A modular nodal method for solving the neutron transport equation using spherical harmonics in two-dimensions

Thesis/Dissertation · Sun Jan 01 04:00:00 EST 1989

OSTI ID:6095997

Inanc, F

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{sub 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.

• Research Organization: Iowa State Univ. of Science and Technology, Ames, IA (USA)
• OSTI ID: 6095997
• Country of Publication: United States
• Language: English

Related Subjects

654003* -- Radiation & Shielding Physics-- Neutron Interactions with Matter
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BOUNDARY CONDITIONS
CALCULATION METHODS
COORDINATES
EQUATIONS
FUNCTIONS
LEGENDRE POLYNOMIALS
NEUTRAL-PARTICLE TRANSPORT
NEUTRON TRANSPORT
NEUTRON TRANSPORT THEORY
POLYNOMIALS
RADIATION TRANSPORT
SPHERICAL HARMONICS METHOD
TRANSPORT THEORY