Date of Award
Doctor of Philosophy
A. F. Rohach
A modular nodal method is developed for solving the neutron transport equation by using the spherical harmonics approximation in two dimensional Cartesian coordinates. The spherical harmonics approximation is based upon the second order even-parity form of the neutron transport equation. The boundary conditions of the spherical harmonics approximation are manipulated to have the forms analogous to the partial currents in the neutron diffusion equation. The relationships are developed for generating both the second order spherical harmonic equations and the boundary conditions in an automatic manner. The nodal method developed is based upon a least squares minimization technique. In that method, the spherical harmonic moments are expanded into fourth order Legendre polynomials. While some of the unknown coefficients are determined through the equations provided by the minimization scheme, the others are obtained through implementation of the boundary conditions in an integral sense. The order of the P[subscript]n approximation in the nodes are determined by the developed scheme in automatic manner. The distribution of the approximations orders may be different in different parts of the problem domain.
Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/
Inanc, Feyzi, "A modular nodal method for solving the neutron transport equation using spherical harmonics in two dimensions " (1989). Retrospective Theses and Dissertations. 9200.