Integral Methods in Science and Engineering pp 309-320 | Cite as

# The Nodal *LTS*_{N} Solution in a Rectangular Domain: A New Method to Determine the Outgoing Angular Flux at the Boundary

## Abstract

In the present contribution we discuss the neutron nodal *S*_{N} equation in a rectangular domain. The nodal method consists in transverse integration of the *S*_{N} equation and results in coupled one-dimensional *S*_{N} equations with unknown angular flux at the border. In the literature, the outgoing angular flux is considered a constant or exponential decreasing function, where the latter is used in this work. It is noteworthy that solutions found with these boundary conditions present unphysical results, i.e. negative angular fluxes in the border region, whereas the scalar flux is semi-positive definite. To overcome these shortcomings a new approach is proposed. The rectangular domain is covered by a finite discrete set of narrow rectangular sub-domains, so that in each rectangle the solution may be approximated by the one from a one-dimensional problem. Upon applying the *LTS*_{N} method combined with the DNI technique, i.e. interpolating the directions of the two-dimensional problem by means of one-dimensional directions, one obtains the angular flux at the border from the known one-dimensional *LTS*_{N} solution for any desired point. Numerical simulations and comparisons with results found in the literature are presented.

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