The Asymptotic Diffusion Limit of Discretized Transport Problems

AbstractA well-known asymptotic analysis describes the transition of transport theory to diffusion theory in the limit of optically thick systems with small absorption and sources. Recently, this analysis has been applied to discretized transport algorithms. The results of this analysis, which provide information on accuracy and iteration efficiency, cannot be obtained from standard truncation error analyses because in the asymptotic limit, the optical thickness of a spatial cell generally tends to infinity. The ideas underlying this analysis are described, the main results are reviewed, and some open questions are discussed.

[1]  G. Habetler,et al.  Uniform asymptotic expansions in transport theory with small mean free paths, and the diffusion approximation , 1975 .

[2]  Marvin L. Adams.  Even-parity finite-element transport methods in the diffusion limit , 1991 .

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

[4]  Edward W. Larsen.  On Numerical Solutions of Transport Problems in the Diffusion Limit , 1983 .

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

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

[7]  Edward W. Larsen,et al.  The P sub N theory as an asymptotic limit of transport theory in planar geometry. 2; Numerical results , 1991 .

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

[9]  J. Keller,et al.  Asymptotic solution of neutron transport problems for small mean free paths , 1974 .

[10]  Edward W. Larsen,et al.  The asymptotic diffusion limit of a linear discontinuous discretization of a two-dimensional linear transport equation , 1992 .

[11]  Shi Jin,et al.  The discrete-ordinate method in diffusive regimes , 1991 .

[12]  Warren F. Miller.  An analysis of the finite differenced, even-parity, discrete ordinates equations in slab geometry , 1991 .

[13]  Edward W. Larsen,et al.  The P N Theory as an Asymptotic Limit of Transport Theory in Planar Geometry—I: Analysis , 1991 .

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

[15]  Shi. Jin.  Numerical transport in diffusive regimes , 1991 .

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