Exponential Monte Carlo convergence of a three-dimensional discrete ordinates solution
Recent work on obtaining exponential convergence for three-dimensional solutions to the spatially and angularly continuous monoenergetic transport equation with isotropic scattering using the reduced source method was promising. The method, however, used two separate estimates of the scalar flux, a Legendre expansion (in the spatial variables) and a quadrature of the angular flux. This introduced an inconsistency that may have led to some convergence problems. To remove this inconsistency and provide a fairer test of the combined reduced source/Monte Carlo method, the method was applied to estimate the coefficients of a Legendre expansion of the solution of the discrete ordinates equations. In this case, no supplementary approximations were required. The method was tested on a homogeneous three-dimensional slab of dimensions 1 x 10{sup 6} x 10{sup 6} cm and material parameters {Sigma}{sub t} = 1 and {Sigma}{sub s} = 0.5. The external source of Eq. (2) was S{sub m}(r{sub s}) = S{sub m}(0,y,z) = {mu}{sub m}, {mu}{sub m} {gt} 0. Figure 1 shows the results of the solution of the S{sub 8} equations using a standard quadrature set, 560,000 particles per stage (except the zeroth, in which only 80,000 particles were used), and Legendre expansions of order 10 in each direction with no Legendre product terms in Eq. (5). For this simple problem, Fig. 1 clearly shows exponential convergence of four different residuals and of two estimates of the known source. The difference between two Monte Carlo scalar fluxes (volume midpoint and volume average) and those estimated by THREE-DANT (Ref. 5) using the same S{sub s} quadrature set are shown for verification. For this problem, convergence was achieved after ten adaptive stages in 75.1 min.
- Research Organization:
- Los Alamos National Lab., NM (US)
- OSTI ID:
- 20005776
- Journal Information:
- Transactions of the American Nuclear Society, Vol. 81; Conference: American Nuclear Society 1999 Winter Meeting, Long Beach, CA (US), 11/14/1999--11/18/1999; Other Information: PBD: 1999; ISSN 0003-018X
- Country of Publication:
- United States
- Language:
- English
Similar Records
Exponential Monte Carlo Convergence on a Homogeneous Right Parallelepiped Using the Reduced Source Method with Legendre Expansion
Positive anisotropic group scattering cross sections for radiation transport