Invariant imbedding in space-energy coordinates for semi-infinite media in the range of thermal energies

Thesis/Dissertation · Fri Jan 01 04:00:00 EST 1982

OSTI ID:5497526

Zukor, D J

Starting with a one-dimensional rod model, the method of invariant imbedding was extended to include energy dependence. This was accomplished by developing a system of nonlinear, partial differential equations which permitted an arbitrary number of energy groups. A FORTRAN IV code was written to solve the derived equations using the Runge-Kutta technique for integrating in space and an iterative technique to include both upscattering and downscattering in energy. The one-dimensional rod model was used as a sample case to verify the numerical algorithms for the case of no energy dependence. Agreement for this case was exact. To verify that the code operated properly for semi-infinite media at thermal energies a semi-infinite medium was modeled using a thick slab of hydrogen. Using the HAMMER code, an eight group broad group cross section set was calculated. Using these cross sections, the ANISN transport theory code was used to determine the reflection function from the slab. The results were compared to those obtained using the invariant imbedding code. Good agreement was found and the invariant imbedding code required less computing time.

• Research Organization: Maryland Univ., College Park (USA)
• OSTI ID: 5497526
• Country of Publication: United States
• Language: English

Related Subjects

654001 -- Radiation & Shielding Physics-- Radiation Physics
Shielding Calculations & Experiments
658000* -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
COMPARATIVE EVALUATIONS
ELEMENTS
ENERGY DEPENDENCE
FORTRAN
HYDROGEN
INVARIANT IMBEDDING
ITERATIVE METHODS
NONLINEAR PROBLEMS
NONMETALS
NUMERICAL SOLUTION
ONE-DIMENSIONAL CALCULATIONS
PROGRAMMING LANGUAGES
RUNGE-KUTTA METHOD
SLABS
TRANSPORT THEORY