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# Accession Number:

## ADA239329

# Title:

## A Time Dependent Transport Equation Solver

# Descriptive Note:

## Doctoral thesis

# Corporate Author:

## AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH

# Report Date:

## 1991-05-01

# Pagination or Media Count:

##
159.0

# Abstract:

## A new time dependent neutron and photon transport code was developed. The code, FMP2DT Finite element, Multigroup, P sub n, 2-Dimensional, Time dependent, was discretized in space using finite elements, discretized in energy using a multigroup approximation, and discretized in time using Euler backward differencing scheme. Its angular flux dependency was discretized using spherical harmonics. A P sub 1 angular flux approximation allows some modeling of both anisotropic flux behavior and wave behavior. FMP2DT can model radiation transport in XZ slab or RZ cylindrical geometry. An inherently stable iteration solution scheme, an incomplete Cholesky conjugate gradient algorithm, calculates the total flux coefficients. FMP2DT was benchmarked against exact flux calculations in infinite XZ and RZ geometries. Two problems were solved by FMP2DT which involved the observation of the flux decay after injection of an inhomogeneous pulsed source to the configurations. A nuclear reactor, initially critical, had a pulsed source introduced at its center. This is typically done in so called Rossi-alpha experiments. FMP2DT showed that time must be allowed so that only the fundamental mode is dominant or the flux data will not yield credible information to calculate alpha. A uranium borehole problem was solved where FMP2DT showed that a counting instrument must be calibrated for different distances from a pulsed source because the flux decays with a different decay constant for each spatial point. Previous models did not account for this diffusion effect.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#