Diffusion synthetic methods for computational modeling of one-speed slab-geometry transport problems with linearly anisotropic scattering

Highlights: • Analytical numerical methods. • Fixed-source S_N transport problems. • Spectral nodal methods. • Diffusion synthetic methods. • Analytical angular reconstruction scheme within each region of a multilayer slab. - Abstract: Two diffusion synthetic methods are described for computational modeling of one-speed, slab-geometry transport problems with linearly anisotropic scattering. These methods are referred to as diffusion synthetic methods, since the lower-order diffusion is used to simplify numerical solutions to the higher-order transport equation. In part I of this paper the word simplify is used in the sense of reducing the number of iterations to a prescribed stopping criterion; in other words, in the sense of accelerating the iteration on the scattering source in discrete ordinates (S_N) calculations, by generating an improved initial guess. In part II, the word simplify is used in the sense of generating numerical results for the angular flux by solving analytically the first-order form of the transport equation in slab geometry with diffusion approximation for the scattering source integral terms. As with these two offered synthetic methods, special approximate boundary conditions are used in the diffusion equation to account for prescribed incident flux on the outer boundaries of the slab, including vacuum boundary conditions. Numerical results are given to illustrate the application of these two synthetic methods.