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1. Wenner, Michael. Development of New Source Diagnostic Methods and Variance Reduction Techniques for Monte Carlo Eigenvalue Problems with a Focus on High Dominance Ratio Problems.

Degree: PhD, Nuclear Engineering Sciences - Nuclear and Radiological Engineering, 2010, University of Florida

URL: http://ufdc.ufl.edu/UFE0042505

Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DEVELOPMENT OF NEW SOURCE DIAGNOSTIC METHODS AND VARIANCE REDUCTION TECHNIQUES FOR MONTE CARLO EIGENVALUE PROBLEMS WITH A FOCUS ON HIGH DOMINANCE RATIO PROBLEMS By Michael Todd Wenner December 2010 Chair: Alireza Haghighat Major: Nuclear Engineering Sciences Obtaining the solution to the linear Boltzmann equation is often is often a daunting task. The time-independent form is an equation of six independent variables which cannot be solved analytically in all but some special problems. Instead, numerical approaches have been devised. This work focuses on improving Monte Carlo methods for its solution in eigenvalue form. First, a statistical method of stationarity detection called the KPSS test adapted as a Monte Carlo eigenvalue source convergence test. The KPSS test analyzes the source center of mass series which was chosen since it should be indicative of overall source behavior, and is physically easy to understand. A source center of mass plot alone serves as a good visual source convergence diagnostic. The KPSS test and three different information theoretic diagnostics were implemented into the well known KENOV.a code inside of the SCALE (version 5) code package from Oak Ridge National Laboratory and compared through analysis of a simple problem and several difficult source convergence benchmarks. Results showed that the KPSS test can add to the overall confidence by identifying more problematic simulations than without its usage. Not only this, the source center of mass information on hand visually aids in the understanding of the problem physics. The second major focus of this dissertation concerned variance reduction methodologies for Monte Carlo eigenvalue problems. The CADIS methodology, based on importance sampling, was adapted to the eigenvalue problems. It was shown that the straight adaption of importance sampling can provide a significant variance reduction in determination of keff (in cases studied up to 30%?). A modified version of this methodology was developed which utilizes independent deterministic importance simulations. In this new methodology, each particle is simulated multiple times, once to every other discretized source region utilizing the importance for that region only. Since each particle is simulated multiple times, this methodology often slows down the final keff convergence, but an increase coupling between source zones with important yet low probability interaction is observed. This is an important finding for loosely coupled systems and may be useful in their analysis. The third major focus of this dissertation concerns the use of the standard cumulative fission matrix methodology for high dominance ratio problems which results in high source correlation. Source eigenvector confidence is calculated utilizing a Monte Carlo iterated confidence approach and shown to be superior to the currently used plus and minus…
*Advisors/Committee Members: Haghighat, Alireza (committee chair), Hintenlang, David E. (committee member), Sjoden, Glenn E. (committee member), Entezari, Alireza (committee member), Wagner, John (committee member).*

Subjects/Keywords: Acceleration; Adjoints; Autocorrelation; Eigenvalues; Entropy; Monte Carlo methods; Neutrons; Particle collisions; Simulations; Statistical discrepancies

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Wenner, M. (2010). Development of New Source Diagnostic Methods and Variance Reduction Techniques for Monte Carlo Eigenvalue Problems with a Focus on High Dominance Ratio Problems. (Doctoral Dissertation). University of Florida. Retrieved from http://ufdc.ufl.edu/UFE0042505

Chicago Manual of Style (16^{th} Edition):

Wenner, Michael. “Development of New Source Diagnostic Methods and Variance Reduction Techniques for Monte Carlo Eigenvalue Problems with a Focus on High Dominance Ratio Problems.” 2010. Doctoral Dissertation, University of Florida. Accessed October 20, 2019. http://ufdc.ufl.edu/UFE0042505.

MLA Handbook (7^{th} Edition):

Wenner, Michael. “Development of New Source Diagnostic Methods and Variance Reduction Techniques for Monte Carlo Eigenvalue Problems with a Focus on High Dominance Ratio Problems.” 2010. Web. 20 Oct 2019.

Vancouver:

Wenner M. Development of New Source Diagnostic Methods and Variance Reduction Techniques for Monte Carlo Eigenvalue Problems with a Focus on High Dominance Ratio Problems. [Internet] [Doctoral dissertation]. University of Florida; 2010. [cited 2019 Oct 20]. Available from: http://ufdc.ufl.edu/UFE0042505.

Council of Science Editors:

Wenner M. Development of New Source Diagnostic Methods and Variance Reduction Techniques for Monte Carlo Eigenvalue Problems with a Focus on High Dominance Ratio Problems. [Doctoral Dissertation]. University of Florida; 2010. Available from: http://ufdc.ufl.edu/UFE0042505

University of Florida

2. Yi, Ce. Hybrid Discrete Ordinates and Characteristics Method to Solve the Linear Boltzmann Equation.

Degree: PhD, Nuclear Engineering Sciences - Nuclear and Radiological Engineering, 2007, University of Florida

URL: http://ufdc.ufl.edu/UFE0021243

With the ability of computer hardware and software increasing rapidly, deterministic methods to solve the linear Boltzmann equation (LBE) have attracted some attention for computational applications in both the nuclear engineering and medical physics fields. Among various deterministic methods, the discrete ordinates method (SN) and the method of characteristics (MOC) are two of the most widely used methods. The SN method is the traditional approach to solve the LBE for its stability and efficiency. While the MOC has some advantages in treating complicated geometries. However, in 3-D problems requiring a dense discretization grid in phase space (i.e., a large number of spatial meshes, directions, or energy groups), both methods could suffer from the need for large amounts of memory and computation time. In our study, we developed a new hybrid algorithm by combing the two methods into one code, TITAN. The hybrid approach is specifically designed for application to problems containing low scattering regions. A new serial 3-D time-independent transport code has been developed. Under the hybrid approach, the preferred method can be applied in different regions (blocks) within the same problem model. Since the characteristics method is numerically more efficient in low scattering media, the hybrid approach uses a block-oriented characteristics solver in low scattering regions, and a block-oriented SN solver in the remainder of the physical model. In the TITAN code, a physical problem model is divided into a number of coarse meshes (blocks) in Cartesian geometry. Either the characteristics solver or the SN solver can be chosen to solve the LBE within a coarse mesh. A coarse mesh can be filled with fine meshes or characteristic rays depending on the solver assigned to the coarse mesh. Furthermore, with its object-oriented programming paradigm and layered code structure, TITAN allows different individual spatial meshing schemes and angular quadrature sets for each coarse mesh. Two quadrature types (level-symmetric and Legendre-Chebyshev quadrature) along with the ordinate splitting techniques (rectangular splitting and PN-TN splitting) are implemented. In the SN solver, we apply a memory-efficient 'front-line' style paradigm to handle the fine mesh interface fluxes. In the characteristics solver, we have developed a novel 'backward' ray-tracing approach, in which a bi-linear interpolation procedure is used on the incoming boundaries of a coarse mesh. A CPU-efficient scattering kernel is shared in both solvers within the source iteration scheme. Angular and spatial projection techniques are developed to transfer the angular fluxes on the interfaces of coarse meshes with different discretization grids. The performance of the hybrid algorithm is tested in a number of benchmark problems in both nuclear engineering and medical physics fields. Among them are the Kobayashi benchmark problems and a computational tomography (CT) device model. We also developed an extra sweep procedure with the fictitious quadrature technique to…
*Advisors/Committee Members: Haghighat, Alireza (committee chair), Gilland, David R. (committee member), Sjoden, Glenn E. (committee member), Gopalakrishnan, Jayadeep (committee member), Wagner, John (committee member).*

Subjects/Keywords: Cosine function; Geometry; Integers; Interpolation; Modeling; Numerical quadratures; Projective geometry; Scalars; Subroutines; Symmetry; hybrid, moc, sn

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Yi, C. (2007). Hybrid Discrete Ordinates and Characteristics Method to Solve the Linear Boltzmann Equation. (Doctoral Dissertation). University of Florida. Retrieved from http://ufdc.ufl.edu/UFE0021243

Chicago Manual of Style (16^{th} Edition):

Yi, Ce. “Hybrid Discrete Ordinates and Characteristics Method to Solve the Linear Boltzmann Equation.” 2007. Doctoral Dissertation, University of Florida. Accessed October 20, 2019. http://ufdc.ufl.edu/UFE0021243.

MLA Handbook (7^{th} Edition):

Yi, Ce. “Hybrid Discrete Ordinates and Characteristics Method to Solve the Linear Boltzmann Equation.” 2007. Web. 20 Oct 2019.

Vancouver:

Yi C. Hybrid Discrete Ordinates and Characteristics Method to Solve the Linear Boltzmann Equation. [Internet] [Doctoral dissertation]. University of Florida; 2007. [cited 2019 Oct 20]. Available from: http://ufdc.ufl.edu/UFE0021243.

Council of Science Editors:

Yi C. Hybrid Discrete Ordinates and Characteristics Method to Solve the Linear Boltzmann Equation. [Doctoral Dissertation]. University of Florida; 2007. Available from: http://ufdc.ufl.edu/UFE0021243