemes to arbitrary 2D and 3D meshes. This work contributes to development of general-geometry deterministic transport capability to complement Monte Carlo capability for large, geometrically-complex transport problems. The purpose of this paper is to describe the SBA. We describe the spatial decomposition and mathematical framework and highlight a few interesting properties. We sketch the derivation of two solution schemes, a step characteristic scheme and a diamond-difference-like scheme, to illustrate the approach and we present interesting results for a 2D problem.
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