The Green's function method for nuclear engineering applications

The Green's function method (GFM) is employed to obtain scalar and angular flux distributions in heterogeneous slab geometry with isotropic scattering. All solutions utilize the infinite-medium Green's function to obtain results in finite media. Past Green's function analyses that do not resort to expansions of the angular flux in basis functions have been performed for nonmultiplying media only; in this paper, results are provided, for the first time, for both multiplying and nonmultiplying media using the GFM. Several source configurations are considered, including a beam source on the leftmost face, isotropic incidence on any face, and constant inhomogeneous volume sources in internal materials. Scalar and angular flux distributions compare favorably with those obtained using the FN method as well as the ONEDANT discrete ordinates code. In addition, the single and heterogeneous critical slab problems are investigated and solved using the GFM.