On the importance of effective convergence velocity of synthetic acceleration methods in neutron transport

Abstract The present work concerns some aspects of the optimization of the synthesis acceleration techniques in neutron transport. The importance of non-asymptotic convergence velocity as a theoretical means to characterize and optimize acceleration methods is discussed in detail for isotropic as well as highly anisotropic scattering cases; this shows the innacuracy of results based only on the usual asyptotic analysis. A detailed study of convergence velocity behaviour for space discretized schemes and multidimensional problems is also presented. Finally, various kinds of theoretically-evaluated convergence velocities are reported to study the effective behaviour of some modifications of the classic DSA technique recently proposed to face its loss of effectiveness and optimize performances when dealing with highly anisotropic scattering; comparisons with results of already assessed DSA modification techniques are reported for various scattering cross-section configurations.

[1]  E. M. Gelbard,et al.  The Synthetic Method as Applied to the S n Equations , 1969 .

[2]  H. J. Kopp,et al.  Synthetic Method Solution of the Transport Equation , 1963 .

[3]  R. E. Alcouffe,et al.  Diffusion synthetic acceleration methods for the diamond-differenced discrete-ordinates equations , 1977 .

[4]  P. Zweifel,et al.  Slowing Down of Neutrons by Hydrogenous Moderators , 1955 .

[5]  Piero Ravetto,et al.  Improvements to the Diffusion Synthetic Acceleration method in neutron transport with highly anisotropic scattering , 1995 .

[6]  Edward W. Larsen,et al.  Diffusion-synthetic acceleration methods for discrete-ordinates problems , 1984 .

[7]  Edward W. Larsen,et al.  Synthetic acceleration methods for linear transport problems with highly anisotropic scattering , 1991 .

[8]  Edward W. Larsen,et al.  UNCONDITIONALLY STABLE DIFFUSION-SYNTHETIC ACCELERATION METHODS FOR THE SLAB GEOMETRY DISCRETE ORDINATES EQUATIONS. PART I: THEORY. , 1982 .

[9]  J. E. Morel,et al.  A synthetic acceleration method for discrete ordinates calculations with highly anisotropic scattering , 1982 .

[10]  T. A. Manteuffel,et al.  An Angular Multigrid Acceleration Technique for Sn Equations with Highly Forward-Peaked Scattering , 1991 .

[11]  Jim E. Morel,et al.  Fokker-Planck calculations using standard discrete-ordinates transport codes , 1981 .

[12]  Edward W. Larsen,et al.  Modified diffusion synthetic acceleration algorithms , 1986 .

[13]  Jim E. Morel,et al.  A multigrid acceleration method for the one-dimensional S/sub N/ equations with anisotropic scattering , 1989 .

[14]  Edward W. Larsen.  Unconditionally stable diffusion-acceleration of the transport equation , 1982 .

[15]  H. Khalil,et al.  Effectiveness of a consistently formulated diffusion-synthetic acceleration differencing approach , 1988 .

[16]  E. Lewis,et al.  Computational Methods of Neutron Transport , 1993 .

[17]  Edward W. Larsen,et al.  Fourier Analysis of the Diffusion Synthetic Acceleration Method for Weighted Diamond-Differencing Schemes in Cartesian Geometries , 1987 .

[18]  Edward W. Larsen,et al.  UNCONDITIONALLY STABLE DIFFUSION-SYNTHETIC ACCELERATION METHODS FOR THE SLAB GEOMETRY DISCRETE ORDINATES EQUATIONS. PART II: NUMERICAL RESULTS. , 1982 .

[19]  W. H. Reed.  The Effectiveness of Acceleration Techniques for Iterative Methods in Transport Theory , 1971 .

[20]  Marvin L. Adams,et al.  Diffusion Synthetic Acceleration of Discontinuous Finite Element Transport Iterations , 1992 .

[21]  R. E. Alcouffe.  Stable diffusion synthetic acceleration method for neutron transport iterations , 1976 .

[22]  Edward W. Larsen,et al.  Stability Analysis of Synthetic Acceleration Methods with Anisotropic Scattering , 1988 .

[23]  W. Miller,et al.  Generalized Rebalance: A Common Framework for Transport Acceleration Methods , 1978 .