Browsing by Author "Robin P. Gardner, Committee Member"

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Advanced Computational Methodology for Full-Core Neutronics Calculations
(2004-08-17) Hiruta, Hikaru; Dmitriy Y. Anistratov, Committee Chair; Paul J. Turinsky, Committee Member; Robin P. Gardner, Committee Member; Zhilin Li, Committee Member
The modern computational methodology for reactor physics calculations is based on single–assembly transport calculations with reflective boundary conditions that generate homogenized few–group data, and core–level coarse-mesh diffusion calculations that evaluate a large-scale behavior of the scalar flux. Recently, an alternative approach has been developed. It is based on the low-order equations of the quasidiffusion (QD) method in order to account accurately for complicated transport effects in full–core calculations. The LOQD equations can capture transport effects to an arbitrary degree of accuracy. This approach is combined with single–assembly transport calculations that use special albedo boundary conditions which enable one to simulate efficiently effects of an unlike neighboring assembly on assembly's group data. In this dissertation, we develop homogenization methodology based on the LOQD equations and spatially consistent coarse–mesh finite element discretization methods for the 2D low–order quasidiffusion equations for the full–core calculations. The coarse–mesh solution generated by this method preserves a number of spatial polynomial moments of the fine–mesh transport solution over coarse cells. The proposed method reproduces accurately the complicated large–scale behavior of the transport solution within assemblies. To demonstrate accuracy of the developed method, we present numerical results of calculations of test problems that simulate interaction of MOX and uranium assemblies. We also develop a splitting method that can efficiently solve coarse-mesh discretized low-order quasidiffusion (LOQD) equations. The presented method splits the LOQD problem into two parts: (i) the $D$-problem that captures a significant part of transport solution in the central parts of assemblies and can be reduced to a diffusion-type equation, and (ii) the $Q$-problem that accounts for the complicated behavior of the transport solution near assembly boundaries. Independent coarse-mesh discretizations are applied: the $D$-problem equations are approximated by means of a finite-element method, whereas the $Q$-problem equations are discretized using a finite-volume method. Numerical results demonstrate the efficiency of the presented methodology. This methodology can be used to modify existing diffusion codes for full-core calculations (which already solve a version of the $D$-problem) to account for transport effects.
Nonlinear Weighted Flux Methods for Solving Multidimensional Transport Problems.
(2008-01-24) Roberts, Loren Patrick; Zhilin Li, Committee Member; Robin P. Gardner, Committee Member; Paul J. Turinsky, Committee Member; Dmitriy Y. Anistratov, Committee Chair
The Quasidiffusion Method for Transport Problems on Unstructured Meshes
(2009-02-11) Wieselquist, William Adam; Semyon V. Tsynkov, Committee Member; Robin P. Gardner, Committee Member; Paul J. Turinsky, Committee Member; Yousry Y. Azmy, Committee Member; Dmitriy Y. Anistratov, Committee Chair
In this work, we develop a quasidiffusion (QD) method for solving radiation transport problems on unstructured quadrilateral meshes in 2D Cartesian geometry, for example hanging-node meshes from adaptive mesh refinement (AMR) applications or skewed quadrilateral meshes from radiation hydrodynamics with Lagrangian meshing. The main result of the work is a new low-order quasidiffusion (LOQD) discretization on arbitrary quadrilaterals and a strategy for the efficient iterative solution which uses Krylov methods and incomplete LU factorization (ILU) preconditioning. The LOQD equations are a non-symmetric set of first-order PDEs that in second-order form resembles convection-diffusion with a diffusion tensor, with the difference that the LOQD equations contain extra cross-derivative terms. Our finite volume (FV) discretization of the LOQD equations is compared with three LOQD discretizations from literature. We then present a conservative, short characteristics discretization based on subcell balances (SCSB) that uses polynomial exponential moments to achieve robust behavior in various limits (e.g. small cells and voids) and is second-order accurate in space. A linear representation of the isotropic component of the scattering source based on face-average and cell-average scalar fluxes is also proposed and shown to be effective in some problems. In numerical tests, our QD method with linear scattering source representation shows some advantages compared to other transport methods. We conclude with avenues for future research and note that this QD method may easily be extended to arbitrary meshes in 3D Cartesian geometry.
Radiation damage to materials at SINQ facilities
(2003-12-31) Lu, Wei; Man-Sung Yim, Committee Co-Chair; Monroe S. Wechsler, Committee Co-Chair; Robin P. Gardner, Committee Member; Robert E. Funderlic, Committee Member
SINQ (Swiss Spallation Neutron Source) was built to meet the surging demand for neutrons. It was the first continuous spallation neutron source. Taking advantage of SINQ facilities, the SINQ Target Irradiation Program (STIP) is an international collaboration among many well known laboratories and research agencies to study the microstructures and mechanical properties of structural materials in a spallation spectrum. Target 5 is the currently operating target at SINQ in STIP III. The radiation damage (displacement, hydrogen and helium production) calculations were performed for Target 5 and partly for Target 3. The results of the calculations provide an important basis for further experimental explorations. As a complete investigation, the cross sections were developed for some materials, the physics of spallation reactions was studied to explore the neutron production capability of the material, and a new method was conducted in addition to the conventional calculations. The errors of the calculations were analyzed and some of the calculations results were compared to the available experimental data. The AlMg3 entrance windows of Target 5 received a displacement production of 5.2-5.4 dpa, which indicated a significant radiation-induced strengthening and hardening of the aluminum alloy and suggested further examination on the entrance windows for the working lifetime.