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Pericles and Attila results for the C5G7 MOX benchmark problems

Description: Recently the Nuclear Energy Agency has published a new benchmark entitled, 'C5G7 MOX Benchmark.' This benchmark is to test the ability of current transport codes to treat reactor core problems without spatial homogenization. The benchmark includes both a two- and three-dimensional problem. We have calculated results for these benchmark problems with our Pericles and Attila codes. Pericles is a one-,two-, and three-dimensional unstructured grid discrete-ordinates code and was used for the twodimensional benchmark problem. Attila is a three-dimensional unstructured tetrahedral mesh discrete-ordinate code and was used for the three-dimensional problem. Both codes use discontinuous finite element spatial differencing. Both codes use diffusion synthetic acceleration (DSA) for accelerating the inner iterations.
Date: January 1, 2002
Creator: Wareing, T. A. (Todd A.) & McGhee, J. M. (John M.)
Partner: UNT Libraries Government Documents Department

On the degraded effectiveness of diffusion synthetic acceleration for multidimensional sn calculations in the presence of material discontinuities

Description: We investigate the degradation in performance of diffusion synthetic acceleration (DSA) methods in problems with discontinuities in material properties. A loss in the effectiveness of DSA schemes has been Observed before with other discretizations in two dimensions under certain conditions. We present more evidence in support of the conjecture that DSA effectiveness can degrade in multidimensional problems with discontinuities in total cross section, regardless of the particular physical configuration or spatial discretization. Through Fourier analysis and numerical experiments, we identify a set of representative problems for which established DSA schemes are ineffective, focusing on highly diffusive problems for which DSA is most needed. We consider a lumped, linear discontinuous spatial discretization of the S N transport equation on three-dimensional, unstructured tetrahedral meshes and look ata fully consistent and a 'partially consistent' DSA method for this discretization. We find that the effectiveness of both methods can be significantly degraded in the presence of material discontinuities. A Fourier analysis in the limit of decreasing cell optical thickness is shown that supports the view that the degraded effectiveness of a fully consistent DSA scheme simply reflects the failure of the spatially continuous DSA method in problems where material discontinuities are present. Key Words: diffusion synthetic acceleration, discrete ordinates, deterministic transport methods, unstructured meshes
Date: January 1, 2002
Creator: Warsa, J. S. (James S.); Wareing, T. A. (Todd A.) & Morel, J. E.
Partner: UNT Libraries Government Documents Department

Krylov iterative methods applied to multidimensional S[sub n] calculations in the presence of material discontinuities

Description: We show that a Krylov iterative meihod, preconditioned with DSA, can be used to efficiently compute solutions to diffusive problems with discontinuities in material properties. We consider a lumped, linear discontinuous discretization of the S N transport equation with a 'partially consistent' DSA preconditioner. The Krylov method can be implemented in terms of the original S N source iteration coding with little modification. Results from numerical experiments show that replacing source iteration with a preconditioned Krylov method can efficiently solve problems that are virtually intractable with accelerated source iteration. Key Words: Krylov iterative methods, discrete ordinates, deterministic transport methods, diffusion synthetic acceleration
Date: January 1, 2002
Creator: Warsa, J. S. (James S.); Wareing, T. A. (Todd A.) & Morel, J. E.
Partner: UNT Libraries Government Documents Department

Krylov subspace iterations for the calculation of K-Eigenvalues with sn transport codes

Description: We apply the Implicitly Restarted Arnoldi Method (IRAM), a Krylov subspace iterative method, to the calculation of k-eigenvalues for criticality problems. We show that the method can be implemented with only modest changes to existing power iteration schemes in an SN transport code. Numerical results on three dimensional unstructured tetrahedral meshes are shown. Although we only compare the IRAM to unaccelerated power iteration, the results indicate that the IRAM is a potentially efficient and powerful technique, especially for problems with dominance ratios approaching unity. Key Words: criticality eigenvalues, Implicitly Restarted Arnoldi Method (IRAM), deterministic transport methods
Date: January 1, 2002
Creator: Warsa, J. S. (James S.); Wareing, T. A. (Todd A.); Morel, J. E.; McGhee, J. M. (John M.) & Lehoucq, R. B. (Richard B.)
Partner: UNT Libraries Government Documents Department