Doctor of Philosophy / Department of Mechanical and Nuclear Engineering / J. Kenneth Shultis / A method for deterministically calculating the population variances of Monte
Carlo particle transport calculations involving weight-dependent variance
reduction has been developed. This method solves a set of equations developed by
Booth and Cashwell [1979], but extends them to consider the weight-window variance reduction technique. Furthermore, equations that calculate the duration of a single history in an MCNP5 (RSICC version 1.51) calculation have been developed as well. The calculation cost, defined as the inverse figure of merit, of a Monte Carlo calculation can be deterministically minimized from calculations of the expected variance and expected calculation time per
history.The method has been applied to one- and two-dimensional multi-group and mixed
material problems for optimization of weight-window lower bounds. With the
adjoint (importance) function as a basis for optimization, an optimization mesh
is superimposed on the geometry. Regions of weight-window lower bounds
contained within the same optimization mesh element are optimized together with
a scaling parameter. Using this additional optimization mesh restricts the size
of the optimization problem, thereby eliminating the need to optimize each
individual weight-window lower bound.
Application of the optimization method to a one-dimensional problem, designed to
replicate the variance reduction iron-window effect, obtains a gain in
efficiency by a factor of 2 over standard deterministically generated weight
windows. The gain in two dimensional problems varies. For a 2-D block problem
and a 2-D two-legged duct problem, the efficiency gain is a factor of about 1.2.
The top-hat problem sees an efficiency gain of 1.3, while a 2-D 3-legged duct
problem sees an efficiency gain of only 1.05. This work represents the first attempt at deterministic optimization of Monte
Carlo calculations with weight-dependent variance reduction. However, the
current work is limited in the size of problems that can be run by the amount of
computer memory available in computational systems. This limitation results
primarily from the added discretization of the Monte Carlo particle weight
required to perform the weight-dependent analyses. Alternate discretization
methods for the Monte Carlo weight should be a topic of future investigation.
Furthermore, the accuracy with which the MCNP5 calculation times can be
calculated deterministically merits further study.
| Identifer | oai:union.ndltd.org:KSU/oai:krex.k-state.edu:2097/7014 |
| Date | January 1900 |
| Creators | Solomon, Clell J. Jr. |
| Publisher | Kansas State University |
| Source Sets | K-State Research Exchange |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation |
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