An analysis of the finite differenced, even-parity, discrete ordinates equations in slab geometry

In this paper three spatial differencing schemes to be used with the even-parity, discrete ordinates, neutron transport equations are presented for the case of slab geometry and isotropic scattering and sources. These three schemes are analyzed in accordance with several desirable properties for spatial differencing schemes. The analyzed indicates that cell-edge differencing of the even-parity equations yields a second-order, positive method that satisfies most diffusion limits and leads to an iteration that can be readily accelerated with an effective diffusion synthetic algorithm. The analyses indicate that this approach is quite promising and should be further developed.

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

[2]  Elmer E Lewis,et al.  Ray-effect mitigation in discrete ordinate-like angular finite element approximations in neutron transport , 1975 .

[3]  D. R. Marr,et al.  User's guide for TWODANT: a code package for two-dimensional, diffusion-accelerated, neutral-particle transport. Revision 1 , 1984 .

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

[5]  Edward W. Larsen,et al.  Computational Efficiency of Numerical Methods for the Multigroup, Discrete-Ordinates Neutron Transport Equations: The Slab Geometry Case , 1979 .

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

[7]  E. Larsen,et al.  Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes II , 1989 .

[8]  Edward W. Larsen,et al.  A Multiple Balance Approach for Differencing the S n Equations , 1990 .

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

[10]  Edward W. Larsen,et al.  Convergence Rates of Spatial Difference Equations for the Discrete-Ordinates Neutron Transport Equations in Slab Geometry , 1980 .

[11]  Edward W. Larsen.  Diffusion theory as an asymptotic limit of transport theory for nearly critical systems with small mean free paths , 1980 .