High order variational solutions of time dependent neutron transport problems

Thesis/Dissertation · Tue Jan 01 04:00:00 EST 1985

OSTI ID:5794717

Wilson, B C

High order numerical solutions of the time-dependent one speed neutron transport equation are developed using cubic hermite polynomial trial functions, variational techniques, and exponential matrix operators. Two new numerical solutions are developed that are high order with respect to both time and space variables. In the first method, the time-dependent P/sub N/ equations are transformed into Generalized Telegrapher's Equations (GTE) that are valid for any order P/sub N/ approximation. The Generalized Telegrapher's Equations form a coupled set of second order differential equations with respect to both time and space. In the second method, the time-dependent P/sub N/ equations are transformed into coupled Transport Diffusion Equations (TDE), keeping the additional terms that maintain the transport nature of the solution. The Transport Diffusion Equations are first order in time and second order in space. Numerically evaluated time-dependent analytic solutions are also developed for homogeneous media transport problems in the P/sub 1/ and P/sub 3/ approximations via Laplace Transforms in order to validate the variational GTE and TDE solutions. The analytic solutions allow anisotropic scattering, up to the appropriate P/sub N/ order. The analytic solutions are not limited to the non-precise extrapolation boundary condition, like many time-dependent analytic P/sub N/ solutions, but allow any of the standard transport vacuum boundary condition approximations.

• Research Organization: Texas A and M Univ., College Station (USA)
• OSTI ID: 5794717
• 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
NEUTRON TRANSPORT THEORY
NUMERICAL SOLUTION
P1-APPROXIMATION
P3-APPROXIMATION
SPACE DEPENDENCE
SPHERICAL HARMONICS METHOD
TIME DEPENDENCE
TRANSPORT THEORY
VARIATIONAL METHODS