Criticality by the LTS_N Method

摘要

The one-dimensional discrete ordinates problem in a slab geometry, considering multigroup model and anisotropic scattering, was solved analytically by the LTS_N method. The idea embodied in this method consists in the application of the Laplace transform into the set of discrete ordinates equations (the S_N equations). The resulting algebraic linear system is then solved analytically for the transformed angular fluxes. The angular fluxes are then restored using the Heav-iside expansion technique. This formulation was also extended to two and three-dimensional discrete ordinates problems in Cartesian geometry. To reach this goal, the two and three-dimensional S_N equations are transformed, by integration, into sets of two and three one-dimensional S_N equations, named transverse integrated equations, which are then solved applying the one-dimensional LTS_N formulation. So far, the LTS_N method was derived to solve analytically the multidimensional discrete ordinates problems restricted to Cartesian coordinates system. Indeed, the generalization of this method to curvilinear orthogonal systems has special interest. Fortunately, the LTS_N formulation was extended for two-dimensional discrete ordinates problems, considering curvilinear coordinates system in a convex domain. To this end a transformal conformation, which maps the convex domain into circle, was devised. Notice that the well known transformation which maps the circle into rectangle were also employed. Thus, applying successively the above transformations, the convex domain is mapped into a rectangle.