Higher-order boundary condition perturbation methods in transport and diffusion theory

Boundary condition perturbation techniques have primarily been limited to first-order analysis in flux and eigenvalue. The purpose of this research is to develop higher-order boundary condition perturbation techniques in diffusion and transport theory. The formalisms presented require two adjoint functions to be solved to compute all the higher-order terms. One of the adjoint functions is a Green's function and requires special techniques for a solution. Several examples are provided to verify the validity of the formalisms presented. Analytical and numerical examples are provided for the diffusion approximation examples. Due to the complexity of transport theory, only numerical examples are shown.; Special numerical techniques needed for the solution of the higher-order terms will be discussed. A nodal code that has its homogenization parameters and discontinuity factors corrected by the higher-order perturbation methods is developed for a monoenergetic, one-dimensional slab. This code demonstrates that this theory can increase the accuracy of a coarse mesh code with little additional computational time added.