Iterative acceleration for two-dimensional long-characteristics transport problems /
We extend the transport synthetic acceleration (TSA) scheme
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| Format: | Thesis Book |
| Language: | English |
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[Place of publication not identified] :
[publisher not identified] ;
1997.
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| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=736584781&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | We extend the transport synthetic acceleration (TSA) scheme to the long characteristics spatial discretization for the two-dimensional, assembly-level transport problem. This synthetic method employs a simplified transport operator as its low-order approximation. The TSA equations are expanded to include opposing reflecting boundary conditions by incorporating an angular residual at the problem boundary. We develop a heterogeneous Fourier mode analysis to evaluate the effect of material heterogeneities and mesh properties on the performance of TSA. Our analysis shows that the spectral radius of the TSA iteration operator is determined by the "worst" mesh and material properties (optically-thin and highly-scattering) even if these properties do not occur in the same mesh cell. The Fourier analysis results also show that TSA is effective at reducing the number of high-order iterations required to reach convergence for both homogeneous and heterogeneous model fuel assembly problems. We then address difficulties unique to the long-characteristics discretization with opposing reflecting boundary conditions and describe our methods for overcoming them in a computationally efficient way. Since the boundary angular data exists on different grids in the high- and low-order problems, we define restriction and prolongation operations specific to the method of long characteristics to map between the two grids. We then develop the procedure used to realize the conjugate gradient (CG) method in the presence of opposing reflection boundary conditions. The CG iteration may only be applied to symmetric positive definite matrices; this condition requires the algebraic elimination of the boundary angular corrections from the low-order equations. Evaluating the action of the resulting matrix on an arbitrary vector involves two transport sweeps and a transmission iteration. We present results of our acceleration scheme on a simple test problem, a typical pressurized water reactor assembly, and a typical boiling water reactor assembly. |
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| Item Description: | Vita. "Major Subject: Nuclear Engineering". |
| Physical Description: | xiii, 191 leaves : illustrations ; 28 cm. Issued also on microfiche from University Microfilms Inc. |
| Bibliography: | Includes bibliographical references: pages 156-162. |