Anisotropic Diffusion Approximations for Time-dependent Particle Transport.
dc.contributor.author | Johnson, Seth R. | en_US |
dc.date.accessioned | 2012-06-15T17:30:29Z | |
dc.date.available | NO_RESTRICTION | en_US |
dc.date.available | 2012-06-15T17:30:29Z | |
dc.date.issued | 2012 | en_US |
dc.date.submitted | en_US | |
dc.identifier.uri | https://hdl.handle.net/2027.42/91465 | |
dc.description.abstract | In this thesis, we develop and numerically test new approximations to time-dependent radiation transport with the goal of obtaining more accurate solutions than the diffusion approximation can generate, yet requiring less computational effort than full transport. The first method is the nascent anisotropic diffusion (AD) approximation, which we extend to time-dependent problems in finite domains; the second is a novel anisotropic P_1-like (AP_1) approximation. These methods are ``anisotropic'' in that, rather than operating under the assumption of linearly anisotropic radiation, they incorporate an arbitrary amount of anisotropy via a transport-calculated diffusion coefficient. This anisotropic diffusion tensor is the second angular moment of a simple, purely absorbing transport problem. In this thesis, much of the computational testing of the new methods is performed in ``flatland'' geometry, a fictional two-dimensional universe that provides a realistic but computationally inexpensive testbed. As work ancillary to anisotropic diffusion and the numerical experiments, a complete description of flatland diffusion, including boundary conditions, is developed. Also, implementation details for both Monte Carlo and S_N transport in flatland are provided. The two new anisotropic methods, along with a ``flux limited'' modification to anisotropic diffusion, are tested in a variety of problems. Some aspects of the theory, including the newly formulated boundary conditions, are tested first with diffusive, steady-state problems. The new methods are compared against existing ones in linear, time-dependent radiation transport problems. Finally, the efficacy and performance of the anisotropic methods are investigated in several thermal radiative transfer (TRT) computational experiments. Our results demonstrate that for many multi-dimensional problems, the new anisotropic methods perform much better than their conventional counterparts. In every time-dependent test, the flux-limited anisotropic diffusion approach produced the most accurate solutions of the new methods. Based on our numerical testing, we believe this method to be a strong contender for accurate, inexpensive simulations of time-dependent transport and thermal radiative transfer problems. | en_US |
dc.language.iso | en_US | en_US |
dc.subject | Anisotropic Diffusion | en_US |
dc.subject | Radiation Transport | en_US |
dc.subject | Thermal Radiative Transfer | en_US |
dc.subject | Numerical Methods | en_US |
dc.title | Anisotropic Diffusion Approximations for Time-dependent Particle Transport. | en_US |
dc.type | Thesis | en_US |
dc.description.thesisdegreename | PhD | en_US |
dc.description.thesisdegreediscipline | Nuclear Engineering & Radiological Sciences | en_US |
dc.description.thesisdegreegrantor | University of Michigan, Horace H. Rackham School of Graduate Studies | en_US |
dc.contributor.committeemember | Larsen, Edward | en_US |
dc.contributor.committeemember | Downar, Thomas J. | en_US |
dc.contributor.committeemember | Holloway, James Paul | en_US |
dc.contributor.committeemember | Martin, William R. | en_US |
dc.contributor.committeemember | Thornton, Katsuyo S. | en_US |
dc.subject.hlbsecondlevel | Nuclear Engineering and Radiological Sciences | en_US |
dc.subject.hlbtoplevel | Engineering | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/91465/1/sethrj_1.pdf | |
dc.owningcollname | Dissertations and Theses (Ph.D. and Master's) |
Files in this item
Remediation of Harmful Language
The University of Michigan Library aims to describe library materials in a way that respects the people and communities who create, use, and are represented in our collections. Report harmful or offensive language in catalog records, finding aids, or elsewhere in our collections anonymously through our metadata feedback form. More information at Remediation of Harmful Language.
Accessibility
If you are unable to use this file in its current format, please select the Contact Us link and we can modify it to make it more accessible to you.