Composite Spatial Grid Nodal Method with Exponential Approximations in Discrete Ordinate Formulation for Non-multiplying Homogeneous Mediums

Abstract

Neutron transport problems in non-multiplying media appear in several applications in science and engineering, with emphasis on the design of shielding structures.  In this work, we present the composite spatial grids spectral nodal method with an exponential approximation for neutron transport problems in homogeneous non-multiplying media.  We use as a mathematical model the discrete ordinates formulation in two-dimensional Cartesian geometry with one-speed approximation and isotropic scattering source. The discretization process is done in two steps like is as composite spatial grid methods. An exponential function is used to approximate the transverse leakage terms in the region. The multi-step discretization mechanism transforms the two-dimensional problem into two coupled one-dimensional problems, that are solved using the alternative directions iterative scheme. Numerical results are offered for a model problem, showing that the proposed method generates accurate results with a low computational cost.