Integral transport theory is used to compute transfer matrix elements for neutral particle streaming through r-z rectangular voids. The transfer matrix is utilized in a hybrid method; it interfaces with a conventional discrete ordinates calculation outside the void. Since the hybrid interface is accomplished within the inner iteration of an existing discrete ordinates code, standard sweeping schemes used in SN codes are not adversely affected. The resulting transfer matrix is independent of the multigroup energy structure used in a calculation. Further, the transfer matrix is not affected by changes in materials or cross sections outside the void. For these reasons, once a transfer matrix is calculated it can be used in a wide variety of problems containing a similar void. In this study, the transfer matrix hybrid, standard discrete ordinates, and Monte Carlo methods are applied to two sample problems to compare the accuracy of these methods. The Monte Carlo results are considered correct in order to compute errors in the deterministic calculations. The transfer matrix hybrid method is more accurate than conventional SN methods; the ray effect, persistent in discrete ordinates calculations, is substantially reduced. In addition, the transfer matrix hybrid executes faster than higher order SN calculations.

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The analytical solution to a model time-dependent continuous lethargy photon transport equation is evaluated numerically to obtain a benchmark solution using the Laplace transforms coupled with the multiple collision expansion method. The benchmark solution is then used to check the accuracy of the multigroup approximation. Excellent agreement between continuous lethargy benchmarks and multigroup approximation is obtained.

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Bibliography : leaves 211-216 / 216 leaves : ill ; 20 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics, 1994?

Benchmark calculations are performed for neutron transport in a two material (binary) stochastic multiplying medium. Spatial, angular, and energy dependence are included. The problem considered is based on a fuel assembly of a common pressurized water nuclear reactor. The mean chord length through the assembly is determined and used as the planar geometry system length. According to assumed or calculated material distributions, this system length is populated with alternating fuel and moderator segments of random size. Neutron flux distributions are numerically computed using a discretized form of the Boltzmann transport equation employing diffusion synthetic acceleration. Average quantities (group fluxes and k-eigenvalue) and variances are calculated from an ensemble of realizations of the mixing statistics. The effects of varying two parameters in the fuel, two different boundary conditions, and three different sets of mixing statistics are assessed. A probability distribution function (PDF) of the k-eigenvalue is generated and compared with previous research. Atomic mix solutions are compared with these benchmark ensemble average flux and k-eigenvalue solutions. Mixing statistics with large standard deviations give the most widely varying ensemble solutions of the flux and k-eigenvalue. The shape of the k-eigenvalue PDF qualitatively agrees with previous work. Its overall shape is independent of variations in fuel cross-sections for the problems considered, but its width is impacted by these variations. Statistical distributions with smaller standard deviations alter the shape of this PDF toward a normal distribution. The atomic mix approximation yields large over-predictions of the ensemble average k-eigenvalue and under-predictions of the flux. Qualitatively correct flux shapes are obtained, however. These benchmark calculations indicate that a model which includes higher statistical moments of the mixing statistics is needed for accurate predictions of binary stochastic media k-eigenvalue problems. This is consistent with previous findings. / Graduation date: 2005

The implicit Monte Carlo (IMC) method [16] for radiative transfer, developed in 1971, provides numerical solutions to the tightly-coupled, highly-nonlinear radiative heat transfer equations in many physical situations. Despite its popularity, there are instances of overheating in the solution for particular choices of time steps and spatial grid sizes. To prevent overheating, conditions on teh time step size Δt have been sought to ensure that the implicit Monte Carlo (IMC) equations satisfy a maximum principle. Most recently, a discrete maximum principle (DMP) for teh IMC equations has been developed [32] that predicts the necessary time step size for boundedness given the spatial grid size. Predictions given by this DMP assumed equilibrium thermal initial conditions, was developed using pseudo-analytic and symbolic algebra tools that are computationally expensive, has only been applied to one-dimensional Marshak wave problems, and has not considered the evolution of the DMP predictions over multiple time steps. These limitations restrict the utility of the DMP predictions. We extend the DMP derivation to overcome these limitations and provide an algorithm that can be introduced into IMC codes with minimal impact on simulation CPU time. This extended DMP effectively treats non-equilibrium thermal initial conditions, decreases calculation time by using multigroup approximations in frequency, considers multiple spatial dimensions with an arbitrary number of neighboring sources, and overcomes inherent difficulties for the DMP in time-dependent problems. Disequilibrium in the initial conditions is introduced through a redefinition of existing terms from [32] to different radiation and material temperatures on the first time step. This results in a limiting DMP inequality similar in form to the original. Multifrequency approximations are then applied by assuming separation of variables. Energy deposition from multiple sources is assumed to follow linear superposition and the DMP from [32] is re-derived to incorporate multiple incident sources of energy in multiple dimensions. Lastly, an inherent flaw in the DMP resulting in poor predictions when temperature varies slowly over a region is overcome by developing a threshold temperature difference, above which the DMP operates. We have numerically implemented these improvements and validated the results against IMC solutions, showing the predictive capacity of the more general DMP algorithm. We find the disequlibrium conditions to be properly incorporated into the DMP, and multifrequency approximations to be accurate over a large range of time step and spatial grid sizes. The linear superposition assumption is generally very accurate, but infrequently leads to DMP predictions which are not conservative. We also demonstrate that the temperature difference threshold prevents inaccurate predictions by the DMP while preserving its functionality. / Graduation date: 2013

Several computer codes based on one and two-group diffusion theory models were developed for SHUFFLE. The programs were developed to calculate power distributions in a two-dimensional quarter core geometry of a pressurized power reactor. The various coarse-mesh numerical computations for the power calculations yield the following: the Borresen's scheme applied to the modified one-group power calculation came up with an improved power distribution, the modified Borresen's method yielded a more accurate power calculations than the Borresen's scheme, the face dependent discontinuity factor method have a better prediction of the power distribution than the node averaged discontinuity factor method, Both the face dependent discontinuity factor method and the modified Borresen's methods for the two-group model have quite attractive features. / Graduation date: 1992

Dissolved organic contaminants that decrease the surface tension of water (surfactants) can have an effect on unsaturated flow through porous media due to the dependence of capillary pressure on surface tension. One and two-dimensional (1D, 2D) laboratory experiments and numerical simulations were conducted to study surfactant-induced unsaturated flow. The 1D experiments investigated differences in surfactant-induced flow as a function of contaminant mobility. The flow in a system contaminated with a high solubility, mobile surfactant, butanol, was much different than in a system contaminated with a sparingly soluble, relatively immobile surfactant, myristyl alcohol (MA). Because surface tension depression caused by MA was confined to the original source zone, the MA system was modeled using a standard unsaturated flow model (HYDRUS-1D) by assigning separate sets of hydraulic functions to the initially clean and source zones. To simulate the butanol system, HYDRUS-1D was modified to incorporate surfactant concentration-dependent changes to the moisture content-pressure head and unsaturated hydraulic conductivity functions. Following the 1D study, a two-dimensional flow cell (2.4 x 1.5 x 0.1 m) was used to investigate the infiltration of a surfactant contaminant plume from a point source on the soil surface, through the vadose zone, and toward a shallow aquifer. Above the top of the capillary fringe the advance of the surfactant solution caused a drainage front that radiated from the point source. Upon reaching the capillary fringe, the drainage front caused a localized depression of the capillary fringe and eventually a new capillary fringe height was established. Horizontal transport of surfactant in the depressed capillary fringe caused the propagation of a wedge-shaped drainage front in the downgradient direction. The numerical model HYDRUS-2D was modified to account for surfactant concentration-dependent effects on the unsaturated hydraulic functions and was successfully used to simulate the surfactant infiltration experiment. The extensive propagation of the drying front and the effect of vadose zone drainage on contaminant breakthrough time demonstrate the potential importance of considering surface tension effects on unsaturated flow and transport in systems containing surface-active organic contaminants or in systems where surfactants are used for remediation of the vadose zone or unconfined aquifers.

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