Variational coarse mesh nodal method for the solution of two dimensional neutron transport problems

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

OSTI ID:5570545

Dilber, I R

The even-parity form of the within-group transport equation with isotropic source and cross sections is formulated variationally to yield coarse mesh methods for the solution of two-dimensional neutron transport problems. Two candidate functionals are studied in the diffusion approximation for truncation errors due to flux, partial current, and source approximations. It is observed that one of the methods closely resembles conventional nodal methods successfully used in diffusion theory. However, unlike the conventional modal methods, this method does not necessitate node-to-node interpolation of the transverse leakage term, and it is capable of delivering detailed flux distributions within each coarse mesh node. Moreover, numerical results obtained in the diffusion approximation indicate that this method allows the use of lower orders of flux, current or source approximations compared to the other candidate method. The method is then extended to solve two-dimensional one-group fixed source transport problems. Numerical results obtained with a P3 approximation indicate that the method is capable of delivering average fluxes as well as detailed flux distributions with relatively coarse node sizes. Finally, the code is shown to have substantial parallelism for efficient vectorization, therefore, giving promise for three-dimensional transport calculations.

• Research Organization: Northwestern Univ., Evanston, IL (USA)
• OSTI ID: 5570545
• Country of Publication: United States
• Language: English

Related Subjects

654003* -- Radiation & Shielding Physics-- Neutron Interactions with Matter
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
DIFFERENTIAL EQUATIONS
EQUATIONS
MESH GENERATION
NEUTRON DIFFUSION EQUATION
NEUTRON FLUX
NEUTRON TRANSPORT THEORY
NUMERICAL SOLUTION
P3-APPROXIMATION
RADIATION FLUX
SPHERICAL HARMONICS METHOD
TRANSPORT THEORY
TWO-DIMENSIONAL CALCULATIONS