High order variational solutions of time-dependent neutron transport problems /
| Main Author: | |
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| Other Authors: | , , |
| Format: | Thesis Book |
| Language: | English |
| Published: |
1985.
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| Subjects: | |
| Online Access: | Link to ProQuest copy Link to OAKTrust copy ProQuest, Abstract |
| Abstract: | High order numerical solutions of the time-dependent one speed neutron transport equation are developed using cubic hermite polynomial trial functions, variational techniques, and exponential matrix operators. Two new numerical solutions are developed which are high order with respect to both time and space variables. In the first method, the time-dependent PN equations are transformed into "Generalized Telegrapher's Equations" (GTE) that are valid for any order P[N] approximation. The Generalized Telegrapher's Equations form a coupled set of second order differential equations with respect to both time and space. In the second method, the time-dependent PN equations are transformed into coupled "Transport Diffusion Equations" (TDE), keeping the additional terms that maintain the transport nature of the solution. The Transport Diffusion Equations are first order in time and second order in space. Numerically evaluated time-dependent analytic solutions are also developed for homogeneous media transport problems in the P1 and P3 approximations via Laplace transforms in order to validate the variational GTE and TDE solutions. The analytic solutions allow anisotropic scattering, up to the appropriate PN order. The analytic solutions are not limited to the non-precise extrapolation boundary condition, like many time-dependent analytic PN solutions, but allow any of the standard transport vacuum boundary condition approximations (Mark, Marshak, and Importance Weighted). The variational and analytic solutions were also compared to spatially high order discrete ordinate solutions (linear discontinuous finite elements). The new numerical 4 methods converge rapidly to the analytic solution, O(h^4), and require significantly less computing time than the SN solutions for a given accuracy. For a given spatial mesh, the GTE solutions require approximately 5.65 times more computer time than the TDE solutions. For equivalent spatial meshes, the GTE equations model a transient better. However, both variational methods yield identical steady state results. The TDE equations can be easily modified to solve the energy dependent transport equation via the multigroup approximation, while the GTE equations become very complicated in the multigroup approximation. |
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| Item Description: | "Major subject: Nuclear Engineering." Typescript (photocopy). Vita. |
| Physical Description: | ix, 153 leaves : illustrations ; 29 cm |
| Bibliography: | Includes bibliographical references (leaves 121-127). |