Spatial Transients in Finite Volumes

Abstract

In diffusion theory, the so‐called material buckling gives the length of a vector but not its components. Even in the simplest slab geometry we need two such vectors to construct a solution to a simple boundary‐value problem. One guesses that the more complex the geometry or the more complicated the function prescribed on the boundary, the more buckling vectors are needed to construct the unique analytical solution of a nonhomogeneous problem. We derive a relationship between the bucklings occurring in the analytical solution, on the one hand, and the space‐dependent function prescribed on the boundary as well as the equation of the boundary, on the other hand. We propose a (linear) transport problem solution method based on the Case eigenfunction expansion.

Keywords:

• Neutron transport
• neutron diffusion
• boundary value problem